├── README.md
├── NSGA-II
    ├── main.m
    ├── Crossover.m
    ├── MOP2.m
    ├── Dominates.m
    ├── MOP4.m
    ├── PlotCosts.m
    ├── Mutate.m
    ├── SortPopulation.m
    ├── CalcCrowdingDistance.m
    ├── NonDominatedSorting.m
    └── nsga2.m
└── LICENSE


/README.md:
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 1 | # NSGA-II in MATLAB
 2 | 
 3 | <p align="center">
 4 |     <img src="https://yarpiz.com/wp-content/uploads/2015/09/ypea120-nsga2.jpg" alt="NSGA-II in MATLAB">
 5 | </p>
 6 | 
 7 | This is an implementation of Non-dominated Sorting Genetic Algorithm II (NSGA-II) in MATLAB.
 8 | 
 9 | For more information, visit following URL:
10 | https://yarpiz.com/56/ypea120-nsga2
11 | 
12 | ## Citing This Work
13 | You can cite this code as follows:
14 | 
15 | **Mostapha Kalami Heris, NSGA-II in MATLAB (URL: https://yarpiz.com/56/ypea120-nsga2), Yarpiz, 2015.**
16 | 


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/NSGA-II/main.m:
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 1 | %
 2 | % Copyright (c) 2015, Mostapha Kalami Heris & Yarpiz (www.yarpiz.com)
 3 | % All rights reserved. Please read the "LICENSE" file for license terms.
 4 | %
 5 | % Project Code: YPEA120
 6 | % Project Title: Non-dominated Sorting Genetic Algorithm II (NSGA-II)
 7 | % Publisher: Yarpiz (www.yarpiz.com)
 8 | % 
 9 | % Developer: Mostapha Kalami Heris (Member of Yarpiz Team)
10 | % 
11 | % Cite as:
12 | % Mostapha Kalami Heris, NSGA-II in MATLAB (URL: https://yarpiz.com/56/ypea120-nsga2), Yarpiz, 2015.
13 | % 
14 | % Contact Info: sm.kalami@gmail.com, info@yarpiz.com
15 | %
16 | 
17 | nsga2;
18 | 


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/NSGA-II/Crossover.m:
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 1 | %
 2 | % Copyright (c) 2015, Mostapha Kalami Heris & Yarpiz (www.yarpiz.com)
 3 | % All rights reserved. Please read the "LICENSE" file for license terms.
 4 | %
 5 | % Project Code: YPEA120
 6 | % Project Title: Non-dominated Sorting Genetic Algorithm II (NSGA-II)
 7 | % Publisher: Yarpiz (www.yarpiz.com)
 8 | % 
 9 | % Developer: Mostapha Kalami Heris (Member of Yarpiz Team)
10 | % 
11 | % Cite as:
12 | % Mostapha Kalami Heris, NSGA-II in MATLAB (URL: https://yarpiz.com/56/ypea120-nsga2), Yarpiz, 2015.
13 | % 
14 | % Contact Info: sm.kalami@gmail.com, info@yarpiz.com
15 | %
16 | 
17 | function [y1, y2] = Crossover(x1, x2)
18 | 
19 |     alpha = rand(size(x1));
20 |     
21 |     y1 = alpha.*x1+(1-alpha).*x2;
22 |     y2 = alpha.*x2+(1-alpha).*x1;
23 |     
24 | end


