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⛄ 内容介绍
遗传算法(Genetic Algorithm,简称GA)是一种通过模拟自然进化过程来搜索最优解的启发式搜索算法.由于该算法具有内在的隐并行性,良好的全局寻优能力和较强的鲁棒性,所以被广泛用于求解复杂的组合优化问题,比如旅行商问题(Traveling salesman problem,TSP)和多旅行商问题(Multiple Traveling Salesman Problem,MTSP).TSP是经典的NP-hard组合优化问题,而MTSP是TSP的一种推广,相比TSP,MTSP具有更多的实际应用,但是研究成果却相对较少.
⛄ 部分代码
% Input:
% XY (float) is an Nx2 matrix of city locations, where N is the number of cities
% DMAT (float) is an NxN matrix of point to point distances or costs
% MINTOUR (scalar integer) is the minimum tour length for any of the salesmen
% POPSIZE (scalar integer) is the size of the population (should be divisible by 4)
% NUMITER (scalar integer) is the number of desired iterations for the algorithm to run
% SHOWPROG (scalar logical) shows the GA progress if true
% SHOWRESULT (scalar logical) shows the GA results if true
%
% Output:
% OPTROUTE (integer array) is the best route found by the algorithm
% OPTBREAK (integer array) is the list of route break points (these specify the indices
% into the route used to obtain the individual salesman routes)
% MINDIST (scalar float) is the total distance traveled by the salesmen
%
% Route/Breakpoint Details:
% If there are 10 cities and 3 salesmen, a possible route/break
% combination might be: rte = [5 6 9 1 4 2 8 10 3 7], brks = [3 7]
% Taken together, these represent the solution [5 6 9][1 4 2 8][10 3 7],
% which designates the routes for the 3 salesmen as follows:
% . Salesman 1 travels from city 5 to 6 to 9 and back to 5
% . Salesman 2 travels from city 1 to 4 to 2 to 8 and back to 1
% . Salesman 3 travels from city 10 to 3 to 7 and back to 10
%
% Example:
% n = 35;
% xy = 10*rand(n,2);
% minTour = 3;
% popSize = 40;
% numIter = 5e3;
% a = meshgrid(1:n);
% dmat = reshape(sqrt(sum((xy(a,:)-xy(a',:)).^2,2)),n,n);
% [optRoute,optBreak,minDist] = mtspv_ga(xy,dmat,minTour,popSize,numIter,1,1);
%
% Example:
% n = 50;
% phi = (sqrt(5)-1)/2;
% theta = 2*pi*phi*(0:n-1);
% rho = (1:n).^phi;
% [x,y] = pol2cart(theta(:),rho(:));
% xy = 10*([x y]-min([x;y]))/(max([x;y])-min([x;y]));
% minTour = 3;
% popSize = 40;
% numIter = 1e4;
% a = meshgrid(1:n);
% dmat = reshape(sqrt(sum((xy(a,:)-xy(a',:)).^2,2)),n,n);
% [optRoute,optBreak,minDist] = mtspv_ga(xy,dmat,minTour,popSize,numIter,1,1);
%
% Example:
% n = 35;
% xyz = 10*rand(n,3);
% minTour = 3;
% popSize = 40;
% numIter = 5e3;
% a = meshgrid(1:n);
% dmat = reshape(sqrt(sum((xyz(a,:)-xyz(a',:)).^2,2)),n,n);
% [optRoute,optBreak,minDist] = mtspv_ga(xyz,dmat,minTour,popSize,numIter,1,1);
%
% See also: mtsp_ga, mtspf_ga, mtspo_ga, mtspof_ga, mtspofs_ga, distmat
function varargout = mtspv_ga(xy,dmat,minTour,popSize,numIter,showProg,showResult)
% Process Inputs and Initialize Defaults
nargs = 7;
for k = nargin:nargs-1
switch k
case 0
xy = 10*rand(40,2);
case 1
N = size(xy,1);
a = meshgrid(1:N);
dmat = reshape(sqrt(sum((xy(a,:)-xy(a',:)).^2,2)),N,N);
case 2
minTour = 3;
case 3
popSize = 80;
case 4
numIter = 5e3;
case 5
showProg = 1;
case 6
showResult = 1;
otherwise
end
end
⛄ 运行结果
⛄ 参考文献
[1]温清芳. 遗传算法求解TSP问题的MATLAB实现[J]. 韶关学院学报, 2007, 28(6):5.
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