可调节大功率充电机:基于遗传算法(GA)的多变量旅行商问题(TSP)

MTSPV_GA可变多个旅行商问题（M - TSP）遗传算法（GA）
  找到了（附近）的M - TSP的变化（即具有最佳的解决方案
  可变数量的推销员）设立GA在搜索
  的最短路径（最小距离为推销员需要前往
  每个城市一次，并返回其起始位置）

摘要：
    1。每个业务员一套独特的城市，并完成
       回城的路线，他开始从
    2。每个城市访问过的一个业务员

输入：
    XY（浮动）是一个城市位置的NX2矩阵，其中N是城市数量
    DMAT（浮动）是NxN的矩阵点的距离或成本点
    MIN_TOUR（标量整数）是任何推销员的最低游览长度
    POP_SIZE（标量整数）人口规模（应该是能被4整除）
    NUM_ITER（标量整数）是算法运行所需的迭代数
    如果真正SHOW_PROG（标量逻辑）显示GA进展
    SHOW_RES（标量逻辑）的GA结果显示，如果为true

输出：
    OPT_RTE（整型数组）是由算法发现的最佳途径
    OPT_BRK（整型数组）是路线破发点的名单（这些指定的指数
        到用来获取个人业务员路线路线）
    MIN_DIST（标浮动）由推销员走过的总距离

路由/断点详情：
    如果有10个城市和3个推销员，一个可能的途径/休息
    组合可能是：RTE = [5 6 9 1 4 2 8 10 3 7]，brks = [3 7]
    两者合计，这些代表的解决方案[5 6 9] [1 4 2 8] [10 3 7]
    指定为如下3推销员路线：
        。业务员1旅游城市5到6日至9日，回到5
        。业务员2旅游城市1至4日至2日至8回1
        。业务员3旅游城市10至3日至7回10