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/NSGA-II/MOP2.m:
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 1 | %
 2 | % Copyright (c) 2015, Mostapha Kalami Heris & Yarpiz (www.yarpiz.com)
 3 | % All rights reserved. Please read the "LICENSE" file for license terms.
 4 | %
 5 | % Project Code: YPEA120
 6 | % Project Title: Non-dominated Sorting Genetic Algorithm II (NSGA-II)
 7 | % Publisher: Yarpiz (www.yarpiz.com)
 8 | % 
 9 | % Developer: Mostapha Kalami Heris (Member of Yarpiz Team)
10 | % 
11 | % Cite as:
12 | % Mostapha Kalami Heris, NSGA-II in MATLAB (URL: https://yarpiz.com/56/ypea120-nsga2), Yarpiz, 2015.
13 | % 
14 | % Contact Info: sm.kalami@gmail.com, info@yarpiz.com
15 | %
16 | 
17 | function z = MOP2(x)
18 | 
19 |     n = numel(x);
20 |     
21 |     z1 = 1-exp(-sum((x-1/sqrt(n)).^2));
22 |     
23 |     z2 = 1-exp(-sum((x+1/sqrt(n)).^2));
24 |     
25 |     z = [z1 z2]';
26 | 
27 | end


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/NSGA-II/Dominates.m:
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 1 | %
 2 | % Copyright (c) 2015, Mostapha Kalami Heris & Yarpiz (www.yarpiz.com)
 3 | % All rights reserved. Please read the "LICENSE" file for license terms.
 4 | %
 5 | % Project Code: YPEA120
 6 | % Project Title: Non-dominated Sorting Genetic Algorithm II (NSGA-II)
 7 | % Publisher: Yarpiz (www.yarpiz.com)
 8 | % 
 9 | % Developer: Mostapha Kalami Heris (Member of Yarpiz Team)
10 | % 
11 | % Cite as:
12 | % Mostapha Kalami Heris, NSGA-II in MATLAB (URL: https://yarpiz.com/56/ypea120-nsga2), Yarpiz, 2015.
13 | % 
14 | % Contact Info: sm.kalami@gmail.com, info@yarpiz.com
15 | %
16 | 
17 | function b = Dominates(x, y)
18 | 
19 |     if isstruct(x)
20 |         x = x.Cost;
21 |     end
22 | 
23 |     if isstruct(y)
24 |         y = y.Cost;
25 |     end
26 | 
27 |     b = all(x <= y) && any(x<y);
28 | 
29 | end


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/NSGA-II/MOP4.m:
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 1 | %
 2 | % Copyright (c) 2015, Mostapha Kalami Heris & Yarpiz (www.yarpiz.com)
 3 | % All rights reserved. Please read the "LICENSE" file for license terms.
 4 | %
 5 | % Project Code: YPEA120
 6 | % Project Title: Non-dominated Sorting Genetic Algorithm II (NSGA-II)
 7 | % Publisher: Yarpiz (www.yarpiz.com)
 8 | % 
 9 | % Developer: Mostapha Kalami Heris (Member of Yarpiz Team)
10 | % 
11 | % Cite as:
12 | % Mostapha Kalami Heris, NSGA-II in MATLAB (URL: https://yarpiz.com/56/ypea120-nsga2), Yarpiz, 2015.
13 | % 
14 | % Contact Info: sm.kalami@gmail.com, info@yarpiz.com
15 | %
16 | 
17 | function z = MOP4(x)
18 | 
19 |     a = 0.8;
20 |     
21 |     b = 3;
22 |     
23 |     z1 = sum(-10*exp(-0.2*sqrt(x(1:end-1).^2+x(2:end).^2)));
24 |     
25 |     z2 = sum(abs(x).^a+5*(sin(x)).^b);
26 |     
27 |     z = [z1 z2]';
28 | 
29 | end


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/NSGA-II/PlotCosts.m:
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 1 | %
 2 | % Copyright (c) 2015, Mostapha Kalami Heris & Yarpiz (www.yarpiz.com)
 3 | % All rights reserved. Please read the "LICENSE" file for license terms.
 4 | %
 5 | % Project Code: YPEA120
 6 | % Project Title: Non-dominated Sorting Genetic Algorithm II (NSGA-II)
 7 | % Publisher: Yarpiz (www.yarpiz.com)
 8 | % 
 9 | % Developer: Mostapha Kalami Heris (Member of Yarpiz Team)
10 | % 
11 | % Cite as:
12 | % Mostapha Kalami Heris, NSGA-II in MATLAB (URL: https://yarpiz.com/56/ypea120-nsga2), Yarpiz, 2015.
13 | % 
14 | % Contact Info: sm.kalami@gmail.com, info@yarpiz.com
15 | %
16 | 
17 | function PlotCosts(pop)
18 | 
19 |     Costs = [pop.Cost];
20 |     
21 |     plot(Costs(1, :), Costs(2, :), 'r*', 'MarkerSize', 8);
22 |     xlabel('1^{st} Objective');
23 |     ylabel('2^{nd} Objective');
24 |     title('Non-dominated Solutions (F_{1})');
25 |     grid on;
26 | 
27 | end


