├── DOC └── GAToolbox Documentation.pdf ├── LICENSE ├── README.md ├── Test_fns ├── TEST_FNS.PS ├── demoga1.m ├── mpga.m ├── objbran.m ├── objdopi.m ├── objeaso.m ├── objfun1.m ├── objfun1a.m ├── objfun1b.m ├── objfun2.m ├── objfun6.m ├── objfun7.m ├── objfun8.m ├── objfun9.m ├── objgold.m ├── objharv.m ├── objlinq.m ├── objlinq2.m ├── objpush.m ├── objsixh.m ├── resplot.m ├── sga.m ├── simdopi1.m ├── simdopi2.m ├── simlinq1.m ├── simlinq2.m └── simobjp.m ├── bs2rv.m ├── contents.m ├── crtbase.m ├── crtbp.m ├── crtrp.m ├── migrate.m ├── mpga.m ├── mut.m ├── mutate.m ├── mutbga.m ├── objfun1.m ├── objharv.m ├── ranking.m ├── recdis.m ├── recint.m ├── reclin.m ├── recmut.m ├── recombin.m ├── reins.m ├── rep.m ├── resplot.m ├── rws.m ├── scaling.m ├── select.m ├── sga.m ├── sus.m ├── xovdp.m ├── xovdprs.m ├── xovmp.m ├── xovsh.m ├── xovshrs.m ├── xovsp.m └── xovsprs.m /DOC/GAToolbox Documentation.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/UoS-CODeM/GA-Toolbox/8ca5c5cf806bea948f062832eb52ebf71d9afb7d/DOC/GAToolbox Documentation.pdf -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | GNU GENERAL PUBLIC LICENSE 2 | Version 2, June 1991 3 | 4 | Copyright (C) 1989, 1991 Free Software Foundation, Inc., 5 | 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA 6 | Everyone is permitted to copy and distribute verbatim copies 7 | of this license document, but changing it is not allowed. 8 | 9 | Preamble 10 | 11 | The licenses for most software are designed to take away your 12 | freedom to share and change it. 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If this is what you want to do, use the GNU Lesser General 339 | Public License instead of this License. 340 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | ---------------------------------------------------------------------- 2 | 3 | Genetic Algorithm Toolbox for MATLAB, v1.2 4 | ========================================== 5 | 6 | Thank you for requesting a copy of the Genetic Algorithm Toolbox. 7 | 8 | The Genetic Algorithm Toolbox for MATLAB was developed at the 9 | Department of Automatic Control and Systems Engineering of The 10 | University of Sheffield, UK, in order to make GA's accessible to the 11 | control engineer within the framework of a existing computer-aided 12 | control system design package. The toolbox was written with the 13 | support of a UK SERC grant, and the final version (v1.2) was 14 | completed in 1994. 15 | 16 | The Toolbox was originally developed for MATLAB v4.2. It has also 17 | been successfully used with subsequent versions up to and including 18 | MATLAB 7. 19 | 20 | For a more detailed introduction to the capabilities and use of the 21 | GA Toolbox, please refer to the two introductory papers and the 22 | Toolbox User's Guide, all of which are available at the GA Toolbox 23 | homepage at http://codem.group.shef.ac.uk/index.php/ga-toolbox. 24 | 25 | The GA Toolbox is copyright the original authors and The University 26 | of Sheffield, and is published here under the GNU General Public 27 | License. (See http://www.fsf.org/licenses/licenses.html) 28 | 29 | We would be interested to hear of your experiences with, criticisms 30 | of, and enhancements to, the GA Toolbox. Please direct all such 31 | correspondence to ga-toolbox@acse.sheffield.ac.uk. 32 | 33 | ---------------------------------------------------------------------- 34 | -------------------------------------------------------------------------------- /Test_fns/demoga1.m: -------------------------------------------------------------------------------- 1 | % DEMOGA1.M (DEMO of Genetic Algorithms 1) 2 | % 3 | % This function displays a number of figures. Select a number of these 4 | % figures with the mouse by clicking in the area of the shape. These 5 | % figures are the parents for the next generation. The offspring are 6 | % created by recombination and mutation. The user is the selector. 7 | % 8 | % The shape of the figures is defined by Points X- and Y-values each. 9 | % These points are ploted by patch(), each figure in a rectangle. 10 | % The X- and Y-values are the variables of a individual. 11 | % 12 | % Aim of this demo is, to "construct" a special figure, e.g. a square 13 | % or a star or ..., imagine, what you want and select appropriate points. 14 | % 15 | % Parameters inside function for changing: 16 | % Num - Number of figures (4, 9, 16, 25, ...) 17 | % Points - Number of Points per figure (3, 4, 5...), 5 recommended 18 | % MAXGEN - Number of generations (more than 30 recommended) 19 | % 20 | % Syntax: demoga1(); 21 | % 22 | % Input parameters: 23 | % no input parameter 24 | % Output parameter: 25 | % no output parameter 26 | % 27 | % Author: Hartmut Pohlheim 28 | % History: 24.03.94 file created 29 | % 13.01.03 tested under MATLAB v6 by Alex Shenfield 30 | 31 | function demoga1(); 32 | 33 | Num = 16; % Number of figures 34 | Points = 6; % Number of points per figure 35 | MAXGEN = 30; % Number of generations 36 | FieldDR = rep([0; 1], [1 Points]); % Fielddescription for mutation 37 | 38 | % Function needs as many rows as columns, every place has to be filled 39 | if sqrt(Num) ~= ceil(sqrt(Num)), 40 | error('sqrt(Num) must be an integer'); 41 | end 42 | 43 | ColRowNum = ceil(sqrt(Num)); % Number of columns and rows 44 | Shrink=Num/ColRowNum; % Value for shrinking of area 45 | SelectNumber = ColRowNum; % Number of parents by selection 46 | 47 | Cols = 1:1:ColRowNum; % Index of individuals in first columns 48 | Rows = 1:ColRowNum:Num; % Index of individuals in first row 49 | 50 | h = figure; % Open a new figure for output 51 | axes('Position',[0 0 1 1]); % Set axes to whole figure 52 | set(gca, 'xcolor',[0 0 0]); % Make X-Axis invisible 53 | set(gca, 'ycolor',[0 0 0]); % Make Y-Axis invisible 54 | axis('ij'); % Position start in left-upper corner 55 | axis(axis); % Freeze axes 56 | 57 | XStart = (Cols(1:ColRowNum-1)/Shrink); % Calculate X-start- and Y-endvalues of lines 58 | XLine1 = [XStart; XStart]; % between figures 59 | YLine1 = [zeros(1,ColRowNum-1); ones(1,ColRowNum-1)]; % X-end- and Y-startvalues 60 | XLine = [XLine1 YLine1]; YLine = [YLine1 XLine1]; % Assemble line vectors 61 | 62 | MatX=rand(Points,Num); % Create X-values of figures at random 63 | MatY=rand(Points,Num); % Create Y-values of figures at random 64 | 65 | for igen = 1:MAXGEN, % Loop over all generations 66 | 67 | % Recombine individuals 68 | MatXYOff = recombin('recint', [MatX MatY]',NaN, 2); 69 | 70 | % Mutate individuals 71 | MatXYOff = mutbga(MatXYOff, FieldDR, 1/Points); 72 | 73 | MatXYOff = MatXYOff'; % Invert matrix of individuals 74 | MatX = MatXYOff(:,1:Num); % Select X- and Y-values 75 | MatY = MatXYOff(:,size(MatXYOff,2)/2+1:size(MatXYOff,2)/2+Num); 76 | 77 | PolyMatX = MatX / Shrink; % Shrink X-values for fitting in small area 78 | PolyMatY = MatY / Shrink; % Shrink Y-values for fitting in small area 79 | 80 | % Add a value to the X-value for placing individual in the appropriate column 81 | for irun = 1:ColRowNum-1, 82 | PolyMatX(:,Rows+irun)=PolyMatX(:,Rows+irun)+(irun)/Shrink; 83 | end 84 | 85 | % Add a value to the Y-value for placing individual in the appropriate row 86 | for irun = 1:ColRowNum-1, 87 | PolyMatY(:,Cols+(irun*ColRowNum))= ... 88 | PolyMatY(:,Cols+(irun*ColRowNum))+(irun)/Shrink; 89 | end 90 | 91 | cla; % Clear axes, removes all earlier figures 92 | patch(PolyMatX,PolyMatY,'b'); % Plot shape of figures 93 | lh = line(XLine, YLine); % Plot lines between figures 94 | set(lh,'Color',[.6 .6 .6]); % Set linecolor to grey 95 | 96 | xclick = []; yclick = []; % Reset vectors for storing click points 97 | for isel = 1:SelectNumber, % Loop for as many points as individuals to select 98 | set(gcf,'Name',[ ' Select ' int2str(isel) '. figure (of ' ... 99 | int2str(SelectNumber) ') with mouseclick (Generation ' ... 100 | int2str(igen) ' of ' int2str(MAXGEN) ')']); 101 | [xclick1, yclick1] = ginput(1); % get position of mouse click 102 | xclick = [xclick; xclick1]; yclick = [yclick; yclick1]; % add position to vectors 103 | end 104 | 105 | xpos = ceil(xclick * Shrink); % Calculate column of mouse click 106 | ypos = ceil(yclick * Shrink); % Calculate row of mouse click 107 | 108 | SelNumber = xpos + ColRowNum * (ypos-1); % Calculate numbers of selected figures 109 | 110 | % select X- and Y-values of individuals and repeat them 111 | MatX = rep(MatX(:,SelNumber),[1 ceil(Num/SelectNumber)]); 112 | MatY = rep(MatY(:,SelNumber),[1 ceil(Num/SelectNumber)]); 113 | 114 | end 115 | 116 | 117 | % End of function -------------------------------------------------------------------------------- /Test_fns/mpga.m: -------------------------------------------------------------------------------- 1 | % MPGA.M (Multi Population Genetic Algorithm) 2 | % 3 | % This script implements the Multi Population Genetic Algorithm. 4 | % Real valued representation for the individuals is used. 5 | % 6 | % Author: Hartmut Pohlheim 7 | % History: 23.03.94 file created 8 | % 13.01.03 tested under MATLAB v6 by Alex Shenfield 9 | 10 | GGAP = .8; % Generation gap, how many new individuals are created 11 | INSR = .9; % Insertion rate, how many of the offspring are inserted 12 | XOVR = 1; % Crossover rate 13 | SP = 2; % Selective Pressure 14 | MUTR = 1; % Mutation rate; only a factor; 15 | MIGR = 0.2; % Migration rate between subpopulations 16 | MIGGEN = 20; % Number of generations between migration (isolation time) 17 | 18 | TERMEXACT = 1e-4; % Value for termination if minimum reached 19 | 20 | SEL_F = 'sus'; % Name of selection function 21 | XOV_F = 'recdis'; % Name of recombination function for individuals 22 | MUT_F = 'mutbga'; % Name of mutation function 23 | OBJ_F = 'objharv'; % Name of function for objective values 24 | 25 | % Get boundaries of objective function 26 | FieldDR = feval(OBJ_F,[],1); 27 | 28 | % compute SUBPOP, NIND depending on number of variables (defined in objective function) 29 | NVAR = size(FieldDR,2); % Get number of variables from objective function 30 | SUBPOP = 2 * floor(sqrt(NVAR)); % Number of subpopulations 31 | NIND = 20 + 5 * floor(NVAR/50); % Number of individuals per subpopulations 32 | MAXGEN = 300 * floor(sqrt(NVAR)); % Max number of generations 33 | MUTR = MUTR / NVAR; % Mutation rate depending on NVAR 34 | 35 | % Get value of minimum, defined in objective function 36 | GlobalMin = feval(OBJ_F,[],3); 37 | 38 | % Get title of objective function, defined in objective function 39 | FigTitle = [feval(OBJ_F,[],2) ' (' int2str(SUBPOP) ':' int2str(MAXGEN) ') ']; 40 | 41 | % Clear Best and storing matrix 42 | % Initialise Matrix for storing best results 43 | Best = NaN * ones(MAXGEN,3); 44 | Best(:,3) = zeros(size(Best,1),1); 45 | % Matrix for storing best individuals 46 | IndAll = []; 47 | 48 | % Create real population 49 | Chrom = crtrp(SUBPOP*NIND,FieldDR); 50 | 51 | % reset count variables 52 | gen = 0; 53 | termopt = 0; 54 | 55 | % Calculate objective function for population 56 | ObjV = feval(OBJ_F,Chrom); 57 | % count number of objective function evaluations 58 | Best(gen+1,3) = Best(gen+1,3) + NIND; 59 | 60 | % Iterate subpopulation till termination or MAXGEN 61 | while ((gen < MAXGEN) & (termopt == 0)), 62 | 63 | % Save the best and average objective values and the best individual 64 | [Best(gen+1,1),ix] = min(ObjV); 65 | Best(gen+1,2) = mean(ObjV); 66 | IndAll = [IndAll; Chrom(ix,:)]; 67 | 68 | % Fitness assignment to whole population 69 | FitnV = ranking(ObjV,[2 0],SUBPOP); 70 | 71 | % Select individuals from population 72 | SelCh = select(SEL_F, Chrom, FitnV, GGAP, SUBPOP); 73 | 74 | % Recombine selected individuals 75 | SelCh=recombin(XOV_F, SelCh, XOVR, SUBPOP); 76 | 77 | % Mutate offspring 78 | SelCh=mutate(MUT_F, SelCh, FieldDR, [MUTR], SUBPOP); 79 | 80 | % Calculate objective function for offspring 81 | ObjVOff = feval(OBJ_F,SelCh); 82 | Best(gen+1,3) = Best(gen+1,3) + size(SelCh,1); 83 | 84 | % Insert best offspring in population replacing worst parents 85 | [Chrom, ObjV] = reins(Chrom, SelCh, SUBPOP, [1 INSR], ObjV, ObjVOff); 86 | 87 | gen=gen+1; 88 | 89 | % Plot some results, rename title of figure for graphic output 90 | if ((rem(gen,20) == 1) | (rem(gen,MAXGEN) == 0) | (termopt == 1)), 91 | set(gcf,'Name',[FigTitle ' in ' int2str(gen)]); 92 | resplot(Chrom(1:2:size(Chrom,1),:),... 93 | IndAll(max(1,gen-39):size(IndAll,1),:),... 94 | [ObjV; GlobalMin], Best(max(1,gen-19):gen,[1 2]), gen); 95 | end 96 | 97 | % Check, if best objective value near GlobalMin -> termination criterion 98 | % compute difference between GlobalMin and best objective value 99 | ActualMin = abs(min(ObjV) - GlobalMin); 100 | % if ActualMin smaller than TERMEXACT --> termination 101 | if ((ActualMin < (TERMEXACT * abs(GlobalMin))) | (ActualMin < TERMEXACT)) 102 | termopt = 1; 103 | end 104 | 105 | % migrate individuals between subpopulations 106 | if ((termopt ~= 1) & (rem(gen,MIGGEN) == 0)) 107 | [Chrom, ObjV] = migrate(Chrom, SUBPOP, [MIGR, 1, 0], ObjV); 108 | end 109 | 110 | end 111 | 112 | 113 | % Results 114 | % add number of objective function evaluations 115 | Results = cumsum(Best(1:gen,3)); 116 | % number of function evaluation, mean and best results 117 | Results = [Results Best(1:gen,2) Best(1:gen,1)]; 118 | 119 | % Plot Results and show best individuals => optimum 120 | figure('Name',['Results of ' FigTitle]); 121 | subplot(2,1,1), plot(Results(:,1),Results(:,2),'-',Results(:,1),Results(:,3),':'); 122 | subplot(2,1,2), plot(IndAll(gen-4:gen,:)'); 123 | 124 | 125 | % End of script -------------------------------------------------------------------------------- /Test_fns/objbran.m: -------------------------------------------------------------------------------- 1 | % OBJBRAN.M (OBJective function for BRANin RCOS function) 2 | % 3 | % This function implements the BRANIN RCOS function. 4 | % 5 | % Syntax: ObjVal = objbran(Chrom,rtn_type) 6 | % 7 | % Input parameters: 8 | % Chrom - Matrix containing the chromosomes of the current 9 | % population. Each row corresponds to one individual's 10 | % string representation. 11 | % if Chrom == [], then special values will be returned 12 | % rtn_type - if Chrom == [] and 13 | % rtn_type == 1 (or []) return boundaries 14 | % rtn_type == 2 return title 15 | % rtn_type == 3 return value of global minimum 16 | % 17 | % Output parameters: 18 | % ObjVal - Column vector containing the objective values of the 19 | % individuals in the current population. 20 | % if called with Chrom == [], then ObjVal contains 21 | % rtn_type == 1, matrix with the boundaries of the function 22 | % rtn_type == 2, text for the title of the graphic output 23 | % rtn_type == 3, value of global minimum 24 | % 25 | % Author: Hartmut Pohlheim 26 | % History: 25.11.93 file created 27 | % 27.11.93 text of title and rtn_type added 28 | % 16.12.93 rtn_type == 3, return value of global minimum 29 | % 01.03.94 name changed in obj* 30 | % 13.01.03 updated for MATLAB v6 by Alex Shenfield 31 | 32 | function ObjVal = objbran(Chrom,rtn_type); 33 | 34 | % Compute population parameters 35 | [Nind,Nvar] = size(Chrom); 36 | 37 | % Check size of Chrom and do the appropriate thing 38 | % if Chrom is [] 39 | if Nind == 0 40 | % return text of title for graphic output 41 | if rtn_type == 2 42 | ObjVal = 'BRANINs RCOS function'; 43 | % return value of global minimum 44 | elseif rtn_type == 3 45 | ObjVal = 0.397887; 46 | % define size of boundary-matrix and values 47 | else 48 | % x1 x2 49 | ObjVal = [-5 0; % lower bounds 50 | 10 15]; % upper bounds 51 | end 52 | % if two variables, compute values of function 53 | elseif Nvar == 2 54 | % BRANIN's RCOS function 55 | % -5 <= x1 <= 10 ; 0 <= x2 <= 15 56 | % global minimum at (x1,x2)=(-pi,12.275), (pi,2.275), and 57 | % (9.42478,2.475) ; fmin=0.397887 58 | x1 = Chrom(:,1); 59 | x2 = Chrom(:,2); 60 | ObjVal = 1*(x2-(5.1/(4*pi^2))*x1.^2+(5/pi)*x1-6).^2+10*(1-(1/(8*pi))).*cos(x1)+10; 61 | % otherwise error, wrong format of Chrom 62 | else 63 | error('size of matrix Chrom is not correct for function evaluation'); 64 | end 65 | 66 | % End of function -------------------------------------------------------------------------------- /Test_fns/objdopi.m: -------------------------------------------------------------------------------- 1 | % OBJDOPI.M (OBJective function for DOuble Integrator) 2 | % 3 | % This function implements the Double Integrator. 4 | % 5 | % Syntax: ObjVal = objdopi(Chrom,rtn_type) 6 | % 7 | % Input parameters: 8 | % Chrom - Matrix containing the chromosomes of the current 9 | % population. Each row corresponds to one individual's 10 | % string representation. 11 | % if Chrom == [], then special values will be returned 12 | % rtn_type - if Chrom == [] and 13 | % rtn_type == 1 (or []) return boundaries 14 | % rtn_type == 2 return title 15 | % rtn_type == 3 return value of global minimum 16 | % 17 | % Output parameters: 18 | % ObjVal - Column vector containing the objective values of the 19 | % individuals in the current population. 20 | % if called with Chrom == [], then ObjVal contains 21 | % rtn_type == 1, matrix with the boundaries of the function 22 | % rtn_type == 2, text for the title of the graphic output 23 | % rtn_type == 3, value of global minimum 24 | % 25 | % 26 | % Author: Hartmut Pohlheim 27 | % History: 17.12.93 file created (copy of valfun7.m) 28 | % 19.12.93 Dim reintroduced 29 | % Dim and STEPSIMU independend from each other, rk23 30 | % can compute control between times 31 | % 01.03.94 name changed in obj* 32 | % 05.04.94 trapz used 33 | % 26.01.03 switch changed to rtn_type for compatability with MATLAB v6 34 | % by Alex Shenfield 35 | 36 | function [ObjVal,t,x] = objdopi(Chrom,rtn_type); 37 | 38 | % Define used method 39 | method = 1; % 1 - sim: simulink model 40 | % 2 - ode: ordinary differential equations 41 | % 3 - con: transfer function to state space 42 | 43 | % Dimension of objective function 44 | Dim = 20; 45 | TSTART = 0; 46 | TEND = 1; 47 | STEPSIMU = min(0.1,abs((TEND-TSTART)/(Dim-1))); 48 | TIMEVEC = linspace(TSTART,TEND,Dim)'; 49 | 50 | % initial conditions 51 | XINIT = [ 0; -1]; 52 | 53 | % end conditions 54 | XEND = [ 0; 0]; 55 | 56 | % weights for control and end 57 | XENDWEIGHT = 12 * [1; 1]; % XEND(1); XEND(2) 58 | UWEIGHT = [0.5]; % Control vector 59 | 60 | % Compute population parameters 61 | [Nind,Nvar] = size(Chrom); 62 | 63 | % Check size of Chrom and do the appropriate thing 64 | % if Chrom is [], then 65 | if Nind == 0 66 | % return text of title for graphic output 67 | if rtn_type == 2 68 | if method == 2, ObjVal = ['Double Integrator (ode)-' int2str(Dim)]; 69 | elseif method == 3, ObjVal = ['Double Integrator (con)-' int2str(Dim)]; 70 | else ObjVal = ['Double Integrator (sim)-' int2str(Dim)]; 71 | end 72 | % return value of global minimum 73 | elseif rtn_type == 3 74 | ObjVal = 2; % UWEIGHT * 3 * (TEND - TSTART); 75 | % define size of boundary-matrix and values 76 | else 77 | % lower and upper bound, identical for all n variables 78 | ObjVal1 = [-15; 15]; 79 | ObjVal = rep(ObjVal1,[1 Dim]); 80 | end 81 | % if Dim variables, compute values of function 82 | elseif Nvar == Dim 83 | if method == 3, % Convert transfer function to state space system 84 | [Ai2, Bi2, Ci2, Di2] = tf2ss(1, [1 0 0]); 85 | t = TIMEVEC; 86 | end 87 | ObjVal = zeros(Nind,1); 88 | for indrun = 1:Nind 89 | steuerung = [TIMEVEC [Chrom(indrun,:)]']; 90 | if method == 2, 91 | [t, x] = rk23('simdopi2',[TSTART TEND],XINIT,[1e-3;STEPSIMU;STEPSIMU],steuerung); 92 | elseif method == 3, 93 | [y, x] = lsim(Ai2, Bi2, Ci2, Di2, Chrom(indrun,:),TIMEVEC, XINIT); 94 | else 95 | [t, x] = rk23('simdopi1',[TSTART TEND],[],[1e-3;STEPSIMU;STEPSIMU],steuerung); 96 | end 97 | % Calculate objective function, endvalues, trapez-integration for control vector 98 | ObjVal(indrun) = sum(XENDWEIGHT .* abs( x(size(x,1),:)' - XEND )) + ... 99 | (UWEIGHT / (Dim-1) * trapz(Chrom(indrun,:).