function varargout = mtspv_ga(xy,dmat,min_tour,pop_size,num_iter,show_prog,show_res)
% MTSPV_GA Variable Multiple Traveling Salesman Problem (M-TSP) Genetic Algorithm (GA)
%   Finds a (near) optimal solution to a variation of the M-TSP (that has a
%   variable number of salesmen) by setting up a GA to search for the
%   shortest route (least distance needed for the salesmen to travel to
%   each city exactly once and return to their starting locations)
%
% Summary:
%     1. Each salesman travels to a unique set of cities and completes the
%        route by returning to the city he started from
%     2. Each city is visited by exactly one salesman
%
% 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
%     MIN_TOUR (scalar integer) is the minimum tour length for any of the salesmen
%     POP_SIZE (scalar integer) is the size of the population (should be divisible by 4)
%     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 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);
%     min_tour = 3;
%     pop_size = 40;
%     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] = mtspv_ga(xy,dmat,min_tour,pop_size,num_iter,1,1);
%
% Author: Joseph Kirk
% Email: jdkirk630@gmail.com
% Release: 1.1
% Release Date: 9/21/08% 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
            min_tour = 3;
        case 3
            pop_size = 80;
        case 4
            num_iter = 5e3;
        case 5
            show_prog = 1;
        case 6
            show_res = 1;
        otherwise
    end
end% Verify Inputs
N = size(xy,1);
[nr,nc] = size(dmat);
if N ~= nr || N ~= nc
    error('Invalid XY or DMAT inputs!')
end
n = N;% Sanity Checks
min_tour = max(1,min(n,round(real(min_tour(1)))));
pop_size = max(8,8*ceil(pop_size(1)/8));
num_iter = max(1,round(real(num_iter(1))));
show_prog = logical(show_prog(1));
show_res = logical(show_res(1));% Initialize the Populations
pop_rte = zeros(pop_size,n); % population of routes
pop_brk = cell(pop_size,1);     % population of breaks
for k = 1:pop_size
    pop_rte(k,:) = randperm(n);
    pop_brk{k} = randbreak();
end
tmp_pop_rte = zeros(8,n);
tmp_pop_brk = cell(8,1);
new_pop_rte = zeros(pop_size,n);
new_pop_brk = cell(pop_size,1);% Select the Colors for the Plotted Routes
clr = hsv(floor(n/min_tour));% Run the GA
global_min = Inf;
total_dist = zeros(1,pop_size);
dist_history = zeros(1,num_iter);
if show_prog
    pfig = figure('Name','MTSPV_GA | Current Best Solution','Numbertitle','off');
end
for iter = 1:num_iter
    % Evaluate Each Population Member (Calculate Total Distance)
    for p = 1:pop_size
        d = 0;
        p_rte = pop_rte(p,:);
        p_brk = pop_brk{p};
        salesmen = length(p_brk)+1;
        rng = [[1 p_brk+1];[p_brk n]]';
        for s = 1:salesmen
            d = d + dmat(p_rte(rng(s,2)),p_rte(rng(s,1)));
            for k = rng(s,1):rng(s,2)-1
                d = d + dmat(p_rte(k),p_rte(k+1));
            end
        end
        total_dist(p) = d;
    end    % Find the Best Route in the Population
    [min_dist,index] = min(total_dist);
    dist_history(iter) = min_dist;
    if min_dist < global_min
        global_min = min_dist;
        opt_rte = pop_rte(index,:);
        opt_brk = pop_brk{index};
        salesmen = length(opt_brk)+1;
        rng = [[1 opt_brk+1];[opt_brk n]]';
        if show_prog
            % Plot the Best Route
            figure(pfig);
            for s = 1:salesmen
                rte = opt_rte([rng(s,1):rng(s,2) rng(s,1)]);
                plot(xy(rte,1),xy(rte,2),'.-','Color',clr(s,:));
                title(sprintf(['Total Distance = %1.4f, Salesmen = %d, ' ...
                    'Iterations = %d'],min_dist,salesmen,iter));
                hold on
            end
            hold off
        end
    end    % Genetic Algorithm Operators
    rand_grouping = randperm(pop_size);
    for p = 8:8:pop_size
        rtes = pop_rte(rand_grouping(p-7:p),:);
        brks = pop_brk(rand_grouping(p-7:p));
        dists = total_dist(rand_grouping(p-7:p));
        [ignore,idx] = min(dists);
        best_of_8_rte = rtes(idx,:);
        best_of_8_brk = brks{idx};
        rte_ins_pts = sort(ceil(n*rand(1,2)));
        I = rte_ins_pts(1);
        J = rte_ins_pts(2);
        for k = 1:8 % Generate New Solutions
            tmp_pop_rte(k,:) = best_of_8_rte;
            tmp_pop_brk{k} = best_of_8_brk;
            switch k
                case 2 % Flip
                    tmp_pop_rte(k,I:J) = fliplr(tmp_pop_rte(k,I:J));
                case 3 % Swap
                    tmp_pop_rte(k,[I J]) = tmp_pop_rte(k,[J I]);
                case 4 % Slide
                    tmp_pop_rte(k,I:J) = tmp_pop_rte(k,[I+1:J I]);
                case 5 % Change Breaks
                    tmp_pop_brk{k} = randbreak();
                case 6 % Flip, Change Breaks
                    tmp_pop_rte(k,I:J) = fliplr(tmp_pop_rte(k,I:J));
                    tmp_pop_brk{k} = randbreak();
                case 7 % Swap, Change Breaks
                    tmp_pop_rte(k,[I J]) = tmp_pop_rte(k,[J I]);
                    tmp_pop_brk{k} = randbreak();
                case 8 % Slide, Change Breaks
                    tmp_pop_rte(k,I:J) = tmp_pop_rte(k,[I+1:J I]);
                    tmp_pop_brk{k} = randbreak();
                otherwise % Do Nothing
            end
        end
        new_pop_rte(p-7:p,:) = tmp_pop_rte;
        new_pop_brk(p-7:p) = tmp_pop_brk;
    end
    pop_rte = new_pop_rte;
    pop_brk = new_pop_brk;
endif show_res
    % Plots
    figure('Name','MTSPV_GA | Results','Numbertitle','off');
    subplot(2,2,1);
    plot(xy(:,1),xy(:,2),'k.');
    title('City Locations');
    subplot(2,2,2);
    imagesc(dmat(opt_rte,opt_rte));
    title('Distance Matrix');
    salesmen = length(opt_brk)+1;
    subplot(2,2,3);
    rng = [[1 opt_brk+1];[opt_brk n]]';
    for s = 1:salesmen
        rte = opt_rte([rng(s,1):rng(s,2) rng(s,1)]);
        plot(xy(rte,1),xy(rte,2),'.-','Color',clr(s,:));
        title(sprintf('Total Distance = %1.4f',min_dist));
        hold on;
    end
    subplot(2,2,4);
    plot(dist_history,'b','LineWidth',2)
    title('Best Solution History');
    set(gca,'XLim',[0 num_iter+1],'YLim',[0 1.1*max([1 dist_history])]);
end% Return Outputs
if nargout
    varargout{1} = opt_rte;
    varargout{2} = opt_brk;
    varargout{3} = min_dist;
end    % Generate Random Set of Breaks
    function breaks = randbreak()
        salesmen = ceil(floor(n/min_tour)*rand);
        num_brks = salesmen - 1;
        dof = n - min_tour*salesmen;    % degrees of freedom
        addto = ones(1,dof+1);
        for kk = 2:num_brks
            addto = cumsum(addto);
        end
        cum_prob = cumsum(addto)/sum(addto);
        num_adjust = find(rand < cum_prob,1)-1;
        spaces = ceil(num_brks*rand(1,num_adjust));
        adjust = zeros(1,num_brks);
        for kk = 1:num_brks
            adjust(kk) = sum(spaces == kk);
        end
        breaks = min_tour*(1:num_brks) + cumsum(adjust);
    end
end