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/NSGA-II/Mutate.m:
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 1 | %
 2 | % Copyright (c) 2015, Mostapha Kalami Heris & Yarpiz (www.yarpiz.com)
 3 | % All rights reserved. Please read the "LICENSE" file for license terms.
 4 | %
 5 | % Project Code: YPEA120
 6 | % Project Title: Non-dominated Sorting Genetic Algorithm II (NSGA-II)
 7 | % Publisher: Yarpiz (www.yarpiz.com)
 8 | % 
 9 | % Developer: Mostapha Kalami Heris (Member of Yarpiz Team)
10 | % 
11 | % Cite as:
12 | % Mostapha Kalami Heris, NSGA-II in MATLAB (URL: https://yarpiz.com/56/ypea120-nsga2), Yarpiz, 2015.
13 | % 
14 | % Contact Info: sm.kalami@gmail.com, info@yarpiz.com
15 | %
16 | 
17 | function y = Mutate(x, mu, sigma)
18 | 
19 |     nVar = numel(x);
20 |     
21 |     nMu = ceil(mu*nVar);
22 | 
23 |     j = randsample(nVar, nMu);
24 |     if numel(sigma)>1
25 |         sigma = sigma(j);
26 |     end
27 |     
28 |     y = x;
29 |     
30 |     y(j) = x(j)+sigma.*randn(size(j));
31 | 
32 | end


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/NSGA-II/SortPopulation.m:
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 1 | %
 2 | % Copyright (c) 2015, Mostapha Kalami Heris & Yarpiz (www.yarpiz.com)
 3 | % All rights reserved. Please read the "LICENSE" file for license terms.
 4 | %
 5 | % Project Code: YPEA120
 6 | % Project Title: Non-dominated Sorting Genetic Algorithm II (NSGA-II)
 7 | % Publisher: Yarpiz (www.yarpiz.com)
 8 | % 
 9 | % Developer: Mostapha Kalami Heris (Member of Yarpiz Team)
10 | % 
11 | % Cite as:
12 | % Mostapha Kalami Heris, NSGA-II in MATLAB (URL: https://yarpiz.com/56/ypea120-nsga2), Yarpiz, 2015.
13 | % 
14 | % Contact Info: sm.kalami@gmail.com, info@yarpiz.com
15 | %
16 | 
17 | function [pop, F] = SortPopulation(pop)
18 | 
19 |     % Sort Based on Crowding Distance
20 |     [~, CDSO] = sort([pop.CrowdingDistance], 'descend');
21 |     pop = pop(CDSO);
22 |     
23 |     % Sort Based on Rank
24 |     [~, RSO] = sort([pop.Rank]);
25 |     pop = pop(RSO);
26 |     
27 |     % Update Fronts
28 |     Ranks = [pop.Rank];
29 |     MaxRank = max(Ranks);
30 |     F = cell(MaxRank, 1);
31 |     for r = 1:MaxRank
32 |         F{r} = find(Ranks == r);
33 |     end
34 | 
35 | end