^2)); 100 | end 101 | % otherwise error, wrong format of Chrom 102 | else 103 | error('size of matrix Chrom is not correct for function evaluation'); 104 | end 105 | 106 | 107 | % End of function 108 | 109 |  -------------------------------------------------------------------------------- /Test_fns/objeaso.m: -------------------------------------------------------------------------------- 1 | % OBJEASO.M (OBJective function for EASom function) 2 | % 3 | % This function implements the EASOM function. 4 | % 5 | % Syntax: ObjVal = objeaso(Chrom,rtn_type) 6 | % 7 | % Input parameters: 8 | % Chrom - Matrix containing the chromosomes of the current 9 | % population. Each row corresponds to one individual's 10 | % string representation. 11 | % if Chrom == [], then special values will be returned 12 | % rtn_type - if Chrom == [] and 13 | % rtn_type == 1 (or []) return boundaries 14 | % rtn_type == 2 return title 15 | % rtn_type == 3 return value of global minimum 16 | % 17 | % Output parameters: 18 | % ObjVal - Column vector containing the objective values of the 19 | % individuals in the current population. 20 | % if called with Chrom == [], then ObjVal contains 21 | % rtn_type == 1, matrix with the boundaries of the function 22 | % rtn_type == 2, text for the title of the graphic output 23 | % rtn_type == 3, value of global minimum 24 | % 25 | % Author: Hartmut Pohlheim 26 | % History: 25.11.93 file created 27 | % 27.11.93 text of title and rtn_type added 28 | % 16.12.93 rtn_type == 3, return value of global minimum 29 | % 01.03.94 name changed in obj* 30 | % 13.01.03 updated for MATLAB v6 by Alex Shenfield 31 | 32 | function ObjVal = objeaso(Chrom,rtn_type); 33 | 34 | % Compute population parameters 35 | [Nind,Nvar] = size(Chrom); 36 | 37 | % Check size of Chrom and do the appropriate thing 38 | % if Chrom is [] 39 | if Nind == 0 40 | % return text of title for graphic output 41 | if rtn_type == 2 42 | ObjVal = 'EASOMs function'; 43 | % return value of global minimum 44 | elseif rtn_type == 3 45 | ObjVal = -1; 46 | % define size of boundary-matrix and values 47 | else 48 | % x1 x2 49 | ObjVal = [-100 -100; % lower bounds 50 | 100 100]; % upper bounds 51 | end 52 | % if two variables, compute values of function 53 | elseif Nvar == 2 54 | % EASOM's function 55 | % -100(-5) <= x1 <= 100(5) ; -100(-5) <= x2 <= 100(5) 56 | % global minimum at (x1,x2)=(pi,pi) ; fmin=-1 57 | x1 = Chrom(:,1); 58 | x2 = Chrom(:,2); 59 | ObjVal = -cos(x1).*cos(x2).*exp(-((x1-pi).^2+(x2-pi).^2)); 60 | % otherwise error, wrong format of Chrom 61 | else 62 | error('size of matrix Chrom is not correct for function evaluation'); 63 | end 64 | 65 | % End of function -------------------------------------------------------------------------------- /Test_fns/objfun1.m: -------------------------------------------------------------------------------- 1 | % OBJFUN1.M (OBJective function for de jong's FUNction 1) 2 | % 3 | % This function implements the DE JONG function 1. 4 | % 5 | % Syntax: ObjVal = objfun1(Chrom,rtn_type) 6 | % 7 | % Input parameters: 8 | % Chrom - Matrix containing the chromosomes of the current 9 | % population. Each row corresponds to one individual's 10 | % string representation. 11 | % if Chrom == [], then special values will be returned 12 | % rtn_type - if Chrom == [] and 13 | % rtn_type == 1 (or []) return boundaries 14 | % rtn_type == 2 return title 15 | % rtn_type == 3 return value of global minimum 16 | % 17 | % Output parameters: 18 | % ObjVal - Column vector containing the objective values of the 19 | % individuals in the current population. 20 | % if called with Chrom == [], then ObjVal contains 21 | % rtn_type == 1, matrix with the boundaries of the function 22 | % rtn_type == 2, text for the title of the graphic output 23 | % rtn_type == 3, value of global minimum 24 | % 25 | % Author: Hartmut Pohlheim 26 | % History: 26.11.93 file created 27 | % 27.11.93 text of title and rtn_type added 28 | % 30.11.93 show Dim in figure titel 29 | % 16.12.93 rtn_type == 3, return value of global minimum 30 | % 01.03.94 name changed in obj* 31 | % 13.01.03 updated for MATLAB v6 by Alex Shenfield 32 | 33 | function ObjVal = objfun1(Chrom,rtn_type); 34 | 35 | % Dimension of objective function 36 | Dim = 20; 37 | 38 | % Compute population parameters 39 | [Nind,Nvar] = size(Chrom); 40 | 41 | % Check size of Chrom and do the appropriate thing 42 | % if Chrom is [], then define size of boundary-matrix and values 43 | if Nind == 0 44 | % return text of title for graphic output 45 | if rtn_type == 2 46 | ObjVal = ['DE JONG function 1-' int2str(Dim)]; 47 | % return value of global minimum 48 | elseif rtn_type == 3 49 | ObjVal = 0; 50 | % define size of boundary-matrix and values 51 | else 52 | % lower and upper bound, identical for all n variables 53 | ObjVal = 100*[-5.12; 5.12]; 54 | ObjVal = ObjVal(1:2,ones(Dim,1)); 55 | end 56 | % if Dim variables, compute values of function 57 | elseif Nvar == Dim 58 | % function 1, sum of xi^2 for i = 1:Dim (Dim=30) 59 | % n = Dim, -5.12 <= xi <= 5.12 60 | % global minimum at (xi)=(0) ; fmin=0 61 | ObjVal = sum((Chrom .* Chrom)')'; 62 | % ObjVal = diag(Chrom * Chrom'); % both lines produce the same 63 | % otherwise error, wrong format of Chrom 64 | else 65 | error('size of matrix Chrom is not correct for function evaluation'); 66 | end 67 | 68 | 69 | % End of function -------------------------------------------------------------------------------- /Test_fns/objfun1a.m: -------------------------------------------------------------------------------- 1 | % OBJFUN1A.M (OBJective function for axis parallel hyper-ellipsoid) 2 | % 3 | % This function implements the axis parallel hyper-ellipsoid. 4 | % 5 | % Syntax: ObjVal = objfun1a(Chrom,rtn_type) 6 | % 7 | % Input parameters: 8 | % Chrom - Matrix containing the chromosomes of the current 9 | % population. Each row corresponds to one individual's 10 | % string representation. 11 | % if Chrom == [], then special values will be returned 12 | % rtn_type - if Chrom == [] and 13 | % rtn_type == 1 (or []) return boundaries 14 | % rtn_type == 2 return title 15 | % rtn_type == 3 return value of global minimum 16 | % 17 | % Output parameters: 18 | % ObjVal - Column vector containing the objective values of the 19 | % individuals in the current population. 20 | % if called with Chrom == [], then ObjVal contains 21 | % rtn_type == 1, matrix with the boundaries of the function 22 | % rtn_type == 2, text for the title of the graphic output 23 | % rtn_type == 3, value of global minimum 24 | % 25 | % Author: Hartmut Pohlheim 26 | % History: 07.04.94 file created 27 | % 13.01.03 updated for MATLAB v6 by Alex Shenfield 28 | 29 | function ObjVal = objfun1a(Chrom,rtn_type); 30 | 31 | % Dimension of objective function 32 | Dim = 10; 33 | 34 | % Compute population parameters 35 | [Nind,Nvar] = size(Chrom); 36 | 37 | % Check size of Chrom and do the appropriate thing 38 | % if Chrom is [], then define size of boundary-matrix and values 39 | if Nind == 0 40 | % return text of title for graphic output 41 | if rtn_type == 2 42 | ObjVal = ['Axis Parallel Hyper-Ellipsoid 1a-' int2str(Dim)]; 43 | % return value of global minimum 44 | elseif rtn_type == 3 45 | ObjVal = 0; 46 | % define size of boundary-matrix and values 47 | else 48 | % lower and upper bound, identical for all n variables 49 | ObjVal = 100*[-5.12; 5.12]; 50 | ObjVal = ObjVal(1:2,ones(Dim,1)); 51 | end 52 | % if Dim variables, compute values of function 53 | elseif Nvar == Dim 54 | % function 1a, sum of i * xi^2 for i = 1:Dim (Dim=30) 55 | % n = Dim, -5.12 <= xi <= 5.12 56 | % global minimum at (xi)=(0) ; fmin=0 57 | nummer = rep(1:Dim,[Nind 1]); 58 | ObjVal = sum((nummer .* (Chrom .* Chrom))')'; 59 | % ObjVal = diag((nummer .* (Chrom * Chrom))'); % both lines produce the same 60 | % otherwise error, wrong format of Chrom 61 | else 62 | error('size of matrix Chrom is not correct for function evaluation'); 63 | end 64 | 65 | 66 | % End of function -------------------------------------------------------------------------------- /Test_fns/objfun1b.m: -------------------------------------------------------------------------------- 1 | % OBJFUN1B.M (OBJective function for rotated hyper-ellipsoid) 2 | % 3 | % This function implements the rotated hyper-ellipsoid. 4 | % 5 | % Syntax: ObjVal = objfun1b(Chrom,rtn_type) 6 | % 7 | % Input parameters: 8 | % Chrom - Matrix containing the chromosomes of the current 9 | % population. Each row corresponds to one individual's 10 | % string representation. 11 | % if Chrom == [], then special values will be returned 12 | % rtn_type - if Chrom == [] and 13 | % rtn_type == 1 (or []) return boundaries 14 | % rtn_type == 2 return title 15 | % rtn_type == 3 return value of global minimum 16 | % 17 | % Output parameters: 18 | % ObjVal - Column vector containing the objective values of the 19 | % individuals in the current population. 20 | % if called with Chrom == [], then ObjVal contains 21 | % rtn_type == 1, matrix with the boundaries of the function 22 | % rtn_type == 2, text for the title of the graphic output 23 | % rtn_type == 3, value of global minimum 24 | % 25 | % Author: Hartmut Pohlheim 26 | % History: 07.04.94 file created 27 | % 13.01.03 updated for MATLAB v6 by Alex Shenfield 28 | 29 | function ObjVal = objfun1b(Chrom,rtn_type); 30 | 31 | % Dimension of objective function 32 | Dim = 10; 33 | 34 | % Compute population parameters 35 | [Nind,Nvar] = size(Chrom); 36 | 37 | % Check size of Chrom and do the appropriate thing 38 | % if Chrom is [], then define size of boundary-matrix and values 39 | if Nind == 0 40 | % return text of title for graphic output 41 | if rtn_type == 2 42 | ObjVal = ['Rotated Hyper-Ellipsoid 1b-' int2str(Dim)]; 43 | % return value of global minimum 44 | elseif rtn_type == 3 45 | ObjVal = 0; 46 | % define size of boundary-matrix and values 47 | else 48 | % lower and upper bound, identical for all n variables 49 | ObjVal = [-65; 65]; 50 | ObjVal = ObjVal(1:2,ones(Dim,1)); 51 | end 52 | % if Dim variables, compute values of function 53 | elseif Nvar == Dim 54 | % function 1b, sum over i of ( sum of xj )^2 for i = 1:Dim, j = 1:i (Dim=30) 55 | % n = Dim, -65 <= xj <= 65 56 | % global minimum at (xi)=(0) ; fmin=0 57 | ObjVal = sum(cumsum(Chrom').^2)'; 58 | % otherwise error, wrong format of Chrom 59 | else 60 | error('size of matrix Chrom is not correct for function evaluation'); 61 | end 62 | 63 | 64 | % End of function -------------------------------------------------------------------------------- /Test_fns/objfun2.m: -------------------------------------------------------------------------------- 1 | % OBJFUN2.M (OBJective function for rosenbrock's FUNction) 2 | % 3 | % This function implements the ROSENBROCK valley (DE JONG's Function 2). 4 | % 5 | % Syntax: ObjVal = objfun2(Chrom,rtn_type) 6 | % 7 | % Input parameters: 8 | % Chrom - Matrix containing the chromosomes of the current 9 | % population. Each row corresponds to one 10 | % individual's string representation. 11 | % if called with Chrom == [], then boundaries of 12 | % the function or title for figure will be returned 13 | % rtn_type - if Chrom == [] and rtn_type == 1 (or []) then return 14 | % boundaries, if rtn_type == 2 return title 15 | % 16 | % Output parameters: 17 | % ObjVal - Column vector containing the objective values of the 18 | % individuals in the current population. 19 | % if called with Chrom == [], then ObjVal contains 20 | % the matrix with the boundaries of the function or 21 | % the Text for the title of the graphic output 22 | % 23 | % Author: Hartmut Pohlheim 24 | % History: 26.01.94 file created 25 | % 01.03.94 name changed in obj* 26 | % 13.01.03 updated for MATLAB v6 by Alex Shenfield 27 | 28 | function ObjVal = objfun2(Chrom,rtn_type); 29 | 30 | % Dimension of objective function 31 | Dim = 2; 32 | 33 | % Compute population parameters 34 | [Nind,Nvar] = size(Chrom); 35 | 36 | % Check size of Chrom and do the appropriate thing 37 | % if Chrom is [], then define size of boundary-matrix and values 38 | if Nind == 0 39 | % return text of title for graphic output 40 | if rtn_type == 2 41 | ObjVal = ['ROSENBROCKs function 2-' int2str(Dim)]; 42 | % return value of global minimum 43 | elseif rtn_type == 3 44 | ObjVal = 0; 45 | % define size of boundary-matrix and values 46 | else 47 | % lower and upper bound, identical for all n variables 48 | ObjVal = [-2; 2]; 49 | ObjVal = ObjVal(1:2,ones(Dim,1)); 50 | end 51 | % if Dim variables, compute values of function 52 | elseif Nvar == Dim 53 | % function 11, sum of 100* (x(i+1) -xi^2)^2+(1-xi)^2 for i = 1:Dim (Dim=10) 54 | % n = Dim, -10 <= xi <= 10 55 | % global minimum at (xi)=(1) ; fmin=0 56 | Mat1 = Chrom(:,1:Nvar-1); 57 | Mat2 = Chrom(:,2:Nvar); 58 | if Dim == 2 59 | ObjVal = 100*(Mat2-Mat1.^2).^2+(1-Mat1).^2; 60 | else 61 | ObjVal = sum((100*(Mat2-Mat1.^2).^2+(1-Mat1).^2)')'; 62 | end 63 | % otherwise error, wrong format of Chrom 64 | else 65 | error('size of matrix Chrom is not correct for function evaluation'); 66 | end 67 | 68 | 69 | % End of function -------------------------------------------------------------------------------- /Test_fns/objfun6.m: -------------------------------------------------------------------------------- 1 | % OBJFUN6.M (OBJective function for rastrigins FUNction 6) 2 | % 3 | % This function implements the RASTRIGIN function 6. 4 | % 5 | % Syntax: ObjVal = objfun6(Chrom,rtn_type) 6 | % 7 | % Input parameters: 8 | % Chrom - Matrix containing the chromosomes of the current 9 | % population. Each row corresponds to one individual's 10 | % string representation. 11 | % if Chrom == [], then special values will be returned 12 | % rtn_type - if Chrom == [] and 13 | % rtn_type == 1 (or []) return boundaries 14 | % rtn_type == 2 return title 15 | % rtn_type == 3 return value of global minimum 16 | % 17 | % Output parameters: 18 | % ObjVal - Column vector containing the objective values of the 19 | % individuals in the current population. 20 | % if called with Chrom == [], then ObjVal contains 21 | % rtn_type == 1, matrix with the boundaries of the function 22 | % rtn_type == 2, text for the title of the graphic output 23 | % rtn_type == 3, value of global minimum 24 | % 25 | % Author: Hartmut Pohlheim 26 | % History: 26.11.93 file created 27 | % 27.11.93 text of title and rtn_type added 28 | % 30.11.93 show Dim in figure titel 29 | % 16.12.93 rtn_type == 3, return value of global minimum 30 | % 01.03.94 name changed in obj* 31 | % 13.01.03 updated for MATLAB v6 by Alex Shenfield 32 | 33 | function ObjVal = objfun6(Chrom,rtn_type); 34 | 35 | % Dimension of objective function 36 | Dim = 20; 37 | 38 | % Compute population parameters 39 | [Nind,Nvar] = size(Chrom); 40 | 41 | % Check size of Chrom and do the appropriate thing 42 | % if Chrom is [], then define size of boundary-matrix and values 43 | if Nind == 0 44 | % return text of title for graphic output 45 | if rtn_type == 2 46 | ObjVal = ['RASTRIGINs function 6-' int2str(Dim)]; 47 | % return value of global minimum 48 | elseif rtn_type == 3 49 | ObjVal = 0; 50 | % define size of boundary-matrix and values 51 | else 52 | % lower and upper bound, identical for all n variables 53 | ObjVal = [-5.12; 5.12]; 54 | ObjVal = ObjVal(1:2,ones(Dim,1)); 55 | end 56 | % if Dim variables, compute values of function 57 | elseif Nvar == Dim 58 | % function 6, Dim*A + sum of (xi^2 - A*cos(Omega*xi)) for i = 1:Dim (Dim=20) 59 | % n = Dim, -5.12 <= xi <= 5.12 60 | % global minimum at (xi)=(0) ; fmin=0 61 | A = 10; 62 | Omega = 2 * pi; 63 | ObjVal = Dim * A + sum(((Chrom .* Chrom) - A * cos(Omega * Chrom))')'; 64 | % ObjVal = diag(Chrom * Chrom'); % both lines produce the same 65 | % otherwise error, wrong format of Chrom 66 | else 67 | error('size of matrix Chrom is not correct for function evaluation'); 68 | end 69 | 70 | 71 | % End of function -------------------------------------------------------------------------------- /Test_fns/objfun7.m: -------------------------------------------------------------------------------- 1 | % OBJFUN7.M (OBJective function for schwefel's FUNction) 2 | % 3 | % This function implements the SCHWEFEL function 7. 4 | % 5 | % Syntax: ObjVal = objfun7(Chrom,rtn_type) 6 | % 7 | % Input parameters: 8 | % Chrom - Matrix containing the chromosomes of the current 9 | % population. Each row corresponds to one 10 | % individual's string representation. 11 | % if called with Chrom == [], then boundaries of 12 | % the function or title for figure will be returned 13 | % rtn_type - if Chrom == [] and rtn_type == 1 (or []) then return 14 | % boundaries, if rtn_type == 2 return title 15 | % 16 | % Output parameters: 17 | % ObjVal - Column vector containing the objective values of the 18 | % individuals in the current population. 19 | % if called with Chrom == [], then ObjVal contains 20 | % the matrix with the boundaries of the function or 21 | % the Text for the title of the graphic output 22 | % 23 | % 24 | % Author: Hartmut Pohlheim 25 | % History: 27.11.93 file created 26 | % 30.11.93 show Dim in figure title 27 | % 01.03.94 name changed in obj* 28 | % 14.01.03 updated for MATLAB v6 by Alex Shenfield 29 | 30 | function ObjVal = objfun7(Chrom,rtn_type); 31 | 32 | % Dimension of objective function 33 | Dim = 20; 34 | 35 | % Compute population parameters 36 | [Nind,Nvar] = size(Chrom); 37 | 38 | % Check size of Chrom and do the appropriate thing 39 | % if Chrom is [], then define size of boundary-matrix and values 40 | if Nind == 0 41 | % return text of title for graphic output 42 | if rtn_type == 2 43 | ObjVal = ['SCHWEFELs function 7-' int2str(Dim)]; 44 | % return value of global minimum 45 | elseif rtn_type == 3 46 | xmin = 420.9687; 47 | ObjVal = Dim * (-xmin * sin(sqrt(abs(xmin)))); 48 | % define size of boundary-matrix and values 49 | else 50 | % lower and upper bound, identical for all n variables 51 | ObjVal = [-500; 500]; 52 | ObjVal = ObjVal(1:2,ones(Dim,1)); 53 | end 54 | % if Dim variables, compute values of function 55 | elseif Nvar == Dim 56 | % function 7, sum of -xi*sin(sqrt(abs(xi))) for i = 1:Dim (Dim=10) 57 | % n = Dim, -500 <= xi <= 500 58 | % global minimum at (xi)=(420.9687) ; fmin=? 59 | ObjVal = sum((-Chrom .* sin(sqrt(abs(Chrom))))')'; 60 | % otherwise error, wrong format of Chrom 61 | else 62 | error('size of matrix Chrom is not correct for function evaluation'); 63 | end 64 | 65 | 66 | % End of function -------------------------------------------------------------------------------- /Test_fns/objfun8.m: -------------------------------------------------------------------------------- 1 | % OBJFUN8.M (OBJective function for griewangk's FUNction) 2 | % 3 | % This function implements the GRIEWANGK function 8. 4 | % 5 | % Syntax: ObjVal = objfun8(Chrom,rtn_type) 6 | % 7 | % Input parameters: 8 | % Chrom - Matrix containing the chromosomes of the current 9 | % population. Each row corresponds to one individual's 10 | % string representation. 11 | % if Chrom == [], then special values will be returned 12 | % rtn_type - if Chrom == [] and 13 | % rtn_type == 1 (or []) return boundaries 14 | % rtn_type == 2 return title 15 | % rtn_type == 3 return value of global minimum 16 | % 17 | % Output parameters: 18 | % ObjVal - Column vector containing the objective values of the 19 | % individuals in the current population. 20 | % if called with Chrom == [], then ObjVal contains 21 | % rtn_type == 1, matrix with the boundaries of the function 22 | % rtn_type == 2, text for the title of the graphic output 23 | % rtn_type == 3, value of global minimum 24 | % 25 | % 26 | % Author: Hartmut Pohlheim 27 | % History: 12.12.93 file created (copy of valfun7.m) 28 | % 16.12.93 rtn_type == 3, return value of global minimum 29 | % 27.01.94 20* in formula, correction ?? 