├── LICENSE ├── Readme.txt ├── cp.py ├── disc.py ├── elzinga_hearn.py ├── kmeans.py ├── simulated_annealing.py ├── teitz_bart.py ├── test_1center.py └── welzl.py /LICENSE: -------------------------------------------------------------------------------- 1 | GNU GENERAL PUBLIC LICENSE 2 | Version 3, 29 June 2007 3 | 4 | Copyright (C) 2007 Free Software Foundation, Inc. 5 | Everyone is permitted to copy and distribute verbatim copies 6 | of this license document, but changing it is not allowed. 7 | 8 | Preamble 9 | 10 | The GNU General Public License is a free, copyleft license for 11 | software and other kinds of works. 12 | 13 | The licenses for most software and other practical works are designed 14 | to take away your freedom to share and change the works. By contrast, 15 | the GNU General Public License is intended to guarantee your freedom to 16 | share and change all versions of a program--to make sure it remains free 17 | software for all its users. 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Of course, your program's commands 662 | might be different; for a GUI interface, you would use an "about box". 663 | 664 | You should also get your employer (if you work as a programmer) or school, 665 | if any, to sign a "copyright disclaimer" for the program, if necessary. 666 | For more information on this, and how to apply and follow the GNU GPL, see 667 | . 668 | 669 | The GNU General Public License does not permit incorporating your program 670 | into proprietary programs. If your program is a subroutine library, you 671 | may consider it more useful to permit linking proprietary applications with 672 | the library. If this is what you want to do, use the GNU Lesser General 673 | Public License instead of this License. But first, please read 674 | . 675 | -------------------------------------------------------------------------------- /Readme.txt: -------------------------------------------------------------------------------- 1 | This folder contains Python programs for some spatial 2 | optimization problems, including the p-median problem, 3 | 1-center problem, etc. 4 | 5 | -------------------------------------------------------------------------------- /cp.py: -------------------------------------------------------------------------------- 1 | from math import sqrt, atan2, fabs, pi 2 | from disc import * 3 | import sys 4 | sys.path.append('../geom') 5 | from point import * 6 | import random 7 | 8 | def get_angle(p0, p1, p2): 9 | """ 10 | Returns angle between line p0p1 and p0p2 (using 11 | directions: p0 -> p1, p0 -> p2) 12 | """ 13 | a1 = atan2(p1.y-p0.y, p1.x-p0.x) 14 | a2 = atan2(p2.y-p0.y, p2.x-p0.x) 15 | if a1 < 0: 16 | a1 = 2*pi - fabs(a1) 17 | if a2 < 0: 18 | a2 = 2*pi - fabs(a2) 19 | degree = fabs(a1-a2) 20 | if degree > pi: 21 | degree = 2*pi - degree; 22 | return degree; 23 | 24 | def find_mini_angle(S1, A, B, um): 25 | n = len(S1) 26 | angle = 100 27 | c = -1 28 | for i in xrange(n): 29 | if S1[i] == A or S1[i] == B: 30 | continue 31 | if not um[i]: 32 | continue 33 | angle1 = get_angle(S1[i], A, B) 34 | if angle1 < angle: 35 | angle = angle1 36 | c = i #D = S1[i] 37 | if angle1 < pi/2.0: 38 | continue 39 | um[i] = 0 40 | return angle, c 41 | 42 | def getfirsttwo(S): 43 | b = Point(0, 0) 44 | dist = 0 45 | ix = 0 46 | for i, p in enumerate(S): # farthest point from origin 47 | d1 = p.distance(b) 48 | if d1 > dist: 49 | dist = d1 50 | ix = i 51 | a = p 52 | dist = 0 53 | dd = sqrt(a.x*a.x+a.y*a.y) 54 | for i, p in enumerate(S): 55 | if i==ix: continue 56 | d1 = (a.x-p.x)*(a.x-p.x) + (a.y-p.y)*(a.y-p.y) 57 | d1 = d1*dd / fabs(a.x*(a.x-p.x) + a.y*(a.y-p.y)) 58 | if d1 > dist: 59 | dist = d1 60 | b = p 61 | iy = i 62 | return ix, iy 63 | 64 | def moveminimaxpoints(points): 65 | mini, maxi = getfirsttwo(points) 66 | # set minx to 0, maxx to 1 67 | if maxi != 0: 68 | points[0],points[mini] = points[mini], points[0] 69 | if mini != 1: 70 | points[1],points[maxi] = points[maxi], points[1] 71 | 72 | def onecenter1(P): 73 | n = len(P) 74 | unmarked = [1 for i in range(n)] 75 | done = False 76 | a = 0 77 | b = 1 78 | while not done: 79 | A, B = P[a], P[b] 80 | angle, c = find_mini_angle(P, A, B, unmarked) 81 | C = P[c] 82 | if angle > pi/2.0: 83 | done = True 84 | d = disc(points=[A, B]) 85 | elif get_angle(B, A, C) < pi/2.0 and\ 86 | get_angle(A, B, C) < pi/2.0: 87 | done = True 88 | d = disc(points=[A, B, C]) 89 | else: 90 | if (get_angle(B, A, C)) > pi/2.0: 91 | unmarked[b] = 0 92 | b = c 93 | else: 94 | unmarked[a] = 0 95 | a = c 96 | return d 97 | 98 | def test(): 99 | npts = 5 100 | points = [] 101 | for i in xrange(npts): 102 | p = Point(random.random(), random.random()) 103 | points.append(p) 104 | print points 105 | print onecenter1(points) 106 | moveminimaxpoints(points) 107 | print points 108 | print onecenter1(points) 109 | 110 | if __name__ == '__main__': 111 | test() 112 | -------------------------------------------------------------------------------- /disc.py: -------------------------------------------------------------------------------- 1 | from math import fabs, sqrt 2 | import sys 3 | 4 | sys.path.append('..') 5 | from geom.point import * 6 | 7 | __all__ = ['disc'] 8 | 9 | class disc: 10 | def __init__(self, center=None, radius=None, points=None): 11 | if points == None: 12 | self.center = center 13 | self.radius = radius 14 | else: 15 | if len(points)==2: 16 | res = make_disc2(points[0],points[1]) 17 | elif len(points)==3: 18 | res = make_disc(points[0],points[1],points[2]) 19 | else: 20 | res = [None, None] 21 | self.center = res[0] 22 | self.radius = res[1] 23 | def __eq__(self, other): 24 | return self.center==other.center and\ 25 | self.radius==other.radius 26 | def __repr__(self): 27 | return "({0}, {1})".format( 28 | self.center, self.radius) 29 | def inside(self, p): 30 | dx = fabs(self.center.x - p.x) 31 | dy = fabs(self.center.y - p.y) 32 | if dx>self.radius or dy>self.radius: 33 | return False 34 | if self.center.distance(p) <= self.radius: 35 | return True 36 | return False 37 | 38 | def make_disc2(p1, p2): 39 | dx = fabs(p1.x - p2.x) 40 | dy = fabs(p1.y - p2.y) 41 | radius = sqrt(dx*dx + dy*dy)/2.0 42 | x = min(p1.x, p2.x) + dx/2.0 43 | y = min(p1.y, p2.y) + dy/2.0 44 | return Point(x, y), radius 45 | 46 | def make_disc(p1, p2, p3): 47 | x1, x2, x3 = p1.x, p2.x, p3.x 48 | y1, y2, y3 = p1.y, p2.y, p3.y 49 | a = fabs(x2-x1) 50 | b = fabs(x3-x1) 51 | c = fabs((y2-y1)/a - (y3-y1)/b) 52 | xs = a 53 | if b < xs: 54 | xs = b 55 | if c < xs: 56 | xs = c 57 | a = fabs(y2-y1) 58 | b = fabs(y3-y1) 59 | c = fabs((x2-x1)/a - (x3-x1)/b) 60 | ys = a 61 | if b < ys: 62 | ys = b 63 | if c < ys: 64 | ys = c 65 | if xs < ys: # eliminate x, compute y first 66 | return make_disc_x(p1, p2, p3) 67 | else: 68 | return make_disc_y(p1, p2, p3) 69 | 70 | def make_disc_y(p1, p2, p3): 71 | x1 = p1.x 72 | x2 = p2.x 73 | x3 = p3.x 74 | y1 = p1.y 75 | y2 = p2.y 76 | y3 = p3.y 77 | t1 = (x1*x1-x3*x3+y1*y1-y3*y3)/(2*(x3-x1)) 78 | t2 = (x1*x1-x2*x2+y1*y1-y2*y2)/(2*(x2-x1)) 79 | t3 = (y2-y1)/(x2-x1) - (y3-y1)/(x3-x1) 80 | y = (t1 - t2)/t3 81 | x = -(2*(y2-y1)*y + x1*x1 - x2*x2 + y1*y1 - 82 | y2*y2) / (2*(x2-x1)) 83 | r = sqrt((x1-x)*(x1-x) + (y1-y)*(y1-y)) 84 | return Point(x, y), r 85 | 86 | def make_disc_x(p1, p2, p3): 87 | x1, x2, x3 = p1.x, p2.x, p3.x 88 | y1, y2, y3 = p1.y, p2.y, p3.y 89 | t1 = (x1*x1-x3*x3+y1*y1-y3*y3)/(2*(y3-y1)) 90 | t2 = (x1*x1-x2*x2+y1*y1-y2*y2)/(2*(y2-y1)) 91 | t3 = (x2-x1)/(y2-y1) - (x3-x1)/(y3-y1) 92 | x = (t1 - t2)/t3 93 | y = -(2*(x2-x1)*x + x1*x1 - x2*x2 + y1*y1 - 94 | y2*y2) / (2*(y2-y1)) 95 | r = sqrt((x1-x)*(x1-x) + (y1-y)*(y1-y)) 96 | return Point(x, y), r 97 | -------------------------------------------------------------------------------- /elzinga_hearn.py: -------------------------------------------------------------------------------- 1 | from math import pi 2 | import random 3 | from disc import * 4 | import sys 5 | sys.path.append('../geom') 6 | from point import * 7 | from cp import get_angle 8 | 9 | def right_obtuse_triangle(p3): 10 | """ 11 | if true, set p3[0] and p3[1] to define the longest edge 12 | and p3[2] is on the angle >= 90 13 | """ 14 | angle0 = get_angle(p3[0], p3[1], p3[2]) 15 | angle1 = get_angle(p3[1], p3[0], p3[2]) 16 | angle2 = pi - angle0 - angle1 17 | maxa = -1.0 18 | maxi = -1 19 | for i, a in enumerate([angle0, angle1, angle2]): 20 | if a > maxa: 21 | maxa = a 22 | maxi = i 23 | if maxa >= pi/2.0: 24 | if maxi != 2: 25 | p3[maxi], p3[2] = p3[2], p3[maxi] 26 | return True 27 | return False 28 | 29 | def find_three(p3, D, d): 30 | """ 31 | Given three points in p3, an outside point D, and the 32 | disc d, find A, C, D and assign them to p3[0], p3[1], 33 | and p3[2], respectively 34 | """ 35 | maxd = 0 36 | for i in range(len(p3)): 37 | tmpd = p3[i].distance(D) 38 | if tmpd > maxd: 39 | maxd = tmpd 40 | iA = i 41 | x1 = p3[iA].x 42 | x2 = d.center.x 43 | y1 = p3[iA].y 44 | y2 = d.center.y 45 | a = y2-y1 46 | b = -(x2-x1) 47 | c = (x2-x1)*y1 - (y2-y1)*x1 48 | eqd = a*D.x + b*D.y + c 49 | positive = eqd > 0 50 | eq = [0 for i in range(3)] 51 | iC = -1 52 | for i in range(3): 53 | if i==iA: 54 | eq[i] = 0.0 55 | else: 56 | eq[i] = a*p3[i].x + b*p3[i].y + c 57 | if positive != ((eq[i]>0)): 58 | iC = i 59 | if iC == -1: 60 | tempf = 100000000.0 61 | for i in range(3): 62 | if i == iA: 63 | continue; 64 | if fabs(eq[i]) < tempf: 65 | tempf = fabs(eq[i]) 66 | iC = i 67 | p3[0], p3[1], p3[2] = p3[iA], p3[iC], D 68 | return 69 | 70 | def cover_all(points, d, pp): 71 | for p in points: 72 | if p in pp: # handle precision in float numbers 73 | continue 74 | if not d.inside(p): 75 | return False, p 76 | return True, None 77 | 78 | def onecenter2(P): 79 | p3 = [Point(-1, -1) for i in range(3)] 80 | p3[0] = P[0] 81 | p3[1] = P[1] 82 | d = disc(points=[p3[0], p3[1]]) 83 | n = len(P) 84 | cnt = 0 85 | stop, p3[2] = cover_all(P, d, p3[:2]) 86 | while not stop: 87 | if right_obtuse_triangle(p3): # right/obtuse triangle 88 | d = disc(points=[p3[0], p3[1]]) 89 | stop, p3[2] = cover_all(P, d, p3[:2]) 90 | else: # strict acute triangle 91 | d = disc(points=[p3[0], p3[1], p3[2]]) 92 | stop, pd = cover_all(P, d, p3) # pd outside d 93 | if not stop: 94 | find_three(p3, pd, d) 95 | cnt += 1 96 | return d 97 | 98 | def test(): 99 | npts = 50 100 | points = [] 