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/NSGA-II/CalcCrowdingDistance.m:
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 1 | %
 2 | % Copyright (c) 2015, Mostapha Kalami Heris & Yarpiz (www.yarpiz.com)
 3 | % All rights reserved. Please read the "LICENSE" file for license terms.
 4 | %
 5 | % Project Code: YPEA120
 6 | % Project Title: Non-dominated Sorting Genetic Algorithm II (NSGA-II)
 7 | % Publisher: Yarpiz (www.yarpiz.com)
 8 | % 
 9 | % Developer: Mostapha Kalami Heris (Member of Yarpiz Team)
10 | % 
11 | % Cite as:
12 | % Mostapha Kalami Heris, NSGA-II in MATLAB (URL: https://yarpiz.com/56/ypea120-nsga2), Yarpiz, 2015.
13 | % 
14 | % Contact Info: sm.kalami@gmail.com, info@yarpiz.com
15 | %
16 | 
17 | function pop = CalcCrowdingDistance(pop, F)
18 | 
19 |     nF = numel(F);
20 |     
21 |     for k = 1:nF
22 |         
23 |         Costs = [pop(F{k}).Cost];
24 |         
25 |         nObj = size(Costs, 1);
26 |         
27 |         n = numel(F{k});
28 |         
29 |         d = zeros(n, nObj);
30 |         
31 |         for j = 1:nObj
32 |             
33 |             [cj, so] = sort(Costs(j, :));
34 |             
35 |             d(so(1), j) = inf;
36 |             
37 |             for i = 2:n-1
38 |                 
39 |                 d(so(i), j) = abs(cj(i+1)-cj(i-1))/abs(cj(1)-cj(end));
40 |                 
41 |             end
42 |             
43 |             d(so(end), j) = inf;
44 |             
45 |         end
46 |         
47 |         
48 |         for i = 1:n
49 |             
50 |             pop(F{k}(i)).CrowdingDistance = sum(d(i, :));
51 |             
52 |         end
53 |         
54 |     end
55 | 
56 | 
57 | end
58 | 
59 | 


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/LICENSE:
--------------------------------------------------------------------------------
 1 | Copyright (c) 2015, Mostapha Kalami Heris & Yarpiz (www.yarpiz.com)
 2 | All rights reserved.
 3 | 
 4 | Cite as:
 5 | Mostapha Kalami Heris, NSGA-II in MATLAB (URL: https://yarpiz.com/56/ypea120-nsga2), Yarpiz, 2015.
 6 | 
 7 | Redistribution and use in source and binary forms, with or without
 8 | modification, are permitted provided that the following conditions are
 9 | met:
10 | 
11 |     * Redistributions of source code must retain the above copyright
12 |       notice, this list of conditions and the following disclaimer.
13 | 	  
14 |     * Redistributions in binary form must reproduce the above copyright
15 |       notice, this list of conditions and the following disclaimer in
16 |       the documentation and/or other materials provided with the distribution
17 | 
18 | THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
19 | AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
20 | IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
21 | ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
22 | LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
23 | CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
24 | SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
25 | INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
26 | CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
27 | ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
28 | POSSIBILITY OF SUCH DAMAGE.