30 | % 01.03.94 name changed in obj* 31 | % 14.01.03 updated for MATLAB v6 by Alex Shenfield 32 | 33 | function ObjVal = objfun8(Chrom,rtn_type); 34 | 35 | % Dimension of objective function 36 | Dim = 10; 37 | 38 | % Compute population parameters 39 | [Nind,Nvar] = size(Chrom); 40 | 41 | % Check size of Chrom and do the appropriate thing 42 | % if Chrom is [], then define size of boundary-matrix and values 43 | if Nind == 0 44 | % return text of title for graphic output 45 | if rtn_type == 2 46 | ObjVal = ['GRIEWANGKs function 8-' int2str(Dim)]; 47 | % return value of global minimum 48 | elseif rtn_type == 3 49 | ObjVal = 0; 50 | % define size of boundary-matrix and values 51 | else 52 | % lower and upper bound, identical for all n variables 53 | ObjVal = [-600; 600]; 54 | ObjVal = ObjVal(1:2,ones(Dim,1)); 55 | end 56 | % if Dim variables, compute values of function 57 | elseif Nvar == Dim 58 | % function 8, sum(xi^2/4000) - 20*prod(cos(xi/sqrt(i))) + 1 for i = 1:Dim (Dim=10) 59 | % n = Dim, -600 <= xi <= 600 60 | % global minimum at (xi)=(0) ; fmin=0 61 | % nummer = 1:Dim; 62 | nummer = rep(1:Dim,[Nind 1]); 63 | ObjVal = sum(((Chrom.^2) / 4000)')' - prod(cos(Chrom ./ sqrt(nummer))')' + 1; 64 | % otherwise error, wrong format of Chrom 65 | else 66 | error('size of matrix Chrom is not correct for function evaluation'); 67 | end 68 | 69 | 70 | % End of function -------------------------------------------------------------------------------- /Test_fns/objfun9.m: -------------------------------------------------------------------------------- 1 | % OBJFUN9.M (OBJective function for sum of different power FUNction 9) 2 | % 3 | % This function implements the sum of different power. 4 | % 5 | % Syntax: ObjVal = objfun9(Chrom,rtn_type) 6 | % 7 | % Input parameters: 8 | % Chrom - Matrix containing the chromosomes of the current 9 | % population. Each row corresponds to one individual's 10 | % string representation. 11 | % if Chrom == [], then special values will be returned 12 | % rtn_type - if Chrom == [] and 13 | % rtn_type == 1 (or []) return boundaries 14 | % rtn_type == 2 return title 15 | % rtn_type == 3 return value of global minimum 16 | % 17 | % Output parameters: 18 | % ObjVal - Column vector containing the objective values of the 19 | % individuals in the current population. 20 | % if called with Chrom == [], then ObjVal contains 21 | % rtn_type == 1, matrix with the boundaries of the function 22 | % rtn_type == 2, text for the title of the graphic output 23 | % rtn_type == 3, value of global minimum 24 | % 25 | % 26 | % Author: Hartmut Pohlheim 27 | % History: 07.04.94 file created 28 | % 14.01.03 updated for MATLAB v6 by Alex Shenfield 29 | 30 | function ObjVal = objfun9(Chrom,rtn_type); 31 | 32 | % Dimension of objective function 33 | Dim = 10; 34 | 35 | % Compute population parameters 36 | [Nind,Nvar] = size(Chrom); 37 | 38 | % Check size of Chrom and do the appropriate thing 39 | % if Chrom is [], then define size of boundary-matrix and values 40 | if Nind == 0 41 | % return text of title for graphic output 42 | if rtn_type == 2 43 | ObjVal = ['Sum of different Power 9-' int2str(Dim)]; 44 | % return value of global minimum 45 | elseif rtn_type == 3 46 | ObjVal = 0; 47 | % define size of boundary-matrix and values 48 | else 49 | % lower and upper bound, identical for all n variables 50 | ObjVal = [-1; 1]; 51 | ObjVal = ObjVal(1:2,ones(Dim,1)); 52 | end 53 | % if Dim variables, compute values of function 54 | elseif Nvar == Dim 55 | % function 9, sum of abs(xi)^(i+1) for i = 1:Dim (Dim=30) 56 | % n = Dim, -1 <= xi <= 1 57 | % global minimum at (xi)=(0) ; fmin=0 58 | nummer = rep(1:Dim,[Nind 1]); 59 | ObjVal = sum((abs(Chrom).^(nummer+1))')'; 60 | % otherwise error, wrong format of Chrom 61 | else 62 | error('size of matrix Chrom is not correct for function evaluation'); 63 | end 64 | 65 | 66 | % End of function -------------------------------------------------------------------------------- /Test_fns/objgold.m: -------------------------------------------------------------------------------- 1 | % OBJGOLD.M (OBJective function for GOLDstein-price function) 2 | % 3 | % This function implements the GOLDSTEIN-PRICE function. 4 | % 5 | % Syntax: ObjVal = objgold(Chrom,rtn_type) 6 | % 7 | % Input parameters: 8 | % Chrom - Matrix containing the chromosomes of the current 9 | % population. Each row corresponds to one individual's 10 | % string representation. 11 | % if Chrom == [], then special values will be returned 12 | % rtn_type - if Chrom == [] and 13 | % rtn_type == 1 (or []) return boundaries 14 | % rtn_type == 2 return title 15 | % rtn_type == 3 return value of global minimum 16 | % 17 | % Output parameters: 18 | % ObjVal - Column vector containing the objective values of the 19 | % individuals in the current population. 20 | % if called with Chrom == [], then ObjVal contains 21 | % rtn_type == 1, matrix with the boundaries of the function 22 | % rtn_type == 2, text for the title of the graphic output 23 | % rtn_type == 3, value of global minimum 24 | % 25 | % 26 | % Author: Hartmut Pohlheim 27 | % History: 25.11.93 file created 28 | % 27.11.93 text of title and rtn_type added 29 | % 16.12.93 rtn_type == 3, return value of global minimum 30 | % 01.03.94 name changed in obj* 31 | % 14.01.03 updated for MATLAB v6 by Alex Shenfield 32 | 33 | function ObjVal = objgold(Chrom,rtn_type); 34 | 35 | % Compute population parameters 36 | [Nind,Nvar] = size(Chrom); 37 | 38 | % Check size of Chrom and do the appropriate thing 39 | % if Chrom is [], then define size of boundary-matrix and values 40 | if Nind == 0 41 | % return text of title for graphic output 42 | if rtn_type == 2 43 | ObjVal = 'GOLDSTEIN-PRICE function'; 44 | % return value of global minimum 45 | elseif rtn_type == 3 46 | ObjVal = 3; 47 | % define size of boundary-matrix and values 48 | else 49 | brd = 3; 50 | % x1 x2 51 | ObjVal = [-brd -brd; % lower bounds 52 | brd brd]; % upper bounds 53 | end 54 | % if two variables, compute values of function 55 | elseif Nvar == 2 56 | % GOLDSTEIN-PRICE function 57 | % -2 <= x1 <= 2 ; -2 <= x2 <= 2 (or -10 <= xi <= 10) 58 | % global minimum at (x1,x2)=(0,-1) ; fmin=3 59 | x1 = Chrom(:,1); 60 | x2 = Chrom(:,2); 61 | ObjVal = ((1+(x1+x2+1).^2.*(19-14*x1+3*x1.^2-14*x2+6*x1.*x2+3*x2.^2))... 62 | .*(30+(2*x1-3*x2).^2.*(18-32*x1+12*x1.^2+48*x2-36*x1.*x2+27*x2.^2))); 63 | % otherwise error, wrong format of Chrom 64 | else 65 | error('size of matrix Chrom is not correct for function evaluation'); 66 | end 67 | 68 | 69 | % End of function -------------------------------------------------------------------------------- /Test_fns/objharv.m: -------------------------------------------------------------------------------- 1 | % OBJHARV.M (OBJective function for HARVest problem) 2 | % 3 | % This function implements the HARVEST PROBLEM. 4 | % 5 | % Syntax: ObjVal = objharv(Chrom,rtn_type) 6 | % 7 | % Input parameters: 8 | % Chrom - Matrix containing the chromosomes of the current 9 | % population. Each row corresponds to one individual's 10 | % string representation. 11 | % if Chrom == [], then special values will be returned 12 | % rtn_type - if Chrom == [] and 13 | % rtn_type == 1 (or []) return boundaries 14 | % rtn_type == 2 return title 15 | % rtn_type == 3 return value of global minimum 16 | % 17 | % Output parameters: 18 | % ObjVal - Column vector containing the objective values of the 19 | % individuals in the current population. 20 | % if called with Chrom == [], then ObjVal contains 21 | % rtn_type == 1, matrix with the boundaries of the function 22 | % rtn_type == 2, text for the title of the graphic output 23 | % rtn_type == 3, value of global minimum 24 | % 25 | % 26 | % Author: Hartmut Pohlheim 27 | % History: 18.02.94 file created (copy of vallinq.m) 28 | % 01.03.94 name changed in obj* 29 | % 14.01.03 updated for MATLAB v6 by Alex Shenfield 30 | 31 | function ObjVal = objharv(Chrom,rtn_type); 32 | 33 | % global gen; 34 | 35 | % Dimension of objective function 36 | Dim = 20; 37 | 38 | % values from MICHALEWICZ 39 | a = 1.1; 40 | x0 = 100; 41 | xend = x0; 42 | XENDWEIGHT = 0.4/(Dim^0.6); 43 | 44 | % Compute population parameters 45 | [Nind,Nvar] = size(Chrom); 46 | 47 | % Check size of Chrom and do the appropriate thing 48 | % if Chrom is [], then define size of boundary-matrix and values 49 | if Nind == 0 50 | % return text of title for graphic output 51 | if rtn_type == 2 52 | ObjVal = ['HARVEST PROBLEM-' int2str(Dim)]; 53 | % return value of global minimum 54 | elseif rtn_type == 3 55 | ObjVal = -sqrt(x0*(a^Dim-1)^2/(a^(Dim-1)*(a-1))); 56 | % define size of boundary-matrix and values 57 | else 58 | % lower and upper bound, identical for all n variables 59 | ObjVal1 = [0; 10*Dim]; 60 | ObjVal = rep(ObjVal1,[1 Dim]); 61 | end 62 | % if Dim variables, compute values of function 63 | elseif Nvar == Dim 64 | ObjVal = zeros(Nind,1); 65 | X = rep(x0,[Nind 1]); 66 | for irun = 1:Nvar, 67 | X = a*X - Chrom(:,irun); 68 | end 69 | X; 70 | ObjVal = -(sum(sqrt(Chrom)')' - XENDWEIGHT * abs(X-x0)); 71 | % otherwise error, wrong format of Chrom 72 | else 73 | error('size of matrix Chrom is not correct for function evaluation'); 74 | end 75 | 76 | 77 | % End of function -------------------------------------------------------------------------------- /Test_fns/objlinq.m: -------------------------------------------------------------------------------- 1 | % OBJLINQ.M (OBJective function for LINear Quadratic problem) 2 | % 3 | % This function implements the discret LINEAR-QUADRATIC PROBLEM. 4 | % 5 | % Syntax: ObjVal = objlinq(Chrom,rtn_type) 6 | % 7 | % Input parameters: 8 | % Chrom - Matrix containing the chromosomes of the current 9 | % population. Each row corresponds to one individual's 10 | % string representation. 11 | % if Chrom == [], then special values will be returned 12 | % rtn_type - if Chrom == [] and 13 | % rtn_type == 1 (or []) return boundaries 14 | % rtn_type == 2 return title 15 | % rtn_type == 3 return value of global minimum 16 | % 17 | % Output parameters: 18 | % ObjVal - Column vector containing the objective values of the 19 | % individuals in the current population. 20 | % if called with Chrom == [], then ObjVal contains 21 | % rtn_type == 1, matrix with the boundaries of the function 22 | % rtn_type == 2, text for the title of the graphic output 23 | % rtn_type == 3, value of global minimum 24 | % 25 | % 26 | % Author: Hartmut Pohlheim 27 | % History: 18.02.94 file created (copy of valfun7.m) 28 | % 01.03.94 name changed in obj* 29 | % 14.01.03 updated for MATLAB v6 by Alex Shenfield 30 | 31 | function ObjVal = objlinq(Chrom,rtn_type); 32 | 33 | % Dimension of objective function 34 | Dim = 45; 35 | 36 | % values from MICHALEWICZ 37 | x0 = 100; % start of X 38 | var = 1; % 1 - 10 possible 39 | Para = [ 1 1 1 1 1 16180.3399; 40 | 10 1 1 1 1 109160.7978; 41 | 1000 1 1 1 1 10009990.0200; 42 | 1 10 1 1 1 37015.6212; 43 | 1 1000 1 1 1 287569.3725; 44 | 1 1 0 1 1 16180.3399; 45 | 1 1 1000 1 1 16180.3399; 46 | 1 1 1 0.01 1 10000.5000; 47 | 1 1 1 1 0.01 431004.0987; 48 | 1 1 1 1 100 10000.9999]; 49 | s = Para(var,1); r = Para(var,2); q = Para(var,3); 50 | a = Para(var,4); b = Para(var,5); GlobalMinimum = Para(var,6); 51 | 52 | % Compute population parameters 53 | [Nind,Nvar] = size(Chrom); 54 | 55 | % Check size of Chrom and do the appropriate thing 56 | % if Chrom is [], then define size of boundary-matrix and values 57 | if Nind == 0 58 | % return text of title for graphic output 59 | if rtn_type == 2 60 | ObjVal = ['Linear-quadratic problem (dis)-' int2str(Dim)]; 61 | % return value of global minimum 62 | elseif rtn_type == 3 63 | ObjVal = GlobalMinimum; 64 | % define size of boundary-matrix and values 65 | else 66 | % lower and upper bound, identical for all n variables 67 | ObjVal1 = [-100 -70 -50; 20 20 20]; 68 | ObjVal = [ObjVal1 rep([-30;20],[1 Dim-3])]; 69 | end 70 | % if Dim variables, compute values of function 71 | elseif Nvar == Dim 72 | ObjVal = zeros(Nind,1); 73 | X = zeros(Nind,Nvar+1); 74 | X(:,1) = rep(x0,[Nind 1]); 75 | for irun = 1:Nvar, 76 | X(:,irun+1) = a*X(:,irun) + b*Chrom(:,irun); 77 | end 78 | ObjVal = q * X(:,Nvar+1).^2 + sum((s * X(:,1:Nvar).^2 + r * Chrom.^2)')'; 79 | % otherwise error, wrong format of Chrom 80 | else 81 | error('size of matrix Chrom is not correct for function evaluation'); 82 | end 83 | 84 | 85 | % End of function -------------------------------------------------------------------------------- /Test_fns/objlinq2.m: -------------------------------------------------------------------------------- 1 | % OBJLINQ2.M (OBJective function for LINear Quadratic problem) 2 | % 3 | % This function implements the continuous LINear Quadratic problem. 4 | % 5 | % Syntax: ObjVal = objlinq2(Chrom,rtn_type) 6 | % 7 | % Input parameters: 8 | % Chrom - Matrix containing the chromosomes of the current 9 | % population. Each row corresponds to one individual's 10 | % string representation. 11 | % if Chrom == [], then special values will be returned 12 | % rtn_type - if Chrom == [] and 13 | % rtn_type == 1 (or []) return boundaries 14 | % rtn_type == 2 return title 15 | % rtn_type == 3 return value of global minimum 16 | % 17 | % Output parameters: 18 | % ObjVal - Column vector containing the objective values of the 19 | % individuals in the current population. 20 | % if called with Chrom == [], then ObjVal contains 21 | % rtn_type == 1, matrix with the boundaries of the function 22 | % rtn_type == 2, text for the title of the graphic output 23 | % rtn_type == 3, value of global minimum 24 | % 25 | % 26 | % Author: Hartmut Pohlheim 27 | % History: 03.03.94 file created 28 | % 06.04.94 all linq (sim, ode, con) in 1 file 29 | % 26.01.03 switch changed to rtn_type for compatability with MATLAB v6 30 | % by Alex Shenfield 31 | 32 | function [ObjVal,t,x] = objlinq2(Chrom,rtn_type); 33 | 34 | % Define used method 35 | method = 1; % 1 - sim: simulink model 36 | % 2 - ode: ordinary differential equations 37 | % 3 - con: transfer function to state space 38 | 39 | % Dimension of objective function 40 | Dim = 50; 41 | TSTART = 0; 42 | TEND = 1; 43 | STEPSIMU = min(0.1,abs((TEND-TSTART)/(Dim-1))); 44 | TIMEVEC = linspace(TSTART,TEND,Dim)'; 45 | 46 | % initial conditions 47 | XINIT = [100]; 48 | 49 | % end conditions 50 | XEND = [0]; 51 | 52 | % weights for control and end 53 | XENDWEIGHT = [20]; % XEND 54 | XWEIGHT = [2]; % State vector 55 | UWEIGHT = [1]; % Control vector 56 | 57 | % Compute population parameters 58 | [Nind,Nvar] = size(Chrom); 59 | 60 | % Check size of Chrom and do the appropriate thing 61 | % if Chrom is [], then 62 | if Nind == 0 63 | % return text of title for graphic output 64 | if rtn_type == 2 65 | if method == 2, ObjVal = ['Linear-quadratic problem (ode)-' int2str(Dim)]; 66 | elseif method == 3, ObjVal = ['Linear-quadratic problem (con)-' int2str(Dim)]; 67 | else ObjVal = ['Linear-quadratic problem (sim)-' int2str(Dim)]; 68 | end 69 | % return value of global minimum 70 | elseif rtn_type == 3 71 | ObjVal = 16180.3399; 72 | % define size of boundary-matrix and values 73 | else 74 | % lower and upper bound, identical for all n variables 75 | ObjVal = rep([-600; 0],[1 Dim]); 76 | end 77 | % if Dim variables, compute values of function 78 | elseif Nvar == Dim 79 | if method == 3, % Convert transfer function to state space system 80 | [NC DC]=cloop(1, [1 0], +1); 81 | [Ai2 Bi2 Ci2 Di2] = tf2ss(NC, DC); 82 | t = TIMEVEC; 83 | end 84 | ObjVal = zeros(Nind,1); 85 | for indrun = 1:Nind 86 | steuerung = [TIMEVEC Chrom(indrun,:)']; 87 | if method == 2, 88 | [t x] = linsim('simlinq2',[TSTART TEND],[],[1e-3;STEPSIMU;STEPSIMU],steuerung); 89 | elseif method == 3, 90 | [y x] = lsim(Ai2, Bi2, Ci2, Di2, Chrom(indrun,:),TIMEVEC, XINIT); 91 | else 92 | [t x] = linsim('simlinq1',[TSTART TEND],[],[1e-3;STEPSIMU;STEPSIMU],steuerung); 93 | end 94 | % Calculate objective function, endvalues, trapez-integration for control vector 95 | ObjVal(indrun) = (XENDWEIGHT * ( x(size(x,1),:)^2 )) + ... 96 | (UWEIGHT / (Dim-1) * trapz(Chrom(indrun,:).^2)) + ... 97 | (XWEIGHT / size(x,1) * sum(x.^2)); 98 | end 99 | % otherwise error, wrong format of Chrom 100 | else 101 | error('size of matrix Chrom is not correct for function evaluation'); 102 | end 103 | 104 | % End of function -------------------------------------------------------------------------------- /Test_fns/objpush.m: -------------------------------------------------------------------------------- 1 | % OBJPUSH.M (OBJective function for PUSH-cart problem) 2 | % 3 | % This function implements the PUSH-CART PROBLEM. 4 | % 5 | % Syntax: ObjVal = objpush(Chrom,rtn_type) 6 | % 7 | % Input parameters: 8 | % Chrom - Matrix containing the chromosomes of the current 9 | % population. Each row corresponds to one individual's 10 | % string representation. 11 | % if Chrom == [], then special values will be returned 12 | % rtn_type - if Chrom == [] and 13 | % rtn_type == 1 (or []) return boundaries 14 | % rtn_type == 2 return title 15 | % rtn_type == 3 return value of global minimum 16 | % 17 | % Output parameters: 18 | % ObjVal - Column vector containing the objective values of the 19 | % individuals in the current population. 20 | % if called with Chrom == [], then ObjVal contains 21 | % rtn_type == 1, matrix with the boundaries of the function 22 | % rtn_type == 2, text for the title of the graphic output 23 | % rtn_type == 3, value of global minimum 24 | % 25 | % 26 | % Author: Hartmut Pohlheim 27 | % History: 19.02.94 file created (copy of valharv.m) 28 | % 01.03.94 name changed in obj* 29 | % 15.01.03 updated for MATLAB v6 by Alex Shenfield 30 | 31 | function ObjVal = objpush(Chrom,rtn_type); 32 | 33 | % Dimension of objective function 34 | Dim = 20; 35 | 36 | % values from MICHALEWICZ 37 | x0 = [0 0]; 38 | 39 | % Compute population parameters 40 | [Nind,Nvar] = size(Chrom); 41 | 42 | % Check size of Chrom and do the appropriate thing 43 | % if Chrom is [], then define size of boundary-matrix and values 44 | if Nind == 0 45 | % return text of title for graphic output 46 | if rtn_type == 2 47 | ObjVal = ['PUSH-CART PROBLEM-' int2str(Dim)]; 48 | % return value of global minimum 49 | elseif rtn_type == 3 50 | ObjVal = -(1/3 - ((3*Dim-1)/(6*Dim^2)) - (1/(2*Dim^3))*sum((1:Dim-1).^2)); 51 | % define size of boundary-matrix and values 52 | else 53 | % lower and upper bound, identical for all n variables 54 | ObjVal = [0; 5]; 55 | ObjVal = rep(ObjVal,[1 Dim]); 56 | end 57 | % if Dim variables, compute values of function 58 | elseif Nvar == Dim 59 | ObjVal = zeros(Nind,1); 60 | X = rep(x0,[Nind 1]); 61 | for irun = 1:Nvar, 62 | Xsave = X; 63 | X(:,1) = Xsave(:,2); 64 | X(:,2) = 2 * X(:,2) - Xsave(:,1) + (1/Dim^2) * Chrom(:,irun); 65 | end 66 | X; 67 | ObjVal = -(X(:,1) - (1/(2*Dim)) * sum((Chrom.^2)')'); 68 | % otherwise error, wrong format of Chrom 69 | else 70 | error('size of matrix Chrom is not correct for function evaluation'); 71 | end 72 | 73 | 74 | % End of function -------------------------------------------------------------------------------- /Test_fns/objsixh.m: -------------------------------------------------------------------------------- 1 | % OBJSIXH.M (OBJective function for SIX Hump camelback function) 2 | % 3 | % This function implements the six hump camelback function. 4 | % 5 | % Syntax: ObjVal = objsixh(Chrom,rtn_type) 6 | % 7 | % Input parameters: 8 | % Chrom - Matrix containing the chromosomes of the current 9 | % population. Each row corresponds to one individual's 10 | % string representation. 11 | % if Chrom == [], then special values will be returned 12 | % rtn_type - if Chrom == [] and 13 | % rtn_type == 1 (or []) return boundaries 14 | % rtn_type == 2 return title 15 | % rtn_type == 3 return value of global minimum 16 | % 17 | % Output parameters: 18 | % ObjVal - Column vector containing the objective values of the 19 | % individuals in the current population. 