101 | for i in xrange(npts): 102 | p = Point(random.random(), random.random()) 103 | points.append(p) 104 | print onecenter2(points) 105 | 106 | if __name__ == '__main__': 107 | test() 108 | -------------------------------------------------------------------------------- /kmeans.py: -------------------------------------------------------------------------------- 1 | """ 2 | k-means 3 | 4 | History 5 | December 2, 2017 6 | Use exception to check initialization method 7 | Tried kd tree, with no improvement in computing time 8 | (tree construction takes too much time) 9 | 10 | December 4, 2016 11 | verbose option in kmeans 12 | 13 | November 29, 2016 14 | import geom.point 15 | comments added 16 | 17 | Contact: 18 | Ningchuan Xiao 19 | The Ohio State University 20 | Columbus, OH 21 | """ 22 | 23 | __author__ = "Ningchuan Xiao " 24 | 25 | from random import random, sample, uniform 26 | from math import fabs, sqrt 27 | 28 | import os, sys 29 | lib_path = os.path.abspath('../') 30 | sys.path.insert(0, lib_path) 31 | from geom.point import * 32 | 33 | INF = float('inf') 34 | 35 | def clustering_dist(points, means): 36 | """ 37 | Computing distances for the k-means 38 | 39 | Input 40 | points: list of Point objects 41 | means: list of k points that serve as the means 42 | 43 | Output 44 | nearests: list of lists, where each inner list holds the 45 | id of nearest points to each mean 46 | totaldist: average distances between each point to its nearest mean 47 | """ 48 | n = len(points) 49 | k = len(means) 50 | nearests = [[] for i in range(k)] 51 | totaldist = 0 52 | for i in range(n): 53 | dmin = INF 54 | for j in range(k): 55 | d = points[i].distance(means[j]) 56 | if d < dmin: 57 | dmin = d 58 | jmin = j 59 | totaldist += dmin 60 | nearests[jmin].append(i) 61 | totaldist = totaldist/n 62 | return nearests, totaldist 63 | 64 | def initk(points, k, init): 65 | """ 66 | Initialization for k-means 67 | 68 | Input 69 | points: list of Point objects 70 | k: integer 71 | init: initialization method ('forgy' or 'random') 72 | 73 | Output 74 | means: list of k Point objects 75 | nearests: list of lists, where each inner list holds the 76 | id of nearest points to each mean 77 | totaldist: average distances between each point to its nearest mean 78 | """ 79 | n = len(points) 80 | xmin = INF 81 | ymin = INF 82 | xmax = -INF 83 | ymax = -INF 84 | for p in points: 85 | xmin = min([xmin, p.x]) 86 | ymin = min([ymin, p.y]) 87 | xmax = max([xmax, p.x]) 88 | ymax = max([ymax, p.y]) 89 | nearests = [[] for i in range(k)] 90 | while [] in nearests: # until not empty sets in nearests 91 | if init=="forgy": # Forgy initialization 92 | means = [points[i] for i in sample(range(n), k)] 93 | elif init=="random": 94 | means = [ Point(uniform(xmin, xmax), uniform(ymin, ymax)) for i in range(k) ] 95 | else: 96 | raise Exception("kmeans: unknown initialization method") 97 | nearests, totaldist = clustering_dist(points, means) 98 | return means, nearests, totaldist 99 | 100 | def kmeans(points, k, threshold=1e-5, init="forgy", verbose=False): 101 | """ 102 | Input 103 | points: list of Point objects 104 | k: integer, the number of means 105 | threshould: minimal improvement between iterations 106 | init: initialization method ('forgy' or 'random') 107 | verbose: if True, print intermediate result 108 | 109 | Output 110 | totaldist: average distances between each point to its nearest mean 111 | means: list