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/NSGA-II/NonDominatedSorting.m:
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 1 | %
 2 | % Copyright (c) 2015, Mostapha Kalami Heris & Yarpiz (www.yarpiz.com)
 3 | % All rights reserved. Please read the "LICENSE" file for license terms.
 4 | %
 5 | % Project Code: YPEA120
 6 | % Project Title: Non-dominated Sorting Genetic Algorithm II (NSGA-II)
 7 | % Publisher: Yarpiz (www.yarpiz.com)
 8 | % 
 9 | % Developer: Mostapha Kalami Heris (Member of Yarpiz Team)
10 | % 
11 | % Cite as:
12 | % Mostapha Kalami Heris, NSGA-II in MATLAB (URL: https://yarpiz.com/56/ypea120-nsga2), Yarpiz, 2015.
13 | % 
14 | % Contact Info: sm.kalami@gmail.com, info@yarpiz.com
15 | %
16 | 
17 | function [pop, F] = NonDominatedSorting(pop)
18 | 
19 |     nPop = numel(pop);
20 | 
21 |     for i = 1:nPop
22 |         pop(i).DominationSet = [];
23 |         pop(i).DominatedCount = 0;
24 |     end
25 |     
26 |     F{1} = [];
27 |     
28 |     for i = 1:nPop
29 |         for j = i+1:nPop
30 |             p = pop(i);
31 |             q = pop(j);
32 |             
33 |             if Dominates(p, q)
34 |                 p.DominationSet = [p.DominationSet j];
35 |                 q.DominatedCount = q.DominatedCount+1;
36 |             end
37 |             
38 |             if Dominates(q.Cost, p.Cost)
39 |                 q.DominationSet = [q.DominationSet i];
40 |                 p.DominatedCount = p.DominatedCount+1;
41 |             end
42 |             
43 |             pop(i) = p;
44 |             pop(j) = q;
45 |         end
46 |         
47 |         if pop(i).DominatedCount == 0
48 |             F{1} = [F{1} i];
49 |             pop(i).Rank = 1;
50 |         end
51 |     end
52 |     
53 |     k = 1;
54 |     
55 |     while true
56 |         
57 |         Q = [];
58 |         
59 |         for i = F{k}
60 |             p = pop(i);
61 |             
62 |             for j = p.DominationSet
63 |                 q = pop(j);
64 |                 
65 |                 q.DominatedCount = q.DominatedCount-1;
66 |                 
67 |                 if q.DominatedCount == 0
68 |                     Q = [Q j]; %#ok
69 |                     q.Rank = k+1;
70 |                 end
71 |                 
72 |                 pop(j) = q;
73 |             end
74 |         end
75 |         
76 |         if isempty(Q)
77 |             break;
78 |         end
79 |         
80 |         F{k+1} = Q; %#ok
81 |         
82 |         k = k+1;
83 |         
84 |     end
85 |     
86 | 
87 | end