20 | % if called with Chrom == [], then ObjVal contains 21 | % rtn_type == 1, matrix with the boundaries of the function 22 | % rtn_type == 2, text for the title of the graphic output 23 | % rtn_type == 3, value of global minimum 24 | % 25 | % 26 | % Author: Hartmut Pohlheim 27 | % History: 25.11.93 file created 28 | % 27.11.93 text of title and rtn_type added 29 | % 16.12.93 rtn_type == 3, return value of global minimum 30 | % 01.03.94 name changed in obj* 31 | % 15.01.03 updated for MATLAB v6 by Alex Shenfield 32 | 33 | function ObjVal = objsixh(Chrom,rtn_type); 34 | 35 | % Compute population parameters 36 | [Nind,Nvar] = size(Chrom); 37 | 38 | % Check size of Chrom and do the appropriate thing 39 | % if Chrom is [], then define size of boundary-matrix and values 40 | if Nind == 0 41 | % return text of title for graphic output 42 | if rtn_type == 2 43 | ObjVal = 'six-hump camelback function'; 44 | % return value of global minimum 45 | elseif rtn_type == 3 46 | ObjVal = -1.0316; 47 | % define size of boundary-matrix and values 48 | else 49 | % x1 x2 50 | ObjVal = [-3 -2; % lower bounds 51 | 3 2]; % upper bounds 52 | end 53 | % if two variables, compute values of function 54 | elseif Nvar == 2 55 | % six-hump camelback function 56 | % -3 <= x1 <= 3 ; -2 <= x2 <= 2 57 | % global minimum at (x1,x2)=(-0.0898,0.7126),(0.0898,-0.7126) ; fmin=-1.0316 58 | x1 = Chrom(:,1); 59 | x2 = Chrom(:,2); 60 | ObjVal = (4-2.1*x1.^2+1/3*x1.^4).*x1.^2+x1.*x2+(-4+4*x2.^2).*x2.^2; 61 | % otherwise error, wrong format of Chrom 62 | else 63 | error('size of matrix Chrom is not correct for function evaluation'); 64 | end 65 | 66 | % End of function -------------------------------------------------------------------------------- /Test_fns/resplot.m: -------------------------------------------------------------------------------- 1 | % RESPLOT.M (RESult PLOTing) 2 | % 3 | % This function plots some of the results during computation. 4 | % 5 | % Syntax: resplot(Chrom,IndAll,ObjV,Best,gen) 6 | % 7 | % Input parameters: 8 | % Chrom - Matrix containing the chromosomes of the current 9 | % population. Each line corresponds to one individual. 10 | % IndAll - Matrix containing the best individual (variables) of each 11 | % generation. Each line corresponds to one individual. 12 | % ObjV - Vector containing objective values of the current 13 | % generation 14 | % Best - Matrix containing the best and average Objective values of each 15 | % generation, [best value per generation,average value per generation] 16 | % gen - Scalar containing the number of the current generation 17 | % 18 | % Output parameter: 19 | % no output parameter 20 | % 21 | % Author: Hartmut Pohlheim 22 | % History: 27.11.93 file created 23 | % 29.11.93 decision, if plot or not deleted 24 | % yscale not log 25 | % 15.12.93 MutMatrix as parameter and plot added 26 | % 16.03.94 function cleaned, MutMatrix removed, IndAll added 27 | % 15.01.03 tested under MATLAB v6 by Alex Shenfield 28 | 29 | function resplot(Chrom,IndAll,ObjV,Best,gen); 30 | 31 | % plot of best and mean value per generation 32 | subplot(2,2,1), plot(Best); 33 | title('Best and mean objective value'); 34 | xlabel('generation'), ylabel('objective value'); 35 | 36 | % plot of best individuals in all generations 37 | subplot(2,2,2), plot(IndAll); 38 | title(['Best individuals']); 39 | xlabel('generation'), ylabel('value of variable'); 40 | 41 | % plot of variables of all individuals in current generation 42 | subplot(2,2,3), plot(Chrom'); 43 | title(['All individuals in gen ',num2str(gen)]); 44 | xlabel('number of variable'), ylabel('value of variable'); 45 | 46 | % plot of all objective values in current generation 47 | subplot(2,2,4), plot(ObjV,'y.'); 48 | title(['All objective values']); 49 | xlabel('number of individual'), ylabel('objective value'); 50 | 51 | drawnow; 52 | 53 | 54 | % End of function -------------------------------------------------------------------------------- /Test_fns/sga.m: -------------------------------------------------------------------------------- 1 | % SGA.M (Simple Genetic Algorithm) 2 | % 3 | % This script implements the Simple Genetic Algorithm. 4 | % Binary representation for the individuals is used. 5 | % 6 | % Author: Hartmut Pohlheim 7 | % History: 23.03.94 file created 8 | % 15.01.03 tested under MATLAB v6 by Alex Shenfield 9 | 10 | NIND = 20; % Number of individuals per subpopulations 11 | MAXGEN = 300; % max Number of generations 12 | GGAP = .8; % Generation gap, how many new individuals are created 13 | SEL_F = 'sus'; % Name of selection function 14 | XOV_F = 'xovsp'; % Name of recombination function for individuals 15 | MUT_F = 'mut'; % Name of mutation function for individuals 16 | OBJ_F = 'objfun1'; % Name of function for objective values 17 | 18 | % Get boundaries of objective function 19 | FieldDR = feval(OBJ_F,[],1); 20 | 21 | % Number of variables of objective function, in OBJ_F defined 22 | NVAR = size(FieldDR,2); 23 | 24 | % Build fielddescription matrix 25 | PRECI = 20; % Precisicion of binary representation 26 | FieldDD = [rep([PRECI],[1, NVAR]);... 27 | FieldDR;... 28 | rep([1; 0; 1 ;1], [1, NVAR])]; 29 | 30 | % Create population 31 | Chrom = crtbp(NIND, NVAR*PRECI); 32 | 33 | % reset count variables 34 | gen = 0; 35 | Best = NaN*ones(MAXGEN,1); 36 | 37 | % Iterate population 38 | while gen < MAXGEN, 39 | 40 | % Calculate objective function for population 41 | ObjV = feval(OBJ_F,bs2rv(Chrom, FieldDD)); 42 | Best(gen+1) = min(ObjV); 43 | plot(log10(Best),'ro'); 44 | drawnow; 45 | 46 | % Fitness assignement to whole population 47 | FitnV = ranking(ObjV); 48 | 49 | % Select individuals from population 50 | SelCh = select(SEL_F, Chrom, FitnV, GGAP); 51 | 52 | % Recombine selected individuals (crossover) 53 | SelCh=recombin(XOV_F, SelCh); 54 | 55 | % Mutate offspring 56 | SelCh=mutate(MUT_F, SelCh); 57 | 58 | % Insert offspring in population replacing parents 59 | Chrom = reins(Chrom, SelCh); 60 | 61 | gen=gen+1; 62 | 63 | end 64 | 65 | % End of script -------------------------------------------------------------------------------- /Test_fns/simdopi1.m: -------------------------------------------------------------------------------- 1 | function [ret,x0,str]=simdopi1(t,x,u,flag); 2 | %SIMDOPI1 is the M-file description of the SIMULINK system named SIMDOPI1. 3 | % The block-diagram can be displayed by typing: SIMDOPI1. 4 | % 5 | % SYS=SIMDOPI1(T,X,U,FLAG) returns depending on FLAG certain 6 | % system values given time point, T, current state vector, X, 7 | % and input vector, U. 8 | % FLAG is used to indicate the type of output to be returned in SYS. 9 | % 10 | % Setting FLAG=1 causes SIMDOPI1 to return state derivatives, FLAG=2 11 | % discrete states, FLAG=3 system outputs and FLAG=4 next sample 12 | % time. For more information and other options see SFUNC. 13 | % 14 | % Calling SIMDOPI1 with a FLAG of zero: 15 | % [SIZES]=SIMDOPI1([],[],[],0), returns a vector, SIZES, which 16 | % contains the sizes of the state vector and other parameters. 17 | % SIZES(1) number of states 18 | % SIZES(2) number of discrete states 19 | % SIZES(3) number of outputs 20 | % SIZES(4) number of inputs. 21 | % For the definition of other parameters in SIZES, see SFUNC. 22 | % See also, TRIM, LINMOD, LINSIM, EULER, RK23, RK45, ADAMS, GEAR. 23 | 24 | % Note: This M-file is only used for saving graphical information; 25 | % after the model is loaded into memory an internal model 26 | % representation is used. 27 | 28 | % the system will take on the name of this mfile: 29 | sys = mfilename; 30 | new_system(sys) 31 | simver(1.2) 32 | if(0 == (nargin + nargout)) 33 | set_param(sys,'Location',[100,100,600,400]) 34 | open_system(sys) 35 | end; 36 | set_param(sys,'algorithm', 'RK-45') 37 | set_param(sys,'Start time', '0.0') 38 | set_param(sys,'Stop time', '1') 39 | set_param(sys,'Min step size', '0.001') 40 | set_param(sys,'Max step size', '0.01') 41 | set_param(sys,'Relative error','1e-3') 42 | set_param(sys,'Return vars', '') 43 | 44 | add_block('built-in/Inport',[sys,'/','Inport']) 45 | set_param([sys,'/','Inport'],... 46 | 'position',[65,95,85,115]) 47 | 48 | add_block('built-in/Note',[sys,'/','Doppelintegrator']) 49 | set_param([sys,'/','Doppelintegrator'],... 50 | 'position',[225,10,230,15]) 51 | 52 | add_block('built-in/Note',[sys,'/','Steuerung']) 53 | set_param([sys,'/','Steuerung'],... 54 | 'position',[75,65,80,70]) 55 | 56 | add_block('built-in/Integrator',[sys,'/','Integrator1']) 57 | set_param([sys,'/','Integrator1'],... 58 | 'position',[175,95,195,115]) 59 | 60 | add_block('built-in/Integrator',[sys,'/','Integrator2']) 61 | set_param([sys,'/','Integrator2'],... 62 | 'Initial','-1',... 63 | 'position',[280,95,300,115]) 64 | add_line(sys,[90,105;165,105]) 65 | add_line(sys,[200,105;270,105]) 66 | 67 | % Return any arguments. 68 | if (nargin | nargout) 69 | % Must use feval here to access system in memory 70 | if (nargin > 3) 71 | if (flag == 0) 72 | eval(['[ret,x0,str]=',sys,'(t,x,u,flag);']) 73 | else 74 | eval(['ret =', sys,'(t,x,u,flag);']) 75 | end 76 | else 77 | [ret,x0,str] = feval(sys); 78 | end 79 | end 80 |  -------------------------------------------------------------------------------- /Test_fns/simdopi2.m: -------------------------------------------------------------------------------- 1 | % SIMDOPI2.M (Modell of DOPpelINTegrator, s-function) 2 | % 3 | % This function implements the modell of the DOPPELINTEGRATOR. 4 | % 5 | % Syntax: [sys, x0] = simdopi2(t, x, u, flag) 6 | % 7 | % Input parameters: 8 | % t - given time point 9 | % x - current state vector 10 | % u - input vector 11 | % flag - flags 12 | % 13 | % Output parameters: 14 | % sys - Vector containing the new state derivatives 15 | % x0 - initial value 16 | 17 | % Author: Hartmut Pohlheim 18 | % History: 17.12.93 file created 19 | 20 | function [sys, x0] = simdopi2(t, x, u, flag); 21 | 22 | % Linear Systems Description 23 | 24 | if abs(flag) == 1 25 | sys(1) = u(1); % Derivatives 26 | sys(2) = x(1); % Derivatives 27 | elseif abs(flag) == 0 28 | sys=[2,0,0,1,0,0]; x0 = [0; -1]; 29 | else 30 | sys = []; % Real time update (ignored). 31 | end 32 | 33 | 34 | % End of function 35 |  -------------------------------------------------------------------------------- /Test_fns/simlinq1.m: -------------------------------------------------------------------------------- 1 | function [ret,x0,str]=simlinq1(t,x,u,flag); 2 | %SIMLINQ1 is the M-file description of the SIMULINK system named SIMLINQ1. 3 | % The block-diagram can be displayed by typing: SIMLINQ1. 4 | % 5 | % SYS=SIMLINQ1(T,X,U,FLAG) returns depending on FLAG certain 6 | % system values given time point, T, current state vector, X, 7 | % and input vector, U. 8 | % FLAG is used to indicate the type of output to be returned in SYS. 9 | % 10 | % Setting FLAG=1 causes SIMLINQ1 to return state derivatives, FLAG=2 11 | % discrete states, FLAG=3 system outputs and FLAG=4 next sample 12 | % time. For more information and other options see SFUNC. 13 | % 14 | % Calling SIMLINQ1 with a FLAG of zero: 15 | % [SIZES]=SIMLINQ1([],[],[],0), returns a vector, SIZES, which 16 | % contains the sizes of the state vector and other parameters. 17 | % SIZES(1) number of states 18 | % SIZES(2) number of discrete states 19 | % SIZES(3) number of outputs 20 | % SIZES(4) number of inputs. 21 | % For the definition of other parameters in SIZES, see SFUNC. 22 | % See also, TRIM, LINMOD, LINSIM, EULER, RK23, RK45, ADAMS, GEAR. 23 | 24 | % Note: This M-file is only used for saving graphical information; 25 | % after the model is loaded into memory an internal model 26 | % representation is used. 27 | 28 | % the system will take on the name of this mfile: 29 | sys = mfilename; 30 | new_system(sys) 31 | simver(1.2) 32 | if(0 == (nargin + nargout)) 33 | set_param(sys,'Location',[208,245,596,426]) 34 | open_system(sys) 35 | end; 36 | set_param(sys,'algorithm', 'RK-45') 37 | set_param(sys,'Start time', '0.0') 38 | set_param(sys,'Stop time', '1') 39 | set_param(sys,'Min step size', '0.05') 40 | set_param(sys,'Max step size', '0.05') 41 | set_param(sys,'Relative error','1e-3') 42 | set_param(sys,'Return vars', '') 43 | 44 | add_block('built-in/Sum',[sys,'/','Sum']) 45 | set_param([sys,'/','Sum'],... 46 | 'position',[110,65,130,85]) 47 | 48 | add_block('built-in/Integrator',[sys,'/','Integrator']) 49 | set_param([sys,'/','Integrator'],... 50 | 'Initial','100',... 51 | 'position',[180,65,200,85]) 52 | 53 | add_block('built-in/Inport',[sys,'/','Inport']) 54 | set_param([sys,'/','Inport'],... 55 | 'position',[25,70,45,90]) 56 | add_line(sys,[135,75;170,75]) 57 | add_line(sys,[205,75;205,40;90,40;90,70;100,70]) 58 | add_line(sys,[50,80;100,80]) 59 | 60 | % Return any arguments. 61 | if (nargin | nargout) 62 | % Must use feval here to access system in memory 63 | if (nargin > 3) 64 | if (flag == 0) 65 | eval(['[ret,x0,str]=',sys,'(t,x,u,flag);']) 66 | else 67 | eval(['ret =', sys,'(t,x,u,flag);']) 68 | end 69 | else 70 | [ret,x0,str] = feval(sys); 71 | end 72 | end -------------------------------------------------------------------------------- /Test_fns/simlinq2.m: -------------------------------------------------------------------------------- 1 | % SIMLINQ2.M (Model of Linear Quadratic Problem, s-function) 2 | % 3 | % This function implements the model of the Linear Quadratic Problem. 4 | % 5 | % Syntax: [sys, x0] = simlinq2(t, x, u, flag) 6 | % 7 | % Input parameters: 8 | % t - given time point 9 | % x - current state vector 10 | % u - input vector 11 | % flag - flags 12 | % 13 | % Output parameters: 14 | % sys - Vector containing the new state derivatives 15 | % x0 - initial value 16 | % 17 | % Author: Hartmut Pohlheim 18 | % History: 23.03.94 file created 19 | 20 | function [sys, x0] = simlinq2(t, x, u, flag); 21 | 22 | % Linear Systems Description 23 | 24 | if abs(flag) == 1 25 | sys(1) = u(1) + x(1); % Derivatives 26 | elseif abs(flag) == 0 27 | sys=[1,0,0,1,0,0]; x0 = [100]; 28 | else 29 | sys = []; % Real time update (ignored). 30 | end 31 | 32 | 33 | % End of function -------------------------------------------------------------------------------- /Test_fns/simobjp.m: -------------------------------------------------------------------------------- 1 | % SIMOBJP.M (Plot SIMulation results of OBJective function) 2 | % 3 | % This function takes the name of a simulation objective 4 | % function and the matrix of the best individuals and 5 | % plots the states of the system over time for the 6 | % last best individual. 7 | % 8 | % Author: Hartmut Pohlheim 9 | % History: 25.03.94 file created 10 | 11 | function [val, t, x] = simobjp(OBJ_F, IndAll); 12 | 13 | BestInd1=IndAll(size(IndAll,1),:); 14 | 15 | [val t x] = feval(OBJ_F, BestInd1); 16 | 17 | set(gcf,'Name',feval(OBJ_F,[],2)); 18 | plot(t, x); 19 | 20 | % End of function -------------------------------------------------------------------------------- /bs2rv.m: -------------------------------------------------------------------------------- 1 | % BS2RV.m - Binary string to real vector 2 | % 3 | % This function decodes binary chromosomes into vectors of reals. The 4 | % chromosomes are seen as the concatenation of binary strings of given 5 | % length, and decoded into real numbers in a specified interval using 6 | % either standard binary or Gray decoding. 7 | % 8 | % Syntax: Phen = bs2rv(Chrom,FieldD) 9 | % 10 | % Input parameters: 11 | % 12 | % Chrom - Matrix containing the chromosomes of the current 13 | % population. Each line corresponds to one 14 | % individual's concatenated binary string 15 | % representation. Leftmost bits are MSb and 16 | % rightmost are LSb. 17 | % 18 | % FieldD - Matrix describing the length and how to decode 19 | % each substring in the chromosome. It has the 20 | % following structure: 21 | % 22 | % [len; (num) 23 | % lb; (num) 24 | % ub; (num) 25 | % code; (0=binary | 1=gray) 26 | % scale; (0=arithmetic | 1=logarithmic) 27 | % lbin; (0=excluded | 1=included) 28 | % ubin]; (0=excluded | 1=included) 29 | % 30 | % where 31 | % len - row vector containing the length of 32 | % each substring in Chrom. sum(len) 33 | % should equal the individual length. 34 | % lb, 35 | % ub - Lower and upper bounds for each 36 | % variable. 37 | % code - binary row vector indicating how each 38 | % substring is to be decoded. 39 | % scale - binary row vector indicating where to 40 | % use arithmetic and/or logarithmic 41 | % scaling. 42 | % lbin, 43 | % ubin - binary row vectors indicating whether 44 | % or not to include each bound in the 45 | % representation range 46 | % 47 | % Output parameter: 48 | % 49 | % Phen - Real matrix containing the population phenotypes. 50 | % 51 | % Author: Carlos Fonseca, Updated: Andrew Chipperfield, 52 | % Date: 08/06/93, Date: 26-Jan-94, 53 | % 54 | % Tested under MATLAB v6 by Alex Shenfield (17-Jan-03) 55 | 56 | function Phen = bs2rv(Chrom,FieldD) 57 | 58 | % Identify the population size (Nind) 59 | % and the chromosome length (Lind) 60 | [Nind,Lind] = size(Chrom); 61 | 62 | % Identify the number of decision variables (Nvar) 63 | [seven,Nvar] = size(FieldD); 64 | 65 | if seven ~= 7 66 | error('FieldD must have 7 rows.'); 67 | end 68 | 69 | % Get substring properties 70 | len = FieldD(1,:); 71 | lb = FieldD(2,:); 72 | ub = FieldD(3,:); 73 | code = ~(~FieldD(4,:)); 74 | scale = ~(~FieldD(5,:)); 75 | lin = ~(~FieldD(6,:)); 76 | uin = ~(~FieldD(7,:)); 77 | 78 | % Check substring properties for consistency 79 | if sum(len) ~= Lind, 80 | error('Data in FieldD must agree with chromosome length'); 81 | end 82 | 83 | if ~all(lb(scale).*ub(scale)>0) 84 | error('Log-scaled variables must not include 0 in their range'); 85 | end 86 | 87 | % Decode chromosomes 88 | Phen = zeros(Nind,Nvar); 89 | 90 | lf = cumsum(len); 91 | li = cumsum([1 len]); 92 | Prec = .5 .^ len; 93 | 94 | logsgn = sign(lb(scale)); 95 | lb(scale) = log( abs(lb(scale)) ); 96 | ub(scale) = log( abs(ub(scale)) ); 97 | delta = ub - lb; 98 | 99 | Prec = .5 .^ len; 100 | num = (~lin) .* Prec; 101 | den = (lin + uin - 1) .* Prec; 102 | 103 | for i = 1:Nvar, 104 | idx = li(i):lf(i); 105 | if code(i) % Gray decoding 106 | Chrom(:,idx)=rem(cumsum(Chrom(:,idx)')',2); 107 | end 108 | Phen(:,i) = Chrom(:,idx) * [ (.5).^(1:len(i))' ]; 109 | Phen(:,i) = lb(i) + delta(i) * (Phen(:,i) + num(i)) ./ (1 - den(i)); 110 | end 111 | 112 | expand = ones(Nind,1); 113 | if any(scale) 114 | Phen(:,scale) = logsgn(expand,:) .* exp(Phen(:,scale)); 115 | end -------------------------------------------------------------------------------- /contents.m: -------------------------------------------------------------------------------- 1 | % Genetic Algorithm Toolbox. 2 | % Version 1.3 17-Jan-2003 3 | % Department of Automatic Control and Systems Engineering 4 | % University of Sheffield, England 5 | % 6 | % Creating populations 7 | % crtbase - create a base vector 8 | % crtbp - create a binary population 9 | % crtrp - create a real-valued population 10 | % 11 | % Fitness assignment 12 | % ranking - rank-based fitness assignment 13 | % scaling - proportional fitness-scaling 14 | % 15 | % Selection and reinsertion 16 | % reins - uniform random and fitness-based reinsertion 17 | % rws - roulette wheel selection 18 | % select - high-level selection routine 19 | % sus - stochastic universal sampling 20 | % 21 | % Mutation operators 22 | % mut - discrete mutation 23 | % mutate - high-level mutation function 24 | % mutbga - real-value mutation 25 | % 26 | % Crossover operators 27 | % recdis - discrete recombination 28 | % recint - intermediate recombination 29 | % reclin - line recombination 30 | % recmut - line recombination with mutation features 31 | % recombin - high-level recombination function 32 | % xovdp - double-point crossover 33 | % xovdprs - double-point reduced surrogate crossover 34 | % xovmp - general multi-point crossover 35 | % xovsh - shuffle crossover 36 | % xovshrs - shuffle reduced surrogate crossover 37 | % xovsp - single-point crossover 38 | % xovsprs - single-point reduced surrogate crossover 39 | % 40 | % Subpopulation support 41 | % migrate - exchange individuals between subpopulations 42 | % 43 | % 44 | % Utility functions 45 | % bs2rv - binary string to real-value conversion 46 | % rep - matrix replication 47 | % 48 | % Demonstration and other functions 49 | % mpga - multi-population genetic algorithm demonstration 50 | % objfun1 - De Jongs first test function (used by sga) 51 | % objharv - harvest function (used in mpga) 52 | % resplot - result plotting (used in mpga) 53 | % sga - simple genetic algorithm demonstration -------------------------------------------------------------------------------- /crtbase.m: -------------------------------------------------------------------------------- 1 | % CRTBASE.m - Create base vector 2 | % 3 | % This function creates a vector containing the base of the loci 4 | % in a chromosome. 