of k Point objects 112 | """ 113 | bigdiff = True 114 | means, nearests, totaldist = initk(points, k, init) 115 | if verbose: 116 | print(means) 117 | while bigdiff: 118 | means2 = [] 119 | for j in range(k): 120 | cluster = [xx for xx in nearests[j]] 121 | sumx = sum([points[ii].x for ii in cluster]) 122 | sumy = sum([points[ii].y for ii in cluster]) 123 | numpts = len(nearests[j]) 124 | if numpts>0: 125 | sumx = sumx/numpts 126 | sumy = sumy/numpts 127 | means2.append(Point(sumx, sumy)) 128 | nearests, newtotal = clustering_dist(points, means2) 129 | offset = totaldist - newtotal 130 | if offset > threshold: 131 | means = means2 132 | totaldist = newtotal 133 | if verbose: 134 | print(means) 135 | else: 136 | bigdiff = False 137 | return totaldist, means 138 | 139 | def test(): 140 | n = 5000 141 | points1 = [ Point(random(), random()) for i in range(n) ] 142 | 143 | points2 = [ Point(uniform(10, 20), uniform(10, 20)) for i in range(n//2) ] + [ Point(uniform(30, 40), uniform(30, 40)) for i in range(n//2) ] 144 | 145 | points3 = [ Point(uniform(10, 20), uniform(10, 20)) for i in range(n//3) ] + [ Point(uniform(30, 40), uniform(10, 20)) for i in range(n//3) ] + [ Point(uniform(20, 30), uniform(30, 40)) for i in range(n//3) ] 146 | 147 | import time 148 | t1 = time.time() 149 | print(kmeans(points1, 10, init="forgy")[0]) 150 | print(kmeans(points2, 2)[0]) 151 | print(kmeans(points3, 3)[0]) 152 | print(kmeans(points3, 3, init="random")[0]) 153 | t2 = time.time() 154 | 155 | print('Time:', t2-t1, 'seconds') 156 | 157 | if __name__ == "__main__": 158 | test() 159 | -------------------------------------------------------------------------------- /simulated_annealing.py: -------------------------------------------------------------------------------- 1 | """ 2 | A simulated annealing algorithm for the p-median problem 3 | 4 | History 5 | November 17, 2016 6 | moved some imports to the __main__ part of the code 7 | 8 | Contact: 9 | Ningchuan Xiao 10 | The Ohio State University 11 | Columbus, OH 12 | """ 13 | 14 | __author__ = "Ningchuan Xiao " 15 | 16 | import math 17 | import random 18 | from copy import deepcopy 19 | from teitz_bart import update_assignment 20 | 21 | INF = float('inf') 22 | 23 | def evaluate(dist, median, p, N): 24 | sumdist = 0.0 25 | for i in range(N): 26 | dist0 = INF 27 | for j in range(p): 28 | if dist[i][median[j]] < dist0: 29 | dist0 = dist[i][median[j]] 30 | sumdist += dist0 31 | return sumdist 32 | 33 | # test replacing fr with fi in median without reallocating 34 | # all the nodes 35 | def test_replacement(fi, fr, dist, d1, d2, p, N): 36 | total = 0.0 37 | for i in range(N): 38 | if dist[i][fi]dthreshold or i in median: 80 | continue 81 | if random.random() > 0.67: 82 | continue 83 | r1 = test_replacement(i, median[j], dist, d1, d2, p, N) 84 | if r1 < r_min_temp: 85 | r_min_temp = r1 86 | fi_temp = i 87 | if r_min_temp < r_min: 88 | r_min = r_min_temp 89 | fi = fi_temp 90 | fr = j 91 | return r_min, fi, fr 92 | 93 | def next(r, T, median, dist, d1, d2, p, N, 94 | dthreshold, neighbormethod): 95 | r1 = r 96 | if neighbormethod == 0: 97 | r_min, fi, fr = bestGeoNeighbor(median, dist, d1, d2, N, p, dthreshold) 98 | test = acceptable(10*(r_min-r)/r, T) 99 | if test[0] > 0: 100 | median[fr] = fi 101 | r1 = update_assignment(dist, median,d1,d2,p,N) 102 | return test[0], r1, median 103 | else: 104 | r_min, candidate = bestRandomNeighbor(median, dist, N, p) 