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/NSGA-II/nsga2.m:
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  1 | %
  2 | % Copyright (c) 2015, Mostapha Kalami Heris & Yarpiz (www.yarpiz.com)
  3 | % All rights reserved. Please read the "LICENSE" file for license terms.
  4 | %
  5 | % Project Code: YPEA120
  6 | % Project Title: Non-dominated Sorting Genetic Algorithm II (NSGA-II)
  7 | % Publisher: Yarpiz (www.yarpiz.com)
  8 | % 
  9 | % Developer: Mostapha Kalami Heris (Member of Yarpiz Team)
 10 | % 
 11 | % Cite as:
 12 | % Mostapha Kalami Heris, NSGA-II in MATLAB (URL: https://yarpiz.com/56/ypea120-nsga2), Yarpiz, 2015.
 13 | % 
 14 | % Contact Info: sm.kalami@gmail.com, info@yarpiz.com
 15 | %
 16 | 
 17 | clc;
 18 | clear;
 19 | close all;
 20 | 
 21 | %% Problem Definition
 22 | 
 23 | CostFunction = @(x) MOP4(x);      % Cost Function
 24 | 
 25 | nVar = 3;             % Number of Decision Variables
 26 | 
 27 | VarSize = [1 nVar];   % Size of Decision Variables Matrix
 28 | 
 29 | VarMin = -5;          % Lower Bound of Variables
 30 | VarMax = 5;          % Upper Bound of Variables
 31 | 
 32 | % Number of Objective Functions
 33 | nObj = numel(CostFunction(unifrnd(VarMin, VarMax, VarSize)));
 34 | 
 35 | 
 36 | %% NSGA-II Parameters
 37 | 
 38 | MaxIt = 100;      % Maximum Number of Iterations
 39 | 
 40 | nPop = 50;        % Population Size
 41 | 
 42 | pCrossover = 0.7;                         % Crossover Percentage
 43 | nCrossover = 2*round(pCrossover*nPop/2);  % Number of Parnets (Offsprings)
 44 | 
 45 | pMutation = 0.4;                          % Mutation Percentage
 46 | nMutation = round(pMutation*nPop);        % Number of Mutants
 47 | 
 48 | mu = 0.02;                    % Mutation Rate
 49 | 
 50 | sigma = 0.1*(VarMax-VarMin);  % Mutation Step Size
 51 | 
 52 | 
 53 | %% Initialization
 54 | 
 55 | empty_individual.Position = [];
 56 | empty_individual.Cost = [];
 57 | empty_individual.Rank = [];
 58 | empty_individual.DominationSet = [];
 59 | empty_individual.DominatedCount = [];
 60 | empty_individual.CrowdingDistance = [];
 61 | 
 62 | pop = repmat(empty_individual, nPop, 1);
 63 | 
 64 | for i = 1:nPop
 65 |     
 66 |     pop(i).Position = unifrnd(VarMin, VarMax, VarSize);
 67 |     
 68 |     pop(i).Cost = CostFunction(pop(i).Position);
 69 |     
 70 | end
 71 | 
 72 | % Non-Dominated Sorting
 73 | [pop, F] = NonDominatedSorting(pop);
 74 | 
 75 | % Calculate Crowding Distance
 76 | pop = CalcCrowdingDistance(pop, F);
 77 | 
 78 | % Sort Population
 79 | [pop, F] = SortPopulation(pop);
 80 | 
 81 | 
 82 | %% NSGA-II Main Loop
 83 | 
 84 | for it = 1:MaxIt
 85 |     
 86 |     % Crossover
 87 |     popc = repmat(empty_individual, nCrossover/2, 2);
 88 |     for k = 1:nCrossover/2
 89 |         
 90 |         i1 = randi([1 nPop]);
 91 |         p1 = pop(i1);
 92 |         
 93 |         i2 = randi([1 nPop]);
 94 |         p2 = pop(i2);
 95 |         
 96 |         [popc(k, 1).Position, popc(k, 2).Position] = Crossover(p1.Position, p2.Position);
 97 |         
 98 |         popc(k, 1).Cost = CostFunction(popc(k, 1).Position);
 99 |         popc(k, 2).Cost = CostFunction(popc(k, 2).Position);
100 |         
101 |     end
102 |     popc = popc(:);
103 |     
104 |     % Mutation
105 |     popm = repmat(empty_individual, nMutation, 1);
106 |     for k = 1:nMutation
107 |         
108 |         i = randi([1 nPop]);
109 |         p = pop(i);
110 |         
111 |         popm(k).Position = Mutate(p.Position, mu, sigma);
112 |         
113 |         popm(k).Cost = CostFunction(popm(k).Position);
114 |         
115 |     end
116 |     
117 |     % Merge
118 |     pop = [pop
119 |          popc
120 |          popm]; %#ok
121 |      
122 |     % Non-Dominated Sorting
123 |     [pop, F] = NonDominatedSorting(pop);
124 | 
125 |     % Calculate Crowding Distance
126 |     pop = CalcCrowdingDistance(pop, F);
127 | 
128 |     % Sort Population
129 |     pop = SortPopulation(pop);
130 |     
131 |     % Truncate
132 |     pop = pop(1:nPop);
133 |     
134 |     % Non-Dominated Sorting
135 |     [pop, F] = NonDominatedSorting(pop);
136 | 
137 |     % Calculate Crowding Distance
138 |     pop = CalcCrowdingDistance(pop, F);
139 | 
140 |     % Sort Population
141 |     [pop, F] = SortPopulation(pop);
142 |     
143 |     % Store F1
144 |     F1 = pop(F{1});
145 |     
146 |     % Show Iteration Information
147 |     disp(['Iteration ' num2str(it) ': Number of F1 Members = ' num2str(numel(F1))]);
148 |     
149 |     % Plot F1 Costs
150 |     figure(1);
151 |     PlotCosts(F1);
152 |     pause(0.01);
153 |     
154 | end
155 | 
156 | %% Results
157 | 
158 | 


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