5 | % 6 | % Syntax: BaseVec = crtbase(Lind, Base) 7 | % 8 | % Input Parameters: 9 | % 10 | % Lind - A scalar or vector containing the lengths 11 | % of the alleles. Sum(Lind) is the length of 12 | % the corresponding chromosome. 13 | % 14 | % Base - A scalar or vector containing the base of 15 | % the loci contained in the Alleles. 16 | % 17 | % Output Parameters: 18 | % 19 | % BaseVec - A vector whose elements correspond to the base 20 | % of the loci of the associated chromosome structure. 21 | % 22 | % Author: Andrew Chipperfield 23 | % Date: 19-Jan-94 24 | % 25 | % Tested under MATLAB v6 by Alex Shenfield (17-Jan-03) 26 | 27 | function BaseVec = crtbase(Lind, Base) 28 | 29 | [ml LenL] = size(Lind) ; 30 | if nargin < 2 31 | Base = 2 * ones(LenL,1) ; % default to base 2 32 | end 33 | [mb LenB] = size(Base) ; 34 | 35 | % check parameter consistency 36 | if ml > 1 | mb > 1 37 | error( 'Lind or Base is not a vector') ; 38 | elseif (LenL > 1 & LenB > 1 & LenL ~= LenB) | (LenL == 1 & LenB > 1 ) 39 | error( 'Vector dimensions must agree' ) ; 40 | elseif LenB == 1 & LenL > 1 41 | Base = Base * ones(LenL,1) ; 42 | end 43 | 44 | BaseVec = [] ; 45 | for i = 1:LenL 46 | BaseVec = [BaseVec, Base(i)*ones(Lind(i),1)']; 47 | end -------------------------------------------------------------------------------- /crtbp.m: -------------------------------------------------------------------------------- 1 | % CRTBP.m - Create an initial population 2 | % 3 | % This function creates a binary population of given size and structure. 4 | % 5 | % Syntax: [Chrom Lind BaseV] = crtbp(Nind, Lind, Base) 6 | % 7 | % Input Parameters: 8 | % 9 | % Nind - Either a scalar containing the number of individuals 10 | % in the new population or a row vector of length two 11 | % containing the number of individuals and their length. 12 | % 13 | % Lind - A scalar containing the length of the individual 14 | % chromosomes. 15 | % 16 | % Base - A scalar containing the base of the chromosome 17 | % elements or a row vector containing the base(s) 18 | % of the loci of the chromosomes. 19 | % 20 | % Output Parameters: 21 | % 22 | % Chrom - A matrix containing the random valued chromosomes 23 | % row wise. 24 | % 25 | % Lind - A scalar containing the length of the chromosome. 26 | % 27 | % BaseV - A row vector containing the base of the 28 | % chromosome loci. 29 | % 30 | % Author: Andrew Chipperfield 31 | % Date: 19-Jan-94 32 | % 33 | % Tested under MATLAB v6 by Alex Shenfield (20-Jan-03) 34 | 35 | function [Chrom, Lind, BaseV] = crtbp(Nind, Lind, Base) 36 | nargs = nargin ; 37 | 38 | % Check parameter consistency 39 | 40 | if nargs >= 1, [mN, nN] = size(Nind) ; end 41 | if nargs >= 2, [mL, nL] = size(Lind) ; end 42 | if nargs == 3, [mB, nB] = size(Base) ; end 43 | 44 | if nN == 2 45 | if (nargs == 1) 46 | Lind = Nind(2) ; Nind = Nind(1) ; BaseV = crtbase(Lind) ; 47 | elseif (nargs == 2 & nL == 1) 48 | BaseV = crtbase(Nind(2),Lind) ; Lind = Nind(2) ; Nind = Nind(1) ; 49 | elseif (nargs == 2 & nL > 1) 50 | if Lind ~= length(Lind), error('Lind and Base disagree'); end 51 | BaseV = Lind ; Lind = Nind(2) ; Nind = Nind(1) ; 52 | end 53 | elseif nN == 1 54 | if nargs == 2 55 | if nL == 1, BaseV = crtbase(Lind) ; 56 | else, BaseV = Lind ; Lind = nL ; end 57 | elseif nargs == 3 58 | if nB == 1, BaseV = crtbase(Lind,Base) ; 59 | elseif nB ~= Lind, error('Lind and Base disagree') ; 60 | else BaseV = Base ; end 61 | end 62 | else 63 | error('Input parameters inconsistent') ; 64 | end 65 | 66 | % Create a structure of random chromosomes in row wise order, dimensions 67 | % Nind by Lind. The base of each chromosomes loci is given by the value 68 | % of the corresponding element of the row vector base. 69 | 70 | Chrom = floor(rand(Nind,Lind).*BaseV(ones(Nind,1),:)) ; 71 | 72 | 73 | % End of file -------------------------------------------------------------------------------- /crtrp.m: -------------------------------------------------------------------------------- 1 | % CRTRP.M (CReaTe an initial (Real-value) Population) 2 | % 3 | % This function creates a population of given size of random real-values. 4 | % 5 | % Syntax: Chrom = crtrp(Nind,FieldDR); 6 | % 7 | % Input parameters: 8 | % Nind - A scalar containing the number of individuals in the new 9 | % population. 10 | % 11 | % FieldDR - A matrix of size 2 by number of variables describing the 12 | % boundaries of each variable. It has the following structure: 13 | % [lower_bound; (vector with lower bound for each veriable) 14 | % upper_bound] (vector with upper bound for each veriable) 15 | % [lower_bound_var_1 lower_bound_var_2 ... lower_bound_var_Nvar; 16 | % upper_bound_var_1 upper_bound_var_2 ... upper_bound_var_Nvar] 17 | % example - each individuals consists of 4 variables: 18 | % FieldDR = [-100 -50 -30 -20; % lower bound 19 | % 100 50 30 20] % upper bound 20 | % 21 | % Output parameter: 22 | % Chrom - A matrix containing the random valued individuals of the 23 | % new population of size Nind by number of variables. 24 | % 25 | % Author: Hartmut Pohlheim 26 | % History: 23.11.93 file created 27 | % 25.02.94 clean up, check parameter consistency 28 | % 20.01.03 tested under MATLAB v6 by Alex Shenfield 29 | 30 | function Chrom = crtrp(Nind,FieldDR); 31 | 32 | % Check parameter consistency 33 | if nargin < 2, error('parameter FieldDR missing'); end 34 | if nargin > 2, nargin = 2; end 35 | 36 | [mN, nN] = size(Nind); 37 | [mF, Nvar] = size(FieldDR); 38 | 39 | if (mN ~= 1 & nN ~= 1), error('Nind has to be a scalar'); end 40 | if mF ~= 2, error('FieldDR must be a matrix with 2 rows'); end 41 | 42 | % Compute Matrix with Range of variables and Matrix with Lower value 43 | Range = rep((FieldDR(2,:)-FieldDR(1,:)),[Nind 1]); 44 | Lower = rep(FieldDR(1,:), [Nind 1]); 45 | 46 | % Create initial population 47 | % Each row contains one individual, the values of each variable uniformly 48 | % distributed between lower and upper bound (given by FieldDR) 49 | Chrom = rand(Nind,Nvar) .* Range + Lower; 50 | 51 | 52 | % End of function -------------------------------------------------------------------------------- /migrate.m: -------------------------------------------------------------------------------- 1 | % MIGRATE.M (MIGRATion of individuals between subpopulations) 2 | % 3 | % This function performs migration of individuals. 4 | % 5 | % Syntax: [Chrom, ObjV] = migrate(Chrom, SUBPOP, MigOpt, ObjV) 6 | % 7 | % Input parameters: 8 | % Chrom - Matrix containing the individuals of the current 9 | % population. Each row corresponds to one individual. 10 | % SUBPOP - Number of subpopulations 11 | % MigOpt - (optional) Vector containing migration parameters 12 | % MigOpt(1): MIGR - Rate of individuals to be migrated per 13 | % subpopulation (% of subpopulation) 14 | % if omitted or NaN, 0.2 (20%) is assumed 15 | % MigOpt(2): Select - number indicating the selection method 16 | % of replacing individuals 17 | % 0 - uniform selection 18 | % 1 - fitness-based selection (replace worst 19 | % individuals) 20 | % if omitted or NaN, 0 is assumed 21 | % MigOpt(3): Structure - number indicating the structure 22 | % of the subpopulations for migration 23 | % 0 - net structure (unconstrained migration) 24 | % 1 - neighbourhood structure 25 | % 2 - ring structure 26 | % if omitted or NaN, 0 is assumed 27 | % ObjV - (optional) Column vector containing the objective values 28 | % of the individuals in the current population, needed for 29 | % fitness-based migration, this saves the 30 | % recalculation of objective values for population. 31 | % 32 | % Output parameters: 33 | % Chrom - Matrix containing the individuals of the current 34 | % population after migration. 35 | % ObjV - if ObjV is input parameter, than column vector containing 36 | % the objective values of the individuals of the current 37 | % generation after migration. 38 | % 39 | % Author: Hartmut Pohlheim 40 | % History: 16.02.94 file created 41 | % 18.02.94 comments at the beginning added 42 | % exchange of ObjV too 43 | % 25.02.94 clean up 44 | % 26.02.94 ObjV optional input parameter 45 | % Select and Structure added, parameter reordered 46 | % 17.03.94 renamed to migrate.m, more parameter checks 47 | % 20.01.03 tested under MATLAB v6 by Alex Shenfield 48 | 49 | function [Chrom, ObjV] = migrate(Chrom, SUBPOP, MigOpt, ObjV); 50 | 51 | 52 | % Check parameter consistency 53 | if nargin < 2, error('Input parameter SUBPOP missing'); end 54 | if (nargout == 2 & nargin < 4), error('Input parameter ObjV missing'); end 55 | 56 | [Nind, Nvar] = size(Chrom); 57 | if length(SUBPOP) ~= 1, error('SUBPOP must be a scalar'); end 58 | if SUBPOP == 1, return; end 59 | if (Nind/SUBPOP) ~= fix(Nind/SUBPOP), error('Chrom and SUBPOP disagree'); end 60 | NIND = Nind/SUBPOP; % Compute number of individuals per subpopulation 61 | 62 | if nargin > 3, 63 | [mO, nO] = size(ObjV); 64 | if nO ~= 1, error('ObjV must be a column vector'); end 65 | if Nind ~= mO, error('Chrom and ObjV disagree'); end 66 | IsObjV = 1; 67 | else IsObjV = 0; ObjV = []; 68 | end 69 | 70 | if nargin < 3, MIGR = 0.2; Select = 0; Structure = 0; end 71 | if nargin > 2, 72 | if isempty(MigOpt), MIGR = 0.2; Select = 0; Structure = 0; 73 | elseif isnan(MigOpt), MIGR = 0.2; Select = 0; Structure = 0; 74 | else 75 | MIGR = NaN; Select = NaN; Structure = NaN; 76 | if length(MigOpt) > 3, error('Parameter MigOpt is too long'); end 77 | if length(MigOpt) >= 1, MIGR = MigOpt(1); end 78 | if length(MigOpt) >= 2, Select = MigOpt(2); end 79 | if length(MigOpt) >= 3, Structure = MigOpt(3); end 80 | if isnan(MIGR), MIGR =0.2; end 81 | if isnan(Select), Select = 0; end 82 | if isnan(Structure), Structure = 0; end 83 | end 84 | end 85 | 86 | if (MIGR < 0 | MIGR > 1), error('Parameter for migration rate must be a scalar in [0 1]'); end 87 | if (Select ~= 0 & Select ~= 1), error('Parameter for selection method must be 0 or 1'); end 88 | if (Structure < 0 | Structure > 2), error ('Parameter for structure must be 0, 1 or 2'); end 89 | if (Select == 1 & IsObjV == 0), error('ObjV for fitness-based migration needed');end 90 | 91 | if MIGR == 0, return; end 92 | MigTeil = max(floor(NIND * MIGR), 1); % Number of individuals to migrate 93 | 94 | % Perform migration between subpopulations --> create a matrix for migration 95 | % in every subpopulation from best individuals of the other subpopulations 96 | 97 | % Clear storing matrices 98 | ChromMigAll = []; 99 | if IsObjV == 1, ObjVAll = []; end 100 | 101 | % Create matrix with best/uniform individuals of all subpopulations 102 | for irun = 1:SUBPOP 103 | % sort ObjV of actual subpopulation 104 | if Select == 1, % fitness-based selection 105 | [Dummy, IndMigSo]=sort(ObjV((irun-1)*NIND+1:irun*NIND)); 106 | else % if Select == 0 % uniform selection 107 | [Dummy, IndMigSo]=sort(rand(NIND, 1)); 108 | end 109 | % take MigTeil (best) individuals, copy individuals and objective values 110 | IndMigTeil=IndMigSo(1:MigTeil)+(irun-1)*NIND; 111 | ChromMigAll = [ChromMigAll; Chrom(IndMigTeil,:)]; 112 | if IsObjV == 1, ObjVAll = [ObjVAll; ObjV(IndMigTeil,:)]; end 113 | end 114 | 115 | % perform migration 116 | for irun = 1:SUBPOP 117 | ChromMig = ChromMigAll; 118 | if IsObjV == 1, ObjVMig = ObjVAll; end 119 | if Structure == 1, % neighbourhood 120 | % select individuals of neighbourhood subpopulations for ChromMig and ObjVMig 121 | popnum = [SUBPOP 1:SUBPOP 1]; 122 | ins1 = popnum(irun); ins2 = popnum(irun + 2); 123 | InsRows = [(ins1-1)*MigTeil+1:ins1*MigTeil (ins2-1)*MigTeil+1:ins2*MigTeil]; 124 | ChromMig = ChromMig(InsRows,:); 125 | if IsObjV == 1, ObjVMig = ObjVMig(InsRows,:); end 126 | elseif Structure == 2, % ring 127 | % select individuals of actual-1 subpopulation for ChromMig and ObjVMig 128 | popnum = [SUBPOP 1:SUBPOP 1]; 129 | ins1 = popnum(irun); 130 | InsRows = (ins1-1)*MigTeil+1:ins1*MigTeil; 131 | ChromMig = ChromMig(InsRows,:); 132 | if IsObjV == 1, ObjVMig = ObjVMig(InsRows,:); end 133 | else % if Structure == 0, % complete net 134 | % delete individuals of actual subpopulation from ChromMig and ObjVMig 135 | DelRows = (irun-1)*MigTeil+1:irun*MigTeil; 136 | ChromMig(DelRows,:) = []; 137 | if IsObjV == 1, ObjVMig(DelRows,:) = []; end 138 | end 139 | % Create an index from a sorted vector with random numbers 140 | [Dummy,IndMigRa]=sort(rand(size(ChromMig,1),1)); 141 | % Take MigTeil numbers from the random vector 142 | IndMigN=IndMigRa((1:MigTeil)'); 143 | % copy MigTeil individuals into Chrom and ObjV 144 | Chrom((1:MigTeil)+(irun-1)*NIND,:) = ChromMig(IndMigN,:); 145 | if IsObjV == 1, ObjV((1:MigTeil)+(irun-1)*NIND,:) = ObjVMig(IndMigN,:); end 146 | end 147 | 148 | 149 | % End of function -------------------------------------------------------------------------------- /mpga.m: -------------------------------------------------------------------------------- 1 | % MPGA.M Multi Population Genetic Algorithm 2 | % 3 | % This script implements the Multi Population Genetic Algorithm. 4 | % A real-valued representation of the individuals is used. 5 | % 6 | % Author: Andrew Chipperfield 7 | % History: 30-Mar-94 file created 8 | % 21-Jan-03 tested under MATLAB v6 by Alex Shenfield 9 | 10 | NVAR = 20; % No. of decision variables (control steps) 11 | RANGE = [0;200]; % Bounds on decision variables 12 | 13 | % Set field descriptor 14 | FieldD = rep(RANGE,[1,NVAR]); 15 | 16 | % Define GA Parameters 17 | GGAP = .8; % Generation gap, how many new individuals are created 18 | XOVR = 1; % Crossover rate 19 | MUTR = 1/NVAR; % Mutation rate depending on NVAR 20 | MAXGEN = 1200; % Maximum number of generations 21 | TERMEXACT = 1e-4; % Value for termination if minimum reached 22 | INSR = .9; % Insertion rate, how many of the offspring are inserted 23 | SUBPOP = 8; % Number of subpopulations 24 | MIGR = 0.2; % Migration rate between subpopulations 25 | MIGGEN = 20; % Number of generations between migration 26 | NIND = 20; % Number of individuals per subpopulation 27 | 28 | % Specify other routines as strings 29 | SEL_F = 'sus'; % Name of selection function 30 | XOV_F = 'recdis'; % Name of recombination function for individuals 31 | MUT_F = 'mutbga'; % Name of mutation function 32 | OBJ_F = 'objharv'; % Name of function for objective values 33 | 34 | % Get value of minimum, defined in objective function 35 | GlobalMin = feval(OBJ_F,[],3); 36 | 37 | % Get title of objective function, defined in objective function 38 | FigTitle = [feval(OBJ_F,[],2) ' (' int2str(SUBPOP) ':' int2str(MAXGEN) ') ']; 39 | 40 | % Clear Best and storing matrix 41 | % Initialise Matrix for storing best results 42 | Best = NaN * ones(MAXGEN,3); 43 | Best(:,3) = zeros(size(Best,1),1); 44 | % Matrix for storing best individuals 45 | IndAll = []; 46 | 47 | % Create real population 48 | Chrom = crtrp(SUBPOP*NIND,FieldD); 49 | 50 | % reset count variables 51 | gen = 0; 52 | 53 | % Calculate objective function for population 54 | ObjV = feval(OBJ_F,Chrom); 55 | % count number of objective function evaluations 56 | Best(gen+1,3) = Best(gen+1,3) + NIND; 57 | 58 | % Generational loop 59 | while gen < MAXGEN, 60 | 61 | % Save the best and average objective values and the best individual 62 | [Best(gen+1,1),ix] = min(ObjV); 63 | Best(gen+1,2) = mean(ObjV); 64 | IndAll = [IndAll; Chrom(ix,:)]; 65 | 66 | % Fitness assignment to whole population 67 | FitnV = ranking(ObjV,2,SUBPOP); 68 | 69 | % Select individuals from population 70 | SelCh = select(SEL_F, Chrom, FitnV, GGAP, SUBPOP); 71 | 72 | % Recombine selected individuals 73 | SelCh=recombin(XOV_F, SelCh, XOVR, SUBPOP); 74 | 75 | % Mutate offspring 76 | SelCh=mutate(MUT_F, SelCh, FieldD, [MUTR], SUBPOP); 77 | 78 | % Calculate objective function for offsprings 79 | ObjVOff = feval(OBJ_F,SelCh); 80 | Best(gen+1,3) = Best(gen+1,3) + size(SelCh,1); 81 | 82 | % Insert best offspring in population replacing worst parents 83 | [Chrom, ObjV] = reins(Chrom, SelCh, SUBPOP, [1 INSR], ObjV, ObjVOff); 84 | 85 | gen=gen+1; 86 | 87 | % Plot some results, rename title of figure for graphic output 88 | if ((rem(gen,20) == 1) | (rem(gen,MAXGEN) == 0)), 89 | set(gcf,'Name',[FigTitle ' in ' int2str(gen)]); 90 | resplot(Chrom(1:2:size(Chrom,1),:),... 91 | IndAll(max(1,gen-39):size(IndAll,1),:),... 92 | [ObjV; GlobalMin], Best(max(1,gen-19):gen,[1 2]), gen); 93 | end 94 | 95 | % migrate individuals between subpopulations 96 | if (rem(gen,MIGGEN) == 0) 97 | [Chrom, ObjV] = migrate(Chrom, SUBPOP, [MIGR, 1, 0], ObjV); 98 | end 99 | 100 | end 101 | 102 | % Results 103 | % add number of objective function evaluations 104 | Results = cumsum(Best(1:gen,3)); 105 | % number of function evaluation, mean and best results 106 | Results = [Results Best(1:gen,2) Best(1:gen,1)]; 107 | 108 | % Plot Results and show best individuals => optimum 109 | figure('Name',['Results of ' FigTitle]); 110 | subplot(2,1,1), plot(Results(:,1),Results(:,2),'-',Results(:,1),Results(:,3),':'); 111 | subplot(2,1,2), plot(IndAll(gen-4:gen,:)'); 112 | 113 | % End of script -------------------------------------------------------------------------------- /mut.m: -------------------------------------------------------------------------------- 1 | % MUT.m 2 | % 3 | % This function takes the representation of the current population, 4 | % mutates each element with given probability and returns the resulting 5 | % population. 6 | % 7 | % Syntax: NewChrom = mut(OldChrom,Pm,BaseV) 8 | % 9 | % Input parameters: 10 | % 11 | % OldChrom - A matrix containing the chromosomes of the 12 | % current population. Each row corresponds to 13 | % an individuals string representation. 14 | % 15 | % Pm - Mutation probability (scalar). Default value 16 | % of Pm = 0.7/Lind, where Lind is the chromosome 17 | % length is assumed if omitted. 18 | % 19 | % BaseV - Optional row vector of the same length as the 20 | % chromosome structure defining the base of the 21 | % individual elements of the chromosome. Binary 22 | % representation is assumed if omitted. 23 | % 24 | % Output parameter: 25 | % 26 | % NewChrom - A Matrix containing a mutated version of 27 | % OldChrom. 