105 | test = acceptable(10*(r_min-r)/r, T) 106 | if test[0] > 0: 107 | median = candidate 108 | r1 = update_assignment(dist, median, d1, d2, p, N) 109 | return test[0], r1, median 110 | 111 | def acceptable(delta, T): 112 | if delta<0: # better solution 113 | return 1, 1 114 | if delta==0: # same solution, no change 115 | return 0, 0 116 | prob = math.exp(-delta/T) 117 | if random.random() < prob: # worse solution, accept 118 | return 2, prob 119 | return 0, prob # worse solution, reject 120 | 121 | def simulated_annealing(dist, p, neighbormethod=0, verbose=False): 122 | N = len(dist) 123 | dmax = max([max(dist[i]) for i in range(N)]) 124 | dthreshold = dmax/2 125 | d1 = [-1 for i in range(N)] 126 | d2 = [-1 for i in range(N)] 127 | 128 | ## Initialization 129 | median = random.sample(range(N), p) 130 | r = update_assignment(dist, median, d1, d2, p , N) 131 | first = [deepcopy(r), deepcopy(median)] 132 | best = [r, median] 133 | if verbose: print first[0] 134 | 135 | accepted_same = 0 136 | T = 100.0 137 | while True: 138 | result = next(r, T, median, dist, d1, d2, p, N, 139 | dthreshold, neighbormethod) 140 | if result[0]>0: 141 | r = result[1] 142 | if r < best[0]: 143 | best = [r, deepcopy(result[2])] 144 | accepted_same = 0 145 | if result[0]==2: 146 | accepted_same += 1 147 | if r == best[0] and accepted_same > 2: 148 | break 149 | T = 0.9*T 150 | if verbose: 151 | print r 152 | if result[0] == 2: 153 | print '*', 154 | print median 155 | else: break 156 | return first, best 157 | 158 | if __name__ == "__main__": 159 | import sys 160 | sys.path.append('../networks') 161 | from network2listmatrix import network2distancematrix 162 | from allpairdist import allpairs 163 | print 'Problem: simple network' 164 | a = network2distancematrix('../data/network-links', True) 165 | allpairs(a) 166 | result = simulated_annealing(a, 2, verbose=True) 167 | print result[0][0], result[1][0] 168 | 169 | print 'Problem: pmed1 in OR-lib' 170 | a = network2distancematrix('../data/orlib/pmed1.orlib', False) 171 | allpairs(a) 172 | result = simulated_annealing(a, 5, verbose=True) 173 | print result[0][0], result[1][0] 174 | -------------------------------------------------------------------------------- /teitz_bart.py: -------------------------------------------------------------------------------- 1 | """ 2 | Teitz-Bart algorithm for the p-median problem 3 | 4 | History 5 | November 29, 2016 6 | clean up comments 7 | 8 | November 17, 2016 9 | moved some imports to the __main__ part of the code 10 | 11 | Contact: 12 | Ningchuan Xiao 13 | The Ohio State University 14 | Columbus, OH 15 | """ 16 | 17 | __author__ = "Ningchuan Xiao " 18 | 19 | import random 20 | 21 | INF = float('inf') 22 | 23 | def findout(median, fi, dist, d1, d2, N): 24 | """ 25 | Determines, given a candidate for insertion (fi), 26 | the best candidate in the solution to replace or remove (fr). 27 | 28 | INPUT 29 | median: list of integers for selected vertices 30 | fi: candidate none-selected vertex 31 | dist: distance matrix 32 | d1: list of nearest facility for each vertex 33 | d2: list of second nearest facility 34 | N: number of vertices on the network 35 | 36 | OUTPUT 37 | fmin: gain 38 | fr: vertex to be replaced 39 | 40 | This function does not change values in median, d1, and d2. 