遗传算法求解M-TSP问题

function varargout = mtspf_ga(xy,dmat,salesmen,min_tour,pop_size,num_iter,show_prog,show_res)
% MTSPF_GA Fixed Multiple Traveling Salesmen Problem (M-TSP) Genetic Algorithm (GA)
%   Finds a (near) optimal solution to a variation of the M-TSP by setting
%   up a GA to search for the shortest route (least distance needed for
%   each salesman to travel from the start location to individual cities
%   and back to the original starting place)
%
% Summary:
%     1. Each salesman starts at the first point, and ends at the first
%        point, but travels to a unique set of cities in between
%     2. Except for the first, each city is visited by exactly one salesman
%
% Note: The Fixed Start/End location is taken to be the first XY point
%
% Input:
%     XY (float) is an Nx2 matrix of city locations, where N is the number of cities
%     DMAT (float) is an NxN matrix of city-to-city distances or costs
%     SALESMEN (scalar integer) is the number of salesmen to visit the cities
%     MIN_TOUR (scalar integer) is the minimum tour length for any of the
%         salesmen, NOT including the start/end point
%     POP_SIZE (scalar integer) is the size of the population (should be divisible by 8)
%     NUM_ITER (scalar integer) is the number of desired iterations for the algorithm to run
%     SHOW_PROG (scalar logical) shows the GA progress if true
%     SHOW_RES (scalar logical) shows the GA results if true
%
% Output:
%     OPT_RTE (integer array) is the best route found by the algorithm
%     OPT_BRK (integer array) is the list of route break points (these specify the indices
%         into the route used to obtain the individual salesman routes)
%     MIN_DIST (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 4 2 8 10 3 7], brks = [3 7]
%     Taken together, these represent the solution [1 5 6 9 1][1 4 2 8 1][1 10 3 7 1],
%     which designates the routes for the 3 salesmen as follows:
%         . Salesman 1 travels from city 1 to 5 to 6 to 9 and back to 1
%         . Salesman 2 travels from city 1 to 4 to 2 to 8 and back to 1
%         . Salesman 3 travels from city 1 to 10 to 3 to 7 and back to 1
%
% 2D Example:
%     n = 35;
%     xy = 10*rand(n,2);
%     salesmen = 5;
%     min_tour = 3;
%     pop_size = 80;
%     num_iter = 5e3;
%     a = meshgrid(1:n);
%     dmat = reshape(sqrt(sum((xy(a,:)-xy(a',:)).^2,2)),n,n);
%     [opt_rte,opt_brk,min_dist] = mtspf_ga(xy,dmat,salesmen,min_tour, ...
%         pop_size,num_iter,1,1);
%
% 3D Example:
%     n = 35;
%     xyz = 10*rand(n,3);
%     salesmen = 5;
%     min_tour = 3;
%     pop_size = 80;
%     num_iter = 5e3;
%     a = meshgrid(1:n);
%     dmat = reshape(sqrt(sum((xyz(a,:)-xyz(a',:)).^2,2)),n,n);
%     [opt_rte,opt_brk,min_dist] = mtspf_ga(xyz,dmat,salesmen,min_tour, ...
%         pop_size,num_iter,1,1);