28 | % 29 | % Author: Andrew Chipperfield 30 | % Date: 25-Jan-94 31 | % 32 | % Tested under MATLAB v6 by Alex Shenfield (21-Jan-03) 33 | 34 | function NewChrom = mut(OldChrom,Pm,BaseV) 35 | 36 | % get population size (Nind) and chromosome length (Lind) 37 | [Nind, Lind] = size(OldChrom) ; 38 | 39 | % check input parameters 40 | if nargin < 2, Pm = 0.7/Lind ; end 41 | if isnan(Pm), Pm = 0.7/Lind; end 42 | 43 | if (nargin < 3), BaseV = crtbase(Lind); end 44 | if (isnan(BaseV)), BaseV = crtbase(Lind); end 45 | if (isempty(BaseV)), BaseV = crtbase(Lind); end 46 | 47 | if (nargin == 3) & (Lind ~= length(BaseV)) 48 | error('OldChrom and BaseV are incompatible'), end 49 | 50 | % create mutation mask matrix 51 | BaseM = BaseV(ones(Nind,1),:) ; 52 | 53 | % perform mutation on chromosome structure 54 | NewChrom = rem(OldChrom+(rand(Nind,Lind) 4, 63 | if isempty(SUBPOP), SUBPOP = 1; 64 | elseif isnan(SUBPOP), SUBPOP = 1; 65 | elseif length(SUBPOP) ~= 1, error('SUBPOP must be a scalar'); end 66 | end 67 | 68 | if (Nind/SUBPOP) ~= fix(Nind/SUBPOP), error('OldChrom and SUBPOP disagree'); end 69 | Nind = Nind/SUBPOP; % Compute number of individuals per subpopulation 70 | 71 | % Select individuals of one subpopulation and call low level function 72 | NewChrom = []; 73 | for irun = 1:SUBPOP, 74 | ChromSub = OldChrom((irun-1)*Nind+1:irun*Nind,:); 75 | if IsDiscret == 1, NewChromSub = feval(MUT_F, ChromSub, MutOpt, FieldDR); 76 | elseif IsDiscret == 0, NewChromSub = feval(MUT_F, ChromSub, FieldDR, MutOpt); end 77 | NewChrom=[NewChrom; NewChromSub]; 78 | end 79 | 80 | 81 | % End of function -------------------------------------------------------------------------------- /mutbga.m: -------------------------------------------------------------------------------- 1 | % MUTBGA.M (real-value MUTation like Breeder Genetic Algorithm) 2 | % 3 | % This function takes a matrix OldChrom containing the real 4 | % representation of the individuals in the current population, 5 | % mutates the individuals with probability MutR and returns 6 | % the resulting population. 7 | % 8 | % This function implements the mutation operator of the Breeder Genetic 9 | % Algorithm. (Muehlenbein et. al.) 10 | % 11 | % Syntax: NewChrom = mutbga(OldChrom, FieldDR, MutOpt) 12 | % 13 | % Input parameter: 14 | % OldChrom - Matrix containing the chromosomes of the old 15 | % population. Each line corresponds to one individual. 16 | % FieldDR - Matrix describing the boundaries of each variable. 17 | % MutOpt - (optional) Vector containing mutation rate and shrink value 18 | % MutOpt(1): MutR - number containing the mutation rate - 19 | % probability for mutation of a variable 20 | % if omitted or NaN, MutR = 1/variables per individual 21 | % is assumed 22 | % MutOpt(2): MutShrink - (optional) number for shrinking the 23 | % mutation range in the range [0 1], possibility to 24 | % shrink the range of the mutation depending on, 25 | % for instance actual generation. 26 | % if omitted or NaN, MutShrink = 1 is assumed 27 | % 28 | % Output parameter: 29 | % NewChrom - Matrix containing the chromosomes of the population 30 | % after mutation in the same format as OldChrom. 31 | % 32 | % Author: Hartmut Pohlheim 33 | % History: 23.11.93 file created 34 | % 24.11.93 function optimised (for,for-loop to for-loop) 35 | % mutation rate included 36 | % style improved 37 | % 06.12.93 change of function name 38 | % check of boundaries after mutation out of loop 39 | % 16.12.93 NewMutMat and OldMutMat included for compability 40 | % 16.02.94 preparation for multi-subpopulations at once 41 | % 25.02.94 NewMutMat and OldMutMat removed (now in mutran10.m) 42 | % clean up 43 | % change of function name in mutbga.m 44 | % 03.03.94 Lower and Upper directly used (less memory) 45 | % 19.03.94 multipopulation support removed 46 | % more parameter checks 47 | % 27.03.94 Delta exact calculated, for loop saved 48 | % 21.01.03 tested under MATLAB v6 by Alex Shenfield 49 | 50 | function NewChrom = mutbga(OldChrom, FieldDR, MutOpt); 51 | 52 | % Check parameter consistency 53 | if nargin < 2, error('Not enough input parameters'); end 54 | 55 | % Identify the population size (Nind) and the number of variables (Nvar) 56 | [Nind,Nvar] = size(OldChrom); 57 | 58 | [mF, nF] = size(FieldDR); 59 | if mF ~= 2, error('FieldDR must be a matrix with 2 rows'); end 60 | if Nvar ~= nF, error('FieldDR and OldChrom disagree'); end 61 | 62 | if nargin < 3, MutR = 1/Nvar; MutShrink = 1; 63 | elseif isempty(MutOpt), MutR = 1/Nvar; MutShrink = 1; 64 | elseif isnan(MutOpt), MutR = 1/Nvar; MutShrink = 1; 65 | else 66 | if length(MutOpt) == 1, MutR = MutOpt; MutShrink = 1; 67 | elseif length(MutOpt) == 2, MutR = MutOpt(1); MutShrink = MutOpt(2); 68 | else, error(' Too many parameters in MutOpt'); end 69 | end 70 | 71 | if isempty(MutR), MutR = 1/Nvar; 72 | elseif isnan(MutR), MutR = 1/Nvar; 73 | elseif length(MutR) ~= 1, error('Parameter for mutation rate must be a scalar'); 74 | elseif (MutR < 0 | MutR > 1), error('Parameter for mutation rate must be a scalar in [0, 1]'); end 75 | 76 | if isempty(MutShrink), MutShrink = 1; 77 | elseif isnan(MutShrink), MutShrink = 1; 78 | elseif length(MutShrink) ~= 1, error('Parameter for shrinking mutation range must be a scalar'); 79 | elseif (MutShrink < 0 | MutShrink > 1), 80 | error('Parameter for shrinking mutation range must be a scalar in [0, 1]'); 81 | end 82 | 83 | % the variables are mutated with probability MutR 84 | % NewChrom = OldChrom (+ or -) * Range * MutShrink * Delta 85 | % Range = 0.5 * (upperbound - lowerbound) 86 | % Delta = Sum(Alpha_i * 2^-i) from 0 to ACCUR; Alpha_i = rand(ACCUR,1) < 1/ACCUR 87 | 88 | % Matrix with range values for every variable 89 | Range = rep(0.5 * MutShrink *(FieldDR(2,:)-FieldDR(1,:)),[Nind 1]); 90 | 91 | % zeros and ones for mutate or not this variable, together with Range 92 | Range = Range .* (rand(Nind,Nvar) < MutR); 93 | 94 | % compute, if + or - sign 95 | Range = Range .* (1 - 2 * (rand(Nind,Nvar) < 0.5)); 96 | 97 | % used for later computing, here only ones computed 98 | ACCUR = 20; 99 | Vect = 2 .^ (-(0:(ACCUR-1))'); 100 | Delta = (rand(Nind,ACCUR) < 1/ACCUR) * Vect; 101 | Delta = rep(Delta, [1 Nvar]); 102 | 103 | % perform mutation 104 | NewChrom = OldChrom + Range .* Delta; 105 | 106 | % Ensure variables boundaries, compare with lower and upper boundaries 107 | NewChrom = max(rep(FieldDR(1,:),[Nind 1]), NewChrom); 108 | NewChrom = min(rep(FieldDR(2,:),[Nind 1]), NewChrom); 109 | 110 | 111 | % End of function -------------------------------------------------------------------------------- /objfun1.m: -------------------------------------------------------------------------------- 1 | % OBJFUN1.M (OBJective function for De Jong's FUNction 1) 2 | % 3 | % This function implements the De Jong function 1. 4 | % 5 | % Syntax: ObjVal = objfun1(Chrom,rtn_type) 6 | % 7 | % Input parameters: 8 | % Chrom - Matrix containing the chromosomes of the current 9 | % population. Each row corresponds to one individual's 10 | % string representation. 11 | % if Chrom == [], then special values will be returned 12 | % rtn_type - if Chrom == [] and 13 | % rtn_type == 1 (or []) return boundaries 14 | % rtn_type == 2 return title 15 | % rtn_type == 3 return value of global minimum 16 | % 17 | % Output parameters: 18 | % ObjVal - Column vector containing the objective values of the 19 | % individuals in the current population. 20 | % if called with Chrom == [], then ObjVal contains 21 | % rtn_type == 1, matrix with the boundaries of the function 22 | % rtn_type == 2, text for the title of the graphic output 23 | % rtn_type == 3, value of global minimum 24 | % 25 | % 26 | % Author: Hartmut Pohlheim 27 | % History: 26.11.93 file created 28 | % 27.11.93 text of title and rtn_type added 29 | % 30.11.93 show Dim in figure title 30 | % 16.12.93 rtn_type == 3, return value of global minimum 31 | % 01.03.94 name changed in obj* 32 | % 21.01.03 updated for MATLAB v6 by Alex Shenfield 33 | 34 | function ObjVal = objfun1(Chrom,rtn_type); 35 | 36 | % Dimension of objective function 37 | Dim = 20; 38 | 39 | % Compute population parameters 40 | [Nind,Nvar] = size(Chrom); 41 | 42 | % Check size of Chrom and do the appropriate thing 43 | % if Chrom is [], then define size of boundary-matrix and values 44 | if Nind == 0 45 | % return text of title for graphic output 46 | if rtn_type == 2 47 | ObjVal = ['DE JONG function 1-' int2str(Dim)]; 48 | % return value of global minimum 49 | elseif rtn_type == 3 50 | ObjVal = 0; 51 | % define size of boundary-matrix and values 52 | else 53 | % lower and upper bound, identical for all n variables 54 | ObjVal = 100*[-5.12; 5.12]; 55 | ObjVal = ObjVal(1:2,ones(Dim,1)); 56 | end 57 | % if Dim variables, compute values of function 58 | elseif Nvar == Dim 59 | % function 1, sum of xi^2 for i = 1:Dim (Dim=30) 60 | % n = Dim, -5.12 <= xi <= 5.12 61 | % global minimum at (xi)=(0) ; fmin=0 62 | ObjVal = sum((Chrom .* Chrom)')'; 63 | % ObjVal = diag(Chrom * Chrom'); % both lines produce the same 64 | % otherwise error, wrong format of Chrom 65 | else 66 | error('size of matrix Chrom is not correct for function evaluation'); 67 | end 68 | 69 | 70 | % End of function -------------------------------------------------------------------------------- /objharv.m: -------------------------------------------------------------------------------- 1 | % OBJHARV.M (OBJective function for HARVest problem) 2 | % 3 | % This function implements the HARVEST PROBLEM. 4 | % 5 | % Syntax: ObjVal = objharv(Chrom,rtn_type) 6 | % 7 | % Input parameters: 8 | % Chrom - Matrix containing the chromosomes of the current 9 | % population. Each row corresponds to one individual's 10 | % string representation. 11 | % if Chrom == [], then special values will be returned 12 | % rtn_type - if Chrom == [] and 13 | % rtn_type == 1 (or []) return boundaries 14 | % rtn_type == 2 return title 15 | % rtn_type == 3 return value of global minimum 16 | % 17 | % Output parameters: 18 | % ObjVal - Column vector containing the objective values of the 19 | % individuals in the current population. 20 | % if called with Chrom == [], then ObjVal contains 21 | % rtn_type == 1, matrix with the boundaries of the function 22 | % rtn_type == 2, text for the title of the graphic output 23 | % rtn_type == 3, value of global minimum 24 | % 25 | % 26 | % Author: Hartmut Pohlheim 27 | % History: 18.02.94 file created (copy of vallinq.m) 28 | % 01.03.94 name changed in obj* 29 | % 21.01.03 updated for MATLAB v6 by Alex Shenfield 30 | 31 | function ObjVal = objharv(Chrom,rtn_type); 32 | 33 | % global gen; 34 | 35 | % Dimension of objective function 36 | Dim = 20; 37 | 38 | % values from MICHALEWICZ 39 | a = 1.1; 40 | x0 = 100; 41 | xend = x0; 42 | XENDWEIGHT = 0.4/(Dim^0.6); 43 | 44 | % Compute population parameters 45 | [Nind,Nvar] = size(Chrom); 46 | 47 | % Check size of Chrom and do the appropriate thing 48 | % if Chrom is [], then define size of boundary-matrix and values 49 | if Nind == 0 50 | % return text of title for graphic output 51 | if rtn_type == 2 52 | ObjVal = ['HARVEST PROBLEM-' int2str(Dim)]; 53 | % return value of global minimum 54 | elseif rtn_type == 3 55 | ObjVal = -sqrt(x0*(a^Dim-1)^2/(a^(Dim-1)*(a-1))); 56 | % define size of boundary-matrix and values 57 | else 58 | % lower and upper bound, identical for all n variables 59 | ObjVal1 = [0; 10*Dim]; 60 | ObjVal = rep(ObjVal1,[1 Dim]); 61 | end 62 | % if Dim variables, compute values of function 63 | elseif Nvar == Dim 64 | ObjVal = zeros(Nind,1); 65 | X = rep(x0,[Nind 1]); 66 | for irun = 1:Nvar, 67 | X = a*X - Chrom(:,irun); 68 | end 69 | X; 70 | ObjVal = -(sum(sqrt(Chrom)')' - XENDWEIGHT * abs(X-x0)); 71 | % otherwise error, wrong format of Chrom 72 | else 73 | error('size of matrix Chrom is not correct for function evaluation'); 74 | end 75 | 76 | 77 | % End of function -------------------------------------------------------------------------------- /ranking.m: -------------------------------------------------------------------------------- 1 | % RANKING.M (RANK-based fitness assignment) 2 | % 3 | % This function performs ranking of individuals. 4 | % 5 | % Syntax: FitnV = ranking(ObjV, RFun, SUBPOP) 6 | % 7 | % This function ranks individuals represented by their associated 8 | % cost, to be *minimized*, and returns a column vector FitnV 9 | % containing the corresponding individual fitnesses. For multiple 10 | % subpopulations the ranking is performed separately for each 11 | % subpopulation. 12 | % 13 | % Input parameters: 14 | % ObjV - Column vector containing the objective values of the 15 | % individuals in the current population (cost values). 16 | % RFun - (optional) If RFun is a scalar in [1, 2] linear ranking is 17 | % assumed and the scalar indicates the selective pressure. 18 | % If RFun is a 2 element vector: 19 | % RFun(1): SP - scalar indicating the selective pressure 20 | % RFun(2): RM - ranking method 21 | % RM = 0: linear ranking 22 | % RM = 1: non-linear ranking 23 | % If RFun is a vector with length(Rfun) > 2 it contains 24 | % the fitness to be assigned to each rank. It should have 25 | % the same length as ObjV. Usually RFun is monotonously 26 | % increasing. 27 | % If RFun is omitted or NaN, linear ranking 28 | % and a selective pressure of 2 are assumed. 29 | % SUBPOP - (optional) Number of subpopulations 30 | % if omitted or NaN, 1 subpopulation is assumed 31 | % 32 | % Output parameters: 33 | % FitnV - Column vector containing the fitness values of the 34 | % individuals in the current population. 35 | % 36 | % 37 | % Author: Hartmut Pohlheim (Carlos Fonseca) 38 | % History: 01.03.94 non-linear ranking 39 | % 10.03.94 multiple populations 40 | % 21.01.03 updated for MATLAB v6 by Alex Shenfield 41 | 42 | function FitnV = ranking(ObjV, RFun, SUBPOP) 43 | 44 | % Identify the vector size (Nind) 45 | [Nind,~] = size(ObjV); 46 | 47 | if nargin < 2, RFun = []; end 48 | if nargin > 1, if isnan(RFun), RFun = []; end, end 49 | if prod(size(RFun)) == 2, 50 | if RFun(2) == 1, NonLin = 1; 51 | elseif RFun(2) == 0, NonLin = 0; 52 | else error('Parameter for ranking method must be 0 or 1'); end 53 | RFun = RFun(1); 54 | if isnan(RFun), RFun = 2; end 55 | elseif prod(size(RFun)) > 2, 56 | if prod(size(RFun)) ~= Nind, error('ObjV and RFun disagree'); end 57 | elseif prod(size(RFun)) < 2, NonLin = 0; 58 | end 59 | 60 | if nargin < 3, SUBPOP = 1; end 61 | if nargin > 2, 62 | if isempty(SUBPOP), SUBPOP = 1; 63 | elseif isnan(SUBPOP), SUBPOP = 1; 64 | elseif length(SUBPOP) ~= 1, error('SUBPOP must be a scalar'); end 65 | end 66 | 67 | if (Nind/SUBPOP) ~= fix(Nind/SUBPOP), error('ObjV and SUBPOP disagree'); end 68 | Nind = Nind/SUBPOP; % Compute number of individuals per subpopulation 69 | 70 | % Check ranking function and use default values if necessary 71 | if isempty(RFun), 72 | % linear ranking with selective pressure 2 73 | RFun = 2*[0:Nind-1]'/(Nind-1); 74 | elseif prod(size(RFun)) == 1 75 | if NonLin == 1, 76 | % non-linear ranking 77 | if RFun(1) < 1, error('Selective pressure must be greater than 1'); 78 | elseif RFun(1) > Nind-2, error('Selective pressure too big'); end 79 | Root1 = roots([RFun(1)-Nind [RFun(1)*ones(1,Nind-1)]]); 80 | RFun = (abs(Root1(1)) * ones(Nind,1)) .^ [(0:Nind-1)']; 81 | RFun = RFun / sum(RFun) * Nind; 82 | else 83 | % linear ranking with SP between 1 and 2 84 | if (RFun(1) < 1 | RFun(1) > 2), 85 | error('Selective pressure for linear ranking must be between 1 and 2'); 86 | end 87 | RFun = 2-RFun + 2*(RFun-1)*[0:Nind-1]'/(Nind-1); 88 | end 89 | end; 90 | 91 | FitnV = []; 92 | 93 | % loop over all subpopulations 94 | for irun = 1:SUBPOP, 95 | % Copy objective values of actual subpopulation 96 | ObjVSub = ObjV((irun-1)*Nind+1:irun*Nind); 97 | % Sort does not handle NaN values as required. So, find those... 98 | NaNix = isnan(ObjVSub); 99 | Validix = find(~NaNix); 100 | % ... and sort only numeric values (smaller is better). 101 | [~,ix] = sort(-ObjVSub(Validix)); 102 | 103 | % Now build indexing vector assuming NaN are worse than numbers, 104 | % (including Inf!)... 105 | ix = [find(NaNix) ; Validix(ix)]; 106 | % ... and obtain a sorted version of ObjV 107 | Sorted = ObjVSub(ix); 108 | 109 | % Assign fitness according to RFun. 110 | i = 1; 111 | FitnVSub = zeros(Nind,1); 112 | for j = [find(Sorted(1:Nind-1) ~= Sorted(2:Nind)); Nind]', 113 | FitnVSub(i:j) = sum(RFun(i:j)) * ones(j-i+1,1) / (j-i+1); 114 | i =j+1; 115 | end 116 | 117 | % Finally, return unsorted vector. 118 | [~,uix] = sort(ix); 119 | FitnVSub = FitnVSub(uix); 120 | 121 | % Add FitnVSub to FitnV 122 | FitnV = [FitnV; FitnVSub]; 123 | end 124 | 125 | % End of function -------------------------------------------------------------------------------- /recdis.m: -------------------------------------------------------------------------------- 1 | % RECDIS.M (RECombination DIScrete) 2 | % 3 | % This function performs discret recombination between pairs of individuals 4 | % and returns the new individuals after mating. 5 | % 6 | % Syntax: NewChrom = recdis(OldChrom, XOVR) 7 | % 8 | % Input parameters: 9 | % OldChrom - Matrix containing the chromosomes of the old 10 | % population. Each line corresponds to one individual 11 | % (in any form, not necessarily real-values). 12 | % XOVR - Probability of recombination occurring between pairs 13 | % of individuals. (not used, only for compatibility) 14 | % 15 | % Output parameter: 16 | % NewChrom - Matrix containing the chromosomes of the population 17 | % after mating, ready to be mutated and/or evaluated, 18 | % in the same format as OldChrom. 19 | % 20 | % Author: Hartmut Pohlheim 21 | % History: 23.11.93 file created 22 | % 24.11.93 style improved 23 | % 06.12.93 change of name of function 24 | % 25.02.94 clean up 25 | % 19.03.94 multipopulation support removed 26 | % 21.01.03 tested under MATLAB v6 by Alex Shenfield 27 | 28 | function NewChrom = recdis(OldChrom, XOVR); 29 | 30 | % Identify the population size (Nind) and the number of variables (Nvar) 31 | [Nind,Nvar] = size(OldChrom); 32 | 33 | % Identify the number of matings 34 | Xops = floor(Nind/2); 35 | 36 | % which parent gives the value 37 | Mask1 = (rand(Xops,Nvar)<0.5); 38 | Mask2 = (rand(Xops,Nvar)<0.5); 39 | 40 | % Performs crossover 41 | odd = 1:2:Nind-1; 42 | even= 2:2:Nind; 43 | NewChrom(odd,:) = (OldChrom(odd,:).* Mask1) + (OldChrom(even,:).*(~Mask1)); 44 | NewChrom(even,:) = (OldChrom(odd,:).* Mask2) + (OldChrom(even,:).*(~Mask2)); 45 | 46 | % If the number of individuals is odd, the last individual cannot be mated 47 | % but must be included in the new population 48 | if rem(Nind,2), NewChrom(Nind,:)=OldChrom(Nind,:); end 49 | 50 | 51 | % End of function -------------------------------------------------------------------------------- /recint.m: -------------------------------------------------------------------------------- 1 | % RECINT.M (RECombination extended INTermediate) 2 | % 3 | % This function performs extended intermediate recombination between 4 | % pairs of individuals and returns the new individuals after mating. 5 | % 6 | % Syntax: NewChrom = recint(OldChrom, XOVR) 7 | % 8 | % Input parameters: 9 | % OldChrom - Matrix containing the chromosomes of the old 10 | % population. Each line corresponds to one 11 | % individual 12 | % XOVR - Probability of crossover occurring between pairs 13 | % of individuals. (not used, only for compatibility) 14 | % 15 | % Output parameter: 16 | % NewChrom - Matrix containing the chromosomes of the population 17 | % after mating, ready to be mutated and/or evaluated, 18 | % in the same format as OldChrom. 19 | % 20 | % Author: Hartmut Pohlheim 21 | % History: 25.11.93 file created 22 | % 06.12.93 change of name of function 23 | % 25.02.94 clean up 24 | % 19.03.94 multipopulation support removed 25 | % 21.01.03 tested under MATLAB v6 by Alex Shenfield 26 | 27 | function NewChrom = recint(OldChrom, XOVR); 28 | 29 | % Identify the population size (Nind) and the number of variables (Nvar) 30 | [Nind,Nvar] = size(OldChrom); 31 | 32 | % Identify the number of matings 33 | Xops = floor(Nind/2); 34 | 35 | % Performs recombination 36 | odd = 1:2:Nind-1; 37 | even= 2:2:Nind; 38 | 39 | % position of value of offspring compared to parents 40 | Alpha = -0.25 + 1.5 * rand(Xops,Nvar); 41 | 42 | % recombination 43 | NewChrom(odd,:) = OldChrom(odd,:) + Alpha .* (OldChrom(even,:) - OldChrom(odd,:)); 44 | 45 | % the same ones more for second half of offspring 46 | Alpha = -0.25 + 1.5 * rand(Xops,Nvar); 47 | NewChrom(even,:) = OldChrom(odd,:) + Alpha .