41 | """ 42 | w = 0.0 43 | v = [0.0 for i in range(N)] 44 | for i in range(N): 45 | if dist[i][fi] < dist[i][d1[i]]: 46 | w += dist[i][d1[i]] - dist[i][fi] 47 | else: 48 | v[d1[i]] += min(dist[i][fi], 49 | dist[i][d2[i]]) - dist[i][d1[i]] 50 | fmin = INF 51 | fr = 0 52 | for i in median: 53 | if v[i] < fmin: 54 | fmin = v[i] 55 | fr = i 56 | fmin = w-fmin 57 | return fmin, fr # gain and vertex to be replaced 58 | 59 | def update_assignment(dist, median, d1, d2, p, N): 60 | """ 61 | Updates d1 and d2 given median so that d1 holds the 62 | nearest facility for each node and d2 holds the second 63 | 64 | INPUT 65 | dist: distance matrix 66 | median: list of integers for selected vertices 67 | d1: list of nearest facility for each vertex 68 | d2: list of second nearest facility 69 | p: number of facilities to locate 70 | N: number of vertices on the network 71 | 72 | OUTPUT 73 | dist1: total distance 74 | 75 | Also will update d1 and d2 76 | """ 77 | dist1, dist2 = 0.0, 0.0 78 | node1, node2 = -1, -1 79 | for i in range(N): 80 | dist1, dist2 = INF, INF 81 | for j in range(p): 82 | if dist[i][median[j]] < dist1: 83 | dist2 = dist1 84 | node2 = node1 85 | dist1 = dist[i][median[j]] 86 | node1 = median[j] 87 | elif dist[i][median[j]] < dist2: 88 | dist2 = dist[i][median[j]] 89 | node2 = median[j] 90 | d1[i] = node1 91 | d2[i] = node2 92 | dist1 = 0 93 | for i in range(N): 94 | dist1 += dist[i][d1[i]] 95 | return dist1 96 | 97 | def next(dist, median, d1, d2, p, N): 98 | """ 99 | INPUT 100 | dist: distance matrix 101 | median: list of integers for selected vertices 102 | d1: list of nearest facility for each vertex 103 | d2: list of second nearest facility 104 | p: number of facilities to locate 105 | N: number of vertices on the network 106 | 107 | OUTPUT 108 | T/F: True if positive gain, False otherwise 109 | r: total distance 110 | fr: vertex replaced 111 | fi: new vertex inserted into the current solution 112 | 113 | Note: this function may change median, d1, and d2 114 | """ 115 | bestgain = -INF 116 | for i in range(N): 117 | gain, fr1 = findout(median, i, dist, d1, d2, N) 118 | if i in median: 119 | continue 120 | if gain>bestgain: 121 | bestgain = gain 122 | fr = fr1 123 | fi = i 124 | r = 0 125 | if bestgain > 0: 126 | i = median.index(fr) 127 | median[i] = fi 128 | r = update_assignment(dist, median, d1, d2, p, N) 129 | return bestgain>0, r, fr, fi 130 | 131 | def teitz_bart(dist, p, verbose=False): 132 | """ 133 | INPUT 134 | dist: distance matrix 135 | p: number of facilities to be selected 136 | verbose: whether intermediate results are printed 137 | 138 | OUTPUT 139 | r: total distance 140 | median: vertices selected for the solution 141 | """ 142 | N = len(dist) 143 | median = random.sample(range(N), p) 144 | d1 = [-1 for i in range(N)] 145 | d2 = [-1 for i in range(N)] 146 | r = update_assignment(dist, median, d1, d2, p , N) 147 | if verbose: print(r) 148 | while True: 149 | result = next(dist, median, d1, d2, p, N) 150 | if result[0]: 151 | r = result[1] 152 | if verbose: print(r) 153 | else: 154 | break 155 | return r, median 156 | 157 | if __name__ == "__main__": 158 | import sys 159 | sys.path.append('../networks') 160 | from network2listmatrix import network2distancematrix 161 | from allpairdist import allpairs 162 | print('Problem: simple network') 163 | a = network2distancematrix('../data/network-links', True) 164 | allpairs(a) 165 | teitz_bart(a, 2, True) 166 | print('Problem: pmed1 in OR-lib') 167 | a = network2distancematrix('../data/orlib/pmed1.orlib', False) 168 | allpairs(a) 169 | teitz_bart(a, 5, True) 170 | -------------------------------------------------------------------------------- /test_1center.py: -------------------------------------------------------------------------------- 1 | from elzinga_hearn import * 2 | from welzl import * 3 | from cp import * 4 | 5 | import time 6 | 7 | n = 50000 8 | points = [ Point(random.random(), random.random()) 9 | for i in range(n) ] 10 | 11 | ######################################## 12 | # 13 | # Test performance using random start 14 | # 15 | ######################################## 16 | 17 | time1 = time.time() 18 | d1 = minidisc(points) 19 | time2 = time.time() 20 | d1t = time2-time1 21 | 22 | d2 = onecenter2(points) 23 | time3 = time.time() 24 | d2t = time3-time2 25 | 26 | d3 = onecenter1(points) 27 | time4 = time.time() 28 | d3t = time4-time3 29 | 30 | print "Welzl ", d1t, d1 31 | print "Elzinga-Hearn ", d2t, d2 32 | print "Chrystal-Peirce ", d3t, d3 33 | 34 | ######################################## 35 | # 36 | # Test performance after data preparation 37 | # 38 | ######################################## 39 | 40 | time0 = time.time() 41 | moveminimaxpoints(points) 42 | 43 | time1 = time.time() 44 | d1 = minidisc(points) 45 | time2 = time.time() 46 | d1t = time2-time1 47 | 48 | d2 = onecenter2(points) 49 | time3 = time.time() 50 | d2t = time3-time2 51 | 52 | d3 = onecenter1(points) 53 | time4 = time.time() 54 | d3t = time4-time3 55 | 56 | print "Data preparation", time1-time0 57 | 58 | print "Welzl ", d1t, d1 59 | print "Elzinga-Hearn ", d2t, d2 60 | print "Chrystal-Peirce ", d3t, d3 61 | -------------------------------------------------------------------------------- /welzl.py: -------------------------------------------------------------------------------- 1 | import random 2 | import sys 3 | sys.path.append('..') 4 | from optimization.disc import * 5 | from geom.point import * 6 | 7 | def minidiscwith2points(P, q1, q2, D): 8 | D[0] = disc(points = [q1, q2]) 9 | n = len(P) 10 | for k in range(n): 11 | if D[k].inside(P[k]): 12 | D[k+1] = D[k] 13 | else: 14 | D[k+1] = disc(points=[q1, q2, P[k]]) 15 | return D[n] 16 | 17 | def minidiscwithpoint(P, q, D): 18 | D[0] = disc(points = [P[0], q]) 19 | n = len(P) 20 | for j in range(1, n): 21 | if D[j-1].inside(P[j]): 22 | D[j] = D[j-1] 23 | else: 24 | D[j] = minidiscwith2points(P[:j], P[j], q, D) 25 | return D[n-1] 26 | 27 | def minidisc(P, verbose=False): 28 | n = len(P) 29 | D = [ disc() for i in range(n)] 30 | D[1] = disc(points=[P[0], P[1]]) 31 | for i in range(2, n): 32 | if verbose: 33 | very_simple_progress_bar(i, n) 34 | if D[i-1].inside(P[i]): 35 | D[i] = D[i-1] 36 | else: 37 | D[i] = minidiscwithpoint(P[:i], P[i], D) 38 | return D[n-1] 39 | 40 | 41 | def very_simple_progress_bar(current, upper, size=20): 42 | ''' 43 | current an integer indicating the current step 44 | upper an integer indicating the number of iterations 45 | size the length of the progress bar 46 | 47 | we assume the lower end is zero. 48 | ''' 49 | barx = int(size*(current+1)/upper) 50 | print('\r[{}{}] {}/{}'.format('x'*barx, '-'*(size-barx), current+1, upper), end='', flush=True) 51 | 52 | def test(n=5): 53 | points = [Point(random.random(), random.random()) for _ in range(n)] 54 | print(points) 55 | res = minidisc(points, True) 56 | print(res) 57 | 58 | if __name__ == '__main__': 59 | test() 60 | 61 | --------------------------------------------------------------------------------