* (OldChrom(even,:) - OldChrom(odd,:)); 48 | 49 | % If the number of individuals is odd, the last individual cannot be mated 50 | % but must be included in the new population 51 | if rem(Nind,2), NewChrom(Nind,:)=OldChrom(Nind,:); end 52 | 53 | % End of function -------------------------------------------------------------------------------- /reclin.m: -------------------------------------------------------------------------------- 1 | % RECLIN.M (RECombination extended LINe) 2 | % 3 | % This function performs extended line recombination between 4 | % pairs of individuals and returns the new individuals after mating. 5 | % 6 | % Syntax: NewChrom = reclin(OldChrom, XOVR) 7 | % 8 | % Input parameters: 9 | % OldChrom - Matrix containing the chromosomes of the old 10 | % population. Each line corresponds to one 11 | % individual 12 | % XOVR - Probability of crossover occurring between pairs 13 | % of individuals. (not used, only for compatibility) 14 | % 15 | % Output parameter: 16 | % NewChrom - Matrix containing the chromosomes of the population 17 | % after mating, ready to be mutated and/or evaluated, 18 | % in the same format as OldChrom. 19 | % 20 | % Author: Hartmut Pohlheim 21 | % History: 26.11.93 file created 22 | % 06.12.93 change of name of function 23 | % 25.02.94 clean up 24 | % 19.03.94 multipopulation support removed 25 | % 21.01.03 tested under MATLAB v6 by Alex Shenfield 26 | 27 | function NewChrom = reclin(OldChrom, XOVR); 28 | 29 | % Identify the population size (Nind) and the number of variables (Nvar) 30 | [Nind,Nvar] = size(OldChrom); 31 | 32 | % Identify the number of matings 33 | Xops = floor(Nind/2); 34 | 35 | % Performs recombination 36 | odd = 1:2:Nind-1; 37 | even= 2:2:Nind; 38 | 39 | % position of value of offspring compared to parents 40 | Alpha = -0.25 + 1.5 * rand(Xops,1); 41 | Alpha = Alpha(1:Xops,ones(Nvar,1)); 42 | 43 | % recombination 44 | NewChrom(odd,:) = OldChrom(odd,:) + Alpha .* (OldChrom(even,:) - OldChrom(odd,:)); 45 | 46 | % the same ones more for second half of offspring 47 | Alpha = -0.25 + 1.5 * rand(Xops,1); 48 | Alpha = Alpha(1:Xops,ones(Nvar,1)); 49 | NewChrom(even,:) = OldChrom(odd,:) + Alpha .* (OldChrom(even,:) - OldChrom(odd,:)); 50 | 51 | % If the number of individuals is odd, the last individual cannot be mated 52 | % but must be included in the new population 53 | if rem(Nind,2), NewChrom(Nind,:)=OldChrom(Nind,:); end 54 | 55 | 56 | % End of function -------------------------------------------------------------------------------- /recmut.m: -------------------------------------------------------------------------------- 1 | % RECLIN.M (line RECombination with MUTation features) 2 | % 3 | % This function performs line recombination with mutation features between 4 | % pairs of individuals and returns the new individuals after mating. 5 | % 6 | % Syntax: NewChrom = recmut(OldChrom, FieldDR, MutOpt) 7 | % 8 | % Input parameters: 9 | % OldChrom - Matrix containing the chromosomes of the old 10 | % population. Each line corresponds to one individual 11 | % FieldDR - Matrix describing the boundaries of each variable. 12 | % MutOpt - (optional) Vector containing recombination rate and shrink value 13 | % MutOpt(1): MutR - number containing the recombination rate - 14 | % probability for recombine a pair of parents 15 | % if omitted or NaN, MutOpt(1) = 1 is assumed 16 | % MutOpt(2): MutShrink - (optional) number for shrinking the 17 | % recombination range in the range [0 1], possibility to 18 | % shrink the range of the recombination depending on, 19 | % for instance actual generation. 20 | % if omitted or NaN, MutOpt(2) = 1 is assumed 21 | % 22 | % Output parameter: 23 | % NewChrom - Matrix containing the chromosomes of the population 24 | % after mating, ready to be mutated and/or evaluated, 25 | % in the same format as OldChrom. 26 | % 27 | % Author: Hartmut Pohlheim 28 | % History: 27.03.94 file created 29 | % 22.01.03 tested under MATLAB v6 by Alex Shenfield 30 | % (NOTE : doesn't work with higher level recombin.m) 31 | 32 | function NewChrom = recmut(OldChrom, FieldDR, MutOpt); 33 | 34 | % Check parameter consistency 35 | if nargin < 2, error('Not enough input parameter'); end 36 | 37 | % Identify the population size (Nind) and the number of variables (Nvar) 38 | [Nind,Nvar] = size(OldChrom); 39 | 40 | [mF, nF] = size(FieldDR); 41 | if mF ~= 2, error('FieldDR must be a matrix with 2 rows'); end 42 | if Nvar ~= nF, error('FieldDR and OldChrom disagree'); end 43 | 44 | if nargin < 3, MutR = 1; MutShrink = 1; 45 | elseif isempty(MutOpt), MutR = 1; MutShrink = 1; 46 | elseif isnan(MutOpt), MutR = 1; MutShrink = 1; 47 | else 48 | if length(MutOpt) == 1, MutR = MutOpt; MutShrink = 1; 49 | elseif length(MutOpt) == 2, MutR = MutOpt(1); MutShrink = MutOpt(2); 50 | else, error(' Too many parameter in MutOpt'); end 51 | end 52 | 53 | if isempty(MutR), MutR = 1; 54 | elseif isnan(MutR), MutR = 1; 55 | elseif length(MutR) ~= 1, error('Parameter for recombination rate must be a scalar'); 56 | elseif (MutR < 0 | MutR > 1), error('Parameter for recombination rate must be a scalar in [0, 1]'); end 57 | 58 | if isempty(MutShrink), MutShrink = 1; 59 | elseif isnan(MutShrink), MutShrink = 1; 60 | elseif length(MutShrink) ~= 1, error('Parameter for shrinking recombination range must be a scalar'); 61 | elseif (MutShrink < 0 | MutShrink > 1), 62 | error('Parameter for shrinking recombination range must be a scalar in [0, 1]'); 63 | end 64 | 65 | % Identify the number of matings 66 | Xops = floor(Nind/2); 67 | 68 | % NewChrom = OldChrom (+ or -) * Range * MutShrink * Delta * ChromDiff 69 | % - with probability 0.9, + with probability 0.1 70 | % Range = 0.5 * (upperbound - lowerbound), given by FieldDR 71 | % Delta = Sum(Alpha_i * 2^-i) from 0 to ACCUR; Alpha_i = rand(ACCUR,1) < 1/ACCUR 72 | % ChromDiff = (individual1 - individual2) / Distance between individuals 73 | 74 | % Matrix with range values for every variable 75 | Range = rep(0.5 * MutShrink *(FieldDR(2,:)-FieldDR(1,:)),[Xops 1]); 76 | 77 | % zeros and ones for recombine or not this variable, together with Range 78 | if MutR < 1, Range = Range .* rep((rand(Xops,1) < MutR), [1 Nvar]); end 79 | 80 | % compute, if + or - sign 81 | Range = Range .* (1 - 2 * (rand(Xops,Nvar) < 0.9)); 82 | 83 | % compute distance between mating pairs 84 | NormO = zeros(Xops,1); 85 | for irun = 1:Xops, 86 | NormO(irun) = max(realmin,abs(norm(OldChrom(2*irun,:)) - norm(OldChrom(2*irun-1,:)))); 87 | end 88 | 89 | % compute difference between variables divided by distance 90 | ChromDiff = zeros(Xops,Nvar); 91 | for irun = 1:Xops 92 | ChromDiff(irun,:) = diff([OldChrom(2*irun-1,:); OldChrom(2*irun,:)]) / NormO(irun); 93 | end 94 | 95 | % compute delta value for all individuals 96 | ACCUR = 20; 97 | Vect = 2 .^ (-(0:(ACCUR-1))'); 98 | Delta = (rand(Xops,ACCUR) < 1/ACCUR) * Vect; 99 | Delta = rep(Delta, [1 Nvar]); 100 | 101 | % Performs recombination 102 | odd = 1:2:Nind-1; 103 | even= 2:2:Nind; 104 | 105 | % recombination 106 | NewChrom(odd,:) = OldChrom(odd,:) + Range .* Delta .* (ChromDiff); 107 | NewChrom(even,:) = OldChrom(even,:) + Range .* Delta .* (-ChromDiff); 108 | 109 | % If the number of individuals is odd, the last individual cannot be mated 110 | % but must be included in the new population 111 | if rem(Nind,2), NewChrom(Nind,:)=OldChrom(Nind,:); end 112 | 113 | % Ensure variables boundaries, compare with lower and upper boundaries 114 | NewChrom = max(rep(FieldDR(1,:),[Nind 1]), NewChrom); 115 | NewChrom = min(rep(FieldDR(2,:),[Nind 1]), NewChrom); 116 | 117 | 118 | % End of function -------------------------------------------------------------------------------- /recombin.m: -------------------------------------------------------------------------------- 1 | % RECOMBIN.M (RECOMBINation high-level function) 2 | % 3 | % This function performs recombination between pairs of individuals 4 | % and returns the new individuals after mating. The function handles 5 | % multiple populations and calls the low-level recombination function 6 | % for the actual recombination process. 7 | % 8 | % Syntax: NewChrom = recombin(REC_F, OldChrom, RecOpt, SUBPOP) 9 | % 10 | % Input parameters: 11 | % REC_F - String containing the name of the recombination or 12 | % crossover function 13 | % Chrom - Matrix containing the chromosomes of the old 14 | % population. Each line corresponds to one individual 15 | % RecOpt - (optional) Scalar containing the probability of 16 | % recombination/crossover occurring between pairs 17 | % of individuals. 18 | % if omitted or NaN, 1 is assumed 19 | % SUBPOP - (optional) Number of subpopulations 20 | % if omitted or NaN, 1 subpopulation is assumed 21 | % 22 | % Output parameter: 23 | % NewChrom - Matrix containing the chromosomes of the population 24 | % after recombination in the same format as OldChrom. 25 | % 26 | % Author: Hartmut Pohlheim 27 | % History: 18.03.94 file created 28 | % 22.01.03 tested under MATLAB v6 by Alex Shenfield 29 | % (NOTE : doesn't work with low level recmut.m) 30 | 31 | function NewChrom = recombin(REC_F, Chrom, RecOpt, SUBPOP); 32 | 33 | % Check parameter consistency 34 | if nargin < 2, error('Not enough input parameter'); end 35 | 36 | % Identify the population size (Nind) 37 | [Nind,Nvar] = size(Chrom); 38 | 39 | if nargin < 4, SUBPOP = 1; end 40 | if nargin > 3, 41 | if isempty(SUBPOP), SUBPOP = 1; 42 | elseif isnan(SUBPOP), SUBPOP = 1; 43 | elseif length(SUBPOP) ~= 1, error('SUBPOP must be a scalar'); end 44 | end 45 | 46 | if (Nind/SUBPOP) ~= fix(Nind/SUBPOP), error('Chrom and SUBPOP disagree'); end 47 | Nind = Nind/SUBPOP; % Compute number of individuals per subpopulation 48 | 49 | if nargin < 3, RecOpt = 0.7; end 50 | if nargin > 2, 51 | if isempty(RecOpt), RecOpt = 0.7; 52 | elseif isnan(RecOpt), RecOpt = 0.7; 53 | elseif length(RecOpt) ~= 1, error('RecOpt must be a scalar'); 54 | elseif (RecOpt < 0 | RecOpt > 1), error('RecOpt must be a scalar in [0, 1]'); end 55 | end 56 | 57 | % Select individuals of one subpopulation and call low level function 58 | NewChrom = []; 59 | for irun = 1:SUBPOP, 60 | ChromSub = Chrom((irun-1)*Nind+1:irun*Nind,:); 61 | NewChromSub = feval(REC_F, ChromSub, RecOpt); 62 | NewChrom=[NewChrom; NewChromSub]; 63 | end 64 | 65 | % End of function -------------------------------------------------------------------------------- /reins.m: -------------------------------------------------------------------------------- 1 | % REINS.M (RE-INSertion of offspring in population replacing parents) 2 | % 3 | % This function reinserts offspring in the population. 4 | % 5 | % Syntax: [Chrom, ObjVCh] = reins(Chrom, SelCh, SUBPOP, InsOpt, ObjVCh, ObjVSel) 6 | % 7 | % Input parameters: 8 | % Chrom - Matrix containing the individuals (parents) of the current 9 | % population. Each row corresponds to one individual. 10 | % SelCh - Matrix containing the offspring of the current 11 | % population. Each row corresponds to one individual. 12 | % SUBPOP - (optional) Number of subpopulations 13 | % if omitted or NaN, 1 subpopulation is assumed 14 | % InsOpt - (optional) Vector containing the insertion method parameters 15 | % ExOpt(1): Select - number indicating kind of insertion 16 | % 0 - uniform insertion 17 | % 1 - fitness-based insertion 18 | % if omitted or NaN, 0 is assumed 19 | % ExOpt(2): INSR - Rate of offspring to be inserted per 20 | % subpopulation (% of subpopulation) 21 | % if omitted or NaN, 1.0 (100%) is assumed 22 | % ObjVCh - (optional) Column vector containing the objective values 23 | % of the individuals (parents - Chrom) in the current 24 | % population, needed for fitness-based insertion 25 | % saves recalculation of objective values for population 26 | % ObjVSel - (optional) Column vector containing the objective values 27 | % of the offspring (SelCh) in the current population, needed for 28 | % partial insertion of offspring, 29 | % saves recalculation of objective values for population 30 | % 31 | % Output parameters: 32 | % Chrom - Matrix containing the individuals of the current 33 | % population after reinsertion. 34 | % ObjVCh - if ObjVCh and ObjVSel are input parameters, then column 35 | % vector containing the objective values of the individuals 36 | % of the current generation after reinsertion. 37 | % 38 | % Author: Hartmut Pohlheim 39 | % History: 10.03.94 file created 40 | % 19.03.94 parameter checking improved 41 | % 26.01.03 tested under MATLAB v6 by Alex Shenfield 42 | 43 | function [Chrom, ObjVCh] = reins(Chrom, SelCh, SUBPOP, InsOpt, ObjVCh, ObjVSel); 44 | 45 | % Check parameter consistency 46 | if nargin < 2, error('Not enough input parameter'); end 47 | if (nargout == 2 & nargin < 6), error('Input parameter missing: ObjVCh and/or ObjVSel'); end 48 | 49 | [NindP, NvarP] = size(Chrom); 50 | [NindO, NvarO] = size(SelCh); 51 | 52 | if nargin == 2, SUBPOP = 1; end 53 | if nargin > 2, 54 | if isempty(SUBPOP), SUBPOP = 1; 55 | elseif isnan(SUBPOP), SUBPOP = 1; 56 | elseif length(SUBPOP) ~= 1, error('SUBPOP must be a scalar'); end 57 | end 58 | 59 | if (NindP/SUBPOP) ~= fix(NindP/SUBPOP), error('Chrom and SUBPOP disagree'); end 60 | if (NindO/SUBPOP) ~= fix(NindO/SUBPOP), error('SelCh and SUBPOP disagree'); end 61 | NIND = NindP/SUBPOP; % Compute number of individuals per subpopulation 62 | NSEL = NindO/SUBPOP; % Compute number of offspring per subpopulation 63 | 64 | IsObjVCh = 0; IsObjVSel = 0; 65 | if nargin > 4, 66 | [mO, nO] = size(ObjVCh); 67 | if nO ~= 1, error('ObjVCh must be a column vector'); end 68 | if NindP ~= mO, error('Chrom and ObjVCh disagree'); end 69 | IsObjVCh = 1; 70 | end 71 | if nargin > 5, 72 | [mO, nO] = size(ObjVSel); 73 | if nO ~= 1, error('ObjVSel must be a column vector'); end 74 | if NindO ~= mO, error('SelCh and ObjVSel disagree'); end 75 | IsObjVSel = 1; 76 | end 77 | 78 | if nargin < 4, INSR = 1.0; Select = 0; end 79 | if nargin >= 4, 80 | if isempty(InsOpt), INSR = 1.0; Select = 0; 81 | elseif isnan(InsOpt), INSR = 1.0; Select = 0; 82 | else 83 | INSR = NaN; Select = NaN; 84 | if (length(InsOpt) > 2), error('Parameter InsOpt too long'); end 85 | if (length(InsOpt) >= 1), Select = InsOpt(1); end 86 | if (length(InsOpt) >= 2), INSR = InsOpt(2); end 87 | if isnan(Select), Select = 0; end 88 | if isnan(INSR), INSR =1.0; end 89 | end 90 | end 91 | 92 | if (INSR < 0 | INSR > 1), error('Parameter for insertion rate must be a scalar in [0, 1]'); end 93 | if (INSR < 1 & IsObjVSel ~= 1), error('For selection of offspring ObjVSel is needed'); end 94 | if (Select ~= 0 & Select ~= 1), error('Parameter for selection method must be 0 or 1'); end 95 | if (Select == 1 & IsObjVCh == 0), error('ObjVCh for fitness-based exchange needed'); end 96 | 97 | if INSR == 0, return; end 98 | NIns = min(max(floor(INSR*NSEL+.5),1),NIND); % Number of offspring to insert 99 | 100 | % perform insertion for each subpopulation 101 | for irun = 1:SUBPOP, 102 | % Calculate positions in old subpopulation, where offspring are inserted 103 | if Select == 1, % fitness-based reinsertion 104 | [Dummy, ChIx] = sort(-ObjVCh((irun-1)*NIND+1:irun*NIND)); 105 | else % uniform reinsertion 106 | [Dummy, ChIx] = sort(rand(NIND,1)); 107 | end 108 | PopIx = ChIx((1:NIns)')+ (irun-1)*NIND; 109 | % Calculate position of Nins-% best offspring 110 | if (NIns < NSEL), % select best offspring 111 | [Dummy,OffIx] = sort(ObjVSel((irun-1)*NSEL+1:irun*NSEL)); 112 | else 113 | OffIx = (1:NIns)'; 114 | end 115 | SelIx = OffIx((1:NIns)')+(irun-1)*NSEL; 116 | % Insert offspring in subpopulation -> new subpopulation 117 | Chrom(PopIx,:) = SelCh(SelIx,:); 118 | if (IsObjVCh == 1 & IsObjVSel == 1), ObjVCh(PopIx) = ObjVSel(SelIx); end 119 | end 120 | 121 | % End of function -------------------------------------------------------------------------------- /rep.m: -------------------------------------------------------------------------------- 1 | % REP.m Replicate a matrix 2 | % 3 | % This function replicates a matrix in both dimensions. 4 | % 5 | % Syntax: MatOut = rep(MatIn,REPN); 6 | % 7 | % Input parameters: 8 | % MatIn - Input Matrix (before replicating) 9 | % 10 | % REPN - Vector of 2 numbers, how many replications in each dimension 11 | % REPN(1): replicate vertically 12 | % REPN(2): replicate horizontally 13 | % 14 | % Example: 15 | % 16 | % MatIn = [1 2 3] 17 | % REPN = [1 2]: MatOut = [1 2 3 1 2 3] 18 | % REPN = [2 1]: MatOut = [1 2 3; 19 | % 1 2 3] 20 | % REPN = [3 2]: MatOut = [1 2 3 1 2 3; 21 | % 1 2 3 1 2 3; 22 | % 1 2 3 1 2 3] 23 | % 24 | % Output parameter: 25 | % MatOut - Output Matrix (after replicating) 26 | % 27 | % 28 | % Author: Carlos Fonseca & Hartmut Pohlheim 29 | % History: 14.02.94 file created 30 | % 22.01.03 tested under MATLAB v6 by Alex Shenfield 31 | 32 | function MatOut = rep(MatIn,REPN) 33 | 34 | % Get size of input matrix 35 | [N_D,N_L] = size(MatIn); 36 | 37 | % Calculate 38 | Ind_D = rem(0:REPN(1)*N_D-1,N_D) + 1; 39 | Ind_L = rem(0:REPN(2)*N_L-1,N_L) + 1; 40 | 41 | % Create output matrix 42 | MatOut = MatIn(Ind_D,Ind_L); 43 | 44 | % End of function -------------------------------------------------------------------------------- /resplot.m: -------------------------------------------------------------------------------- 1 | % RESPLOT.M (RESult PLOTing) 2 | % 3 | % This function plots some results during computation. 4 | % 5 | % Syntax: resplot(Chrom,IndAll,ObjV,Best,gen) 6 | % 7 | % Input parameters: 8 | % Chrom - Matrix containing the chromosomes of the current 9 | % population. Each line corresponds to one individual. 10 | % IndAll - Matrix containing the best individual (variables) of each 11 | % generation. Each line corresponds to one individual. 12 | % ObjV - Vector containing objective values of the current 13 | % generation 14 | % Best - Matrix containing the best and average Objective values of 15 | % each generation, [best value per generation,average value 16 | % per generation] 17 | % gen - Scalar containing the number of the current generation 18 | % 19 | % Output parameter: 20 | % no output parameter 21 | % 22 | % Author: Hartmut Pohlheim 23 | % History: 27.11.93 file created 24 | % 29.11.93 decision, if plot or not deleted 25 | % yscale not log 26 | % 15.12.93 MutMatrix as parameter and plot added 27 | % 16.03.94 function cleaned, MutMatrix removed, IndAll added 28 | % 22.01.03 tested under MATLAB v6 by Alex Shenfield 29 | 30 | function resplot(Chrom,IndAll,ObjV,Best,gen); 31 | 32 | % plot of best and mean value per generation 33 | subplot(2,2,1), plot(Best); 34 | title('Best and mean objective value'); 35 | xlabel('generation'), ylabel('objective value'); 36 | 37 | % plot of best individuals in all generations 38 | subplot(2,2,2), plot(IndAll); 39 | title(['Best individuals']); 40 | xlabel('generation'), ylabel('value of variable'); 41 | 42 | % plot of variables of all individuals in current generation 43 | subplot(2,2,3), plot(Chrom'); 44 | title(['All individuals in gen ',num2str(gen)]); 45 | xlabel('number of variable'), ylabel('value of variable'); 46 | 47 | % plot of all objective values in current generation 48 | subplot(2,2,4), plot(ObjV,'y.'); 49 | title(['All objective values']); 50 | xlabel('number of individual'), ylabel('objective value'); 51 | 52 | drawnow; 53 | 54 | 55 | % End of function -------------------------------------------------------------------------------- /rws.m: -------------------------------------------------------------------------------- 1 | % RWS.m - Roulette Wheel Selection 2 | % 3 | % Syntax: 4 | % NewChrIx = rws(FitnV, Nsel) 5 | % 6 | % This function selects a given number of individuals Nsel from a 7 | % population. FitnV is a column vector containing the fitness 8 | % values of the individuals in the population. 9 | % 10 | % The function returns another column vector containing the 11 | % indexes of the new generation of chromosomes relative to the 12 | % original population matrix, shuffled. The new population, ready 13 | % for mating, can be obtained by calculating 14 | % OldChrom(NewChrIx, :). 15 | % 16 | % Author: Carlos Fonseca, Updated: Andrew Chipperfield 17 | % Date: 04/10/93, Date: 27-Jan-94 18 | % 19 | % Tested under MATLAB v6 by Alex Shenfield (22-Jan-03) 20 | 21 | function NewChrIx = rws(FitnV,Nsel); 22 | 23 | % Identify the population size (Nind) 24 | [Nind,ans] = size(FitnV); 25 | 26 | % Perform Stochastic Sampling with Replacement 27 | cumfit = cumsum(FitnV); 28 | trials = cumfit(Nind) .* rand(Nsel, 1); 29 | Mf = cumfit(:, ones(1, Nsel)); 30 | Mt = trials(:, ones(1, Nind))'; 31 | [NewChrIx, ans] = find(Mt < Mf & ... 32 | [ zeros(1, Nsel); Mf(1:Nind-1, :) ] <= Mt); 33 | % end of function -------------------------------------------------------------------------------- /scaling.m: -------------------------------------------------------------------------------- 1 | % SCALING.m - linear fitness scaling 2 | % 3 | % This function implements a linear fitness scaling algorithm as described 4 | % by Goldberg in "Genetic Algorithms in Search, Optimization and Machine 5 | % Learning", Addison Wesley, 1989. It use is not recommended when fitness 6 | % functions produce negative results as the scaling will become unreliable. 7 | % It is included in this version of the GA Toolbox only for the sake of 8 | % completeness. 9 | % 10 | % Syntax: FitnV = scaling(ObjV, Smul) 11 | % 12 | % Input parameters: 13 | % 14 | % Objv - A vector containing the values of individuals 15 | % fitness. 16 | % 17 | % Smul - Optional scaling parameter (default 2). 18 | % 19 | % Output parameters: 20 | % 21 | % FitnV - A vector containing the individual fitnesses 22 | % for the current population. 23 | % 24 | % Author: Andrew Chipperfield 25 | % Date: 24-Feb-94 26 | 27 | function FitnV = scaling( ObjV, Smul ) 28 | 29 | if nargin == 1 30 | Smul = 2 ; 31 | end 32 | 33 | [Nind, Nobj] = size( ObjV ) ; 34 | Oave = sum( ObjV ) / Nind ; 35 | Omin = min( ObjV ) ; 36 | Omax = max( ObjV ) ; 37 | 38 | if (Omin > ( Smul * Oave - Omax ) / ( Smul - 1.0 )) 39 | delta = Omax - Oave 40 | a = ( Smul - 1.0 ) * Oave / delta 41 | b = Oave * ( Omax - Smul * Oave ) / delta 42 | else 43 | delta = Oave - Omin ; 44 | a = Oave / delta ; 45 | b = -Omin * Oave / delta ; 46 | end 47 | 48 | FitnV = ObjV.*a + b ; -------------------------------------------------------------------------------- /select.m: -------------------------------------------------------------------------------- 1 | % SELECT.M (universal SELECTion) 2 | % 3 | % This function performs universal selection. The function handles 4 | % multiple populations and calls the low level selection function 5 | % for the actual selection process. 6 | % 7 | % Syntax: SelCh = select(SEL_F, Chrom, FitnV, GGAP, SUBPOP) 8 | % 9 | % Input parameters: 10 | % SEL_F - Name of the selection function 11 | % Chrom - Matrix containing the individuals (parents) of the current 12 | % population. Each row corresponds to one individual. 13 | % FitnV - Column vector containing the fitness values of the 14 | % individuals in the population. 15 | % GGAP - (optional) Rate of individuals to be selected 16 | % if omitted 1.0 is assumed 17 | % SUBPOP - (optional) Number of subpopulations 18 | % if omitted 1 subpopulation is assumed 19 | % 20 | % Output parameters: 21 | % SelCh - Matrix containing the selected individuals. 22 | % 23 | % Author: Hartmut Pohlheim 24 | % History: 10.03.94 file created 25 | % 22.01.03 tested under MATLAB v6 by Alex Shenfield 26 | 27 | function SelCh = select(SEL_F, Chrom, FitnV, GGAP, SUBPOP); 28 | 29 | % Check parameter consistency 30 | if nargin < 3, error('Not enough input parameter'); end 31 | 32 | % Identify the population size (Nind) 33 | [NindCh,Nvar] = size(Chrom); 34 | [NindF,VarF] = size(FitnV); 35 | if NindCh ~= NindF, error('Chrom and FitnV disagree'); end 36 | if VarF ~= 1, error('FitnV must be a column vector'); end 37 | 38 | if nargin < 5, SUBPOP = 1; end 39 | if nargin > 4, 40 | if isempty(SUBPOP), SUBPOP = 1; 41 | elseif isnan(SUBPOP), SUBPOP = 1; 42 | elseif length(SUBPOP) ~= 1, error('SUBPOP must be a scalar'); end 43 | end 44 | 45 | if (NindCh/SUBPOP) ~= fix(NindCh/SUBPOP), error('Chrom and SUBPOP disagree'); end 46 | Nind = NindCh/SUBPOP; % Compute number of individuals per subpopulation 47 | 48 | if nargin < 4, GGAP = 1; end 49 | if nargin > 3, 50 | if isempty(GGAP), GGAP = 1; 51 | elseif isnan(GGAP), GGAP = 1; 52 | elseif length(GGAP) ~= 1, error('GGAP must be a scalar'); 53 | elseif (GGAP < 0), error('GGAP must be a scalar bigger than 0'); end 54 | end 55 | 56 | % Compute number of new individuals (to select) 57 | NSel=max(floor(Nind*GGAP+.5),2); 58 | 59 | % Select individuals from population 60 | SelCh = []; 61 | for irun = 1:SUBPOP, 62 | FitnVSub = FitnV((irun-1)*Nind+1:irun*Nind); 63 | ChrIx=feval(SEL_F, FitnVSub, NSel)+(irun-1)*Nind; 64 | SelCh=[SelCh; Chrom(ChrIx,:)]; 65 | end 66 | 67 | 68 | % End of function -------------------------------------------------------------------------------- /sga.m: -------------------------------------------------------------------------------- 1 | % sga.m 2 | % 3 | % This script implements the Simple Genetic Algorithm described 4 | % in the examples section of the GA Toolbox manual. 5 | % 6 | % Author: Andrew Chipperfield 7 | % History: 23-Mar-94 file created 8 | % 9 | % tested under MATLAB v6 by Alex Shenfield (22-Jan-03) 10 | 11 | NIND = 40; % Number of individuals per subpopulations 12 | MAXGEN = 300; % maximum Number of generations 13 | GGAP = .9; % Generation gap, how many new individuals are created 14 | NVAR = 20; % Number of variables 15 | PRECI = 20; % Precision of binary representation 16 | 17 | % Build field descriptor 18 | FieldD = [rep(PRECI,[1, NVAR]); rep([-512;512],[1, NVAR]);... 19 | rep([1; 0; 1 ;1], [1, NVAR])]; 20 | 21 | % Initialise population 22 | Chrom = crtbp(NIND, NVAR*PRECI); 23 | 24 | % Reset counters 25 | Best = NaN*ones(MAXGEN,1); % best in current population 26 | gen = 0; % generational counter 27 | 28 | % Evaluate initial population 29 | ObjV = objfun1(bs2rv(Chrom,FieldD)); 30 | 31 | % Track best individual and display convergence 32 | Best(gen+1) = min(ObjV); 33 | plot(log10(Best),'ro');xlabel('generation'); ylabel('log10(f(x))'); 34 | text(0.5,0.95,['Best = ', num2str(Best(gen+1))],'Units','normalized'); 35 | drawnow; 36 | 37 | % Generational loop 38 | while gen < MAXGEN, 39 | 40 | % Assign fitness-value to entire population 41 | FitnV = ranking(ObjV); 42 | 43 | % Select individuals for breeding 44 | SelCh = select('sus', Chrom, FitnV, GGAP); 45 | 46 | % Recombine selected individuals (crossover) 47 | SelCh = recombin('xovsp',SelCh,0.7); 48 | 49 | % Perform mutation on offspring 50 | SelCh = mut(SelCh); 51 | 52 | % Evaluate offspring, call objective function 53 | ObjVSel = objfun1(bs2rv(SelCh,FieldD)); 54 | 55 | % Reinsert offspring into current population 56 | [Chrom, ObjV]=reins(Chrom,SelCh,1,1,ObjV,ObjVSel); 57 | 58 | % Increment generational counter 59 | gen = gen+1; 60 | 61 | % Update display and record current best individual 62 | Best(gen+1) = min(ObjV); 63 | plot(log10(Best),'ro'); xlabel('generation'); ylabel('log10(f(x))'); 64 | text(0.5,0.95,['Best = ', num2str(Best(gen+1))],'Units','normalized'); 65 | drawnow; 66 | end 67 | % End of GA -------------------------------------------------------------------------------- /sus.m: -------------------------------------------------------------------------------- 1 | % SUS.M (Stochastic Universal Sampling) 2 | % 3 | % This function performs selection with STOCHASTIC UNIVERSAL SAMPLING. 4 | % 5 | % Syntax: NewChrIx = sus(FitnV, Nsel) 6 | % 7 | % Input parameters: 8 | % FitnV - Column vector containing the fitness values of the 9 | % individuals in the population. 10 | % Nsel - number of individuals to be selected 11 | % 12 | % Output parameters: 13 | % NewChrIx - column vector containing the indexes of the selected 14 | % individuals relative to the original population, shuffled. 15 | % The new population, ready for mating, can be obtained 16 | % by calculating OldChrom(NewChrIx,:). 17 | % 18 | % Author: Hartmut Pohlheim (Carlos Fonseca) 19 | % History: 12.12.93 file created 20 | % 22.02.94 clean up, comments 21 | % 22.01.03 tested under MATLAB v6 by Alex Shenfield 22 | 23 | function NewChrIx = sus(FitnV,Nsel); 24 | 25 | % Identify the population size (Nind) 26 | [Nind,ans] = size(FitnV); 27 | 28 | % Perform stochastic universal sampling 29 | cumfit = cumsum(FitnV); 30 | trials = cumfit(Nind) / Nsel * (rand + (0:Nsel-1)'); 31 | Mf = cumfit(:, ones(1, Nsel)); 32 | Mt = trials(:, ones(1, Nind))'; 33 | [NewChrIx, ans] = find(Mt < Mf & [ zeros(1, Nsel); Mf(1:Nind-1, :) ] <= Mt); 34 | 35 | % Shuffle new population 36 | [ans, shuf] = sort(rand(Nsel, 1)); 37 | NewChrIx = NewChrIx(shuf); 38 | 39 | 40 | % End of function -------------------------------------------------------------------------------- /xovdp.m: -------------------------------------------------------------------------------- 1 | % XOVDP.M (CROSSOVer Double Point) 2 | % 3 | % This function performs double point crossover between pairs of 4 | % individuals and returns the current generation after mating. 5 | % 6 | % Syntax: NewChrom = xovdp(OldChrom, XOVR) 7 | % 8 | % Input parameters: 9 | % OldChrom - Matrix containing the chromosomes of the old 10 | % population. Each line corresponds to one individual 11 | % (in any form, not necessarily real values). 12 | % XOVR - Probability of recombination occurring between pairs 13 | % of individuals. 14 | % 15 | % Output parameter: 16 | % NewChrom - Matrix containing the chromosomes of the population 17 | % after mating, ready to be mutated and/or evaluated, 18 | % in the same format as OldChrom. 19 | 20 | % Author: Hartmut Pohlheim 21 | % History: 28.03.94 file created 22 | % 22.01.03 tested under MATLAB v6 by Alex Shenfield 23 | 24 | function NewChrom = xovdp(OldChrom, XOVR); 25 | 26 | if nargin < 2, XOVR = NaN; end 27 | 28 | % call low level function with appropriate parameters 29 | NewChrom = xovmp(OldChrom, XOVR, 2, 0); 30 | 31 | % End of function -------------------------------------------------------------------------------- /xovdprs.m: -------------------------------------------------------------------------------- 1 | % XOVDPRS.M (CROSSOVer Double-Point with Reduced Surrogate) 2 | % 3 | % This function performs double-point 'reduced surrogate' crossover between 4 | % pairs of individuals and returns the current generation after mating. 5 | % 6 | % Syntax: NewChrom = xovdprs(OldChrom, XOVR) 7 | % 8 | % Input parameters: 9 | % OldChrom - Matrix containing the chromosomes of the old 10 | % population. Each line corresponds to one individual 11 | % (in any form, not necessarily real values). 12 | % XOVR - Probability of recombination occurring between pairs 13 | % of individuals. 14 | % 15 | % Output parameter: 16 | % NewChrom - Matrix containing the chromosomes of the population 17 | % after mating, ready to be mutated and/or evaluated, 18 | % in the same format as OldChrom. 19 | % 20 | % Author: Hartmut Pohlheim 21 | % History: 28.03.94 file created 22 | % 22.01.03 tested under MATLAB v6 by Alex Shenfield 23 | 24 | function NewChrom = xovdprs(OldChrom, XOVR); 25 | 26 | if nargin < 2, XOVR = NaN; end 27 | 28 | % call low-level function with appropriate parameters 29 | NewChrom = xovmp(OldChrom, XOVR, 2, 1); 30 | 31 | % End of function -------------------------------------------------------------------------------- /xovmp.m: -------------------------------------------------------------------------------- 1 | % XOVMP.m Multi-point crossover 2 | % 3 | % Syntax: NewChrom = xovmp(OldChrom, Px, Npt, Rs) 4 | % 5 | % This function takes a matrix OldChrom containing the binary 6 | % representation of the individuals in the current population, 7 | % applies crossover to consecutive pairs of individuals with 8 | % probability Px and returns the resulting population. 9 | % 10 | % Npt indicates how many crossover points to use (1 or 2, zero 11 | % indicates shuffle crossover). 12 | % Rs indicates whether or not to force the production of 13 | % offspring different from their parents. 14 | % 15 | % 16 | % Author: Carlos Fonseca, Updated: Andrew Chipperfield 17 | % Date: 28/09/93, Date: 27-Jan-94 18 | % 19 | % tested under MATLAB v6 by Alex Shenfield (22-Jan-03) 20 | 21 | function NewChrom = xovmp(OldChrom, Px, Npt, Rs); 22 | 23 | % Identify the population size (Nind) and the chromosome length (Lind) 24 | [Nind,Lind] = size(OldChrom); 25 | 26 | if Lind < 2, NewChrom = OldChrom; return; end 27 | 28 | if nargin < 4, Rs = 0; end 29 | if nargin < 3, Npt = 0; Rs = 0; end 30 | if nargin < 2, Px = 0.7; Npt = 0; Rs = 0; end 31 | if isnan(Px), Px = 0.7; end 32 | if isnan(Npt), Npt = 0; end 33 | if isnan(Rs), Rs = 0; end 34 | if isempty(Px), Px = 0.7; end 35 | if isempty(Npt), Npt = 0; end 36 | if isempty(Rs), Rs = 0; end 37 | 38 | Xops = floor(Nind/2); 39 | DoCross = rand(Xops,1) < Px; 40 | odd = 1:2:Nind-1; 41 | even = 2:2:Nind; 42 | 43 | % Compute the effective length of each chromosome pair 44 | Mask = ~Rs | (OldChrom(odd, :) ~= OldChrom(even, :)); 45 | Mask = cumsum(Mask')'; 46 | 47 | % Compute cross sites for each pair of individuals, according to their 48 | % effective length and Px (two equal cross sites mean no crossover) 49 | xsites(:, 1) = Mask(:, Lind); 50 | if Npt >= 2, 51 | xsites(:, 1) = ceil(xsites(:, 1) .* rand(Xops, 1)); 52 | end 53 | xsites(:,2) = rem(xsites + ceil((Mask(:, Lind)-1) .* rand(Xops, 1)) ... 54 | .* DoCross - 1 , Mask(:, Lind) )+1; 55 | 56 | % Express cross sites in terms of a 0-1 mask 57 | Mask = (xsites(:,ones(1,Lind)) < Mask) == ... 58 | (xsites(:,2*ones(1,Lind)) < Mask); 59 | 60 | if ~Npt, 61 | shuff = rand(Lind,Xops); 62 | [ans,shuff] = sort(shuff); 63 | for i=1:Xops 64 | OldChrom(odd(i),:)=OldChrom(odd(i),shuff(:,i)); 65 | OldChrom(even(i),:)=OldChrom(even(i),shuff(:,i)); 66 | end 67 | end 68 | 69 | % Perform crossover 70 | NewChrom(odd,:) = (OldChrom(odd,:).* Mask) + (OldChrom(even,:).*(~Mask)); 71 | NewChrom(even,:) = (OldChrom(odd,:).*(~Mask)) + (OldChrom(even,:).*Mask); 72 | 73 | % If the number of individuals is odd, the last individual cannot be mated 74 | % but must be included in the new population 75 | if rem(Nind,2), 76 | NewChrom(Nind,:)=OldChrom(Nind,:); 77 | end 78 | 79 | if ~Npt, 80 | [ans,unshuff] = sort(shuff); 81 | for i=1:Xops 82 | NewChrom(odd(i),:)=NewChrom(odd(i),unshuff(:,i)); 83 | NewChrom(even(i),:)=NewChrom(even(i),unshuff(:,i)); 84 | end 85 | end 86 | 87 | % end of function -------------------------------------------------------------------------------- /xovsh.m: -------------------------------------------------------------------------------- 1 | % XOVSH.M (CROSSOVer SHuffle) 2 | % 3 | % This function performs shuffle crossover between pairs of 4 | % individuals and returns the current generation after mating. 5 | % 6 | % Syntax: NewChrom = xovsh(OldChrom, XOVR) 7 | % 8 | % Input parameters: 9 | % OldChrom - Matrix containing the chromosomes of the old 10 | % population. Each line corresponds to one individual 11 | % (in any form, not necessarily real values). 12 | % XOVR - Probability of recombination occurring between pairs 13 | % of individuals. 14 | % 15 | % Output parameter: 16 | % NewChrom - Matrix containing the chromosomes of the population 17 | % after mating, ready to be mutated and/or evaluated, 18 | % in the same format as OldChrom. 19 | % 20 | % Author: Hartmut Pohlheim 21 | % History: 28.03.94 file created 22 | % 22.01.03 tested under MATLAB v6 by Alex Shenfield 23 | 24 | function NewChrom = xovsh(OldChrom, XOVR); 25 | 26 | if nargin < 2, XOVR = NaN; end 27 | 28 | % call low level function with appropriate parameters 29 | NewChrom = xovmp(OldChrom, XOVR, 0, 0); 30 | 31 | % End of function -------------------------------------------------------------------------------- /xovshrs.m: -------------------------------------------------------------------------------- 1 | % XOVSHRS.M (CROSSOVer SHuffle with Reduced Surrogate) 2 | % 3 | % This function performs shuffle 'reduced surrogate' crossover between 4 | % pairs of individuals and returns the current generation after mating. 5 | % 6 | % Syntax: NewChrom = xovshrs(OldChrom, XOVR) 7 | % 8 | % Input parameters: 9 | % OldChrom - Matrix containing the chromosomes of the old 10 | % population. Each line corresponds to one individual 11 | % (in any form, not necessarily real values). 12 | % XOVR - Probability of recombination occurring between pairs 13 | % of individuals. 14 | % 15 | % Output parameter: 16 | % NewChrom - Matrix containing the chromosomes of the population 17 | % after mating, ready to be mutated and/or evaluated, 18 | % in the same format as OldChrom. 19 | % 20 | % Author: Hartmut Pohlheim 21 | % History: 28.03.94 file created 22 | % 22.01.03 tested under MATLAB v6 by Alex Shenfield 23 | 24 | function NewChrom = xovshrs(OldChrom, XOVR); 25 | 26 | if nargin < 2, XOVR = NaN; end 27 | 28 | % call low level function with appropriate parameters 29 | NewChrom = xovmp(OldChrom, XOVR, 0, 1); 30 | 31 | % End of function -------------------------------------------------------------------------------- /xovsp.m: -------------------------------------------------------------------------------- 1 | % XOVSP.M (CROSSOVer Single-Point) 2 | % 3 | % This function performs single-point crossover between pairs of 4 | % individuals and returns the current generation after mating. 5 | % 6 | % Syntax: NewChrom = xovsp(OldChrom, XOVR) 7 | % 8 | % Input parameters: 9 | % OldChrom - Matrix containing the chromosomes of the old 10 | % population. Each line corresponds to one individual 11 | % (in any form, not necessarily real values). 12 | % XOVR - Probability of recombination occurring between pairs 13 | % of individuals. 14 | % 15 | % Output parameter: 16 | % NewChrom - Matrix containing the chromosomes of the population 17 | % after mating, ready to be mutated and/or evaluated, 18 | % in the same format as OldChrom. 19 | % 20 | % Author: Hartmut Pohlheim 21 | % History: 28.03.94 file created 22 | % 22.01.03 tested under MATLAB v6 by Alex Shenfield 23 | 24 | function NewChrom = xovsp(OldChrom, XOVR); 25 | 26 | if nargin < 2, XOVR = NaN; end 27 | 28 | % call low level function with appropriate parameters 29 | NewChrom = xovmp(OldChrom, XOVR, 1, 0); 30 | 31 | 32 | % End of function -------------------------------------------------------------------------------- /xovsprs.m: -------------------------------------------------------------------------------- 1 | % XOVSPRS.M (CROSSOVer Single-Point with Reduced Surrogate) 2 | % 3 | % This function performs single-point 'reduced surrogate' crossover between 4 | % pairs of individuals and returns the current generation after mating. 5 | % 6 | % Syntax: NewChrom = xovsprs(OldChrom, XOVR) 7 | % 8 | % Input parameters: 9 | % OldChrom - Matrix containing the chromosomes of the old 10 | % population. Each line corresponds to one individual 11 | % (in any form, not necessarily real-values). 12 | % XOVR - Probability of recombination occurring between pairs 13 | % of individuals. 14 | % 15 | % Output parameter: 16 | % NewChrom - Matrix containing the chromosomes of the population 17 | % after mating, ready to be mutated and/or evaluated, 18 | % in the same format as OldChrom. 19 | % 20 | % Author: Hartmut Pohlheim 21 | % History: 28.03.94 file created 22 | % 22.01.03 tested under MATLAB v6 by Alex Shenfield 23 | 24 | function NewChrom = xovsprs(OldChrom, XOVR); 25 | 26 | if nargin < 2, XOVR = NaN; end 27 | 28 | % call low-level function with appropriate parameters 29 | NewChrom = xovmp(OldChrom, XOVR, 1, 1); 30 | 31 | % End of function --------------------------------------------------------------------------------