差分进化算法(DE)求函数最小值

function z = calobj (pop)% 计算目标函数值% pop       input  种群% z         output 目标函数值z = 3 * cos(pop(:,1) .* pop(:,2)) + pop(:,1) + pop(:,2);end

function pop = initpop(popsize, chromlength, xl, xu)% 生成初始种群% popsize           input  种群规模% chromlengt        input  染色体长度% xl                input  x下限% xu                input  x上限% pop               output 种群pop = rand(popsize, chromlength) * (xu - xl) + xl;end

function mutationpop = mutation (pop, F)% 变异操作% pop           input  种群% F             input  缩放因子% mutationpop   output 变异后种群[popsize, chromlength] = size(pop);mutationpop = zeros(popsize, chromlength);for i = 1:popsize    % 取3个互异的索引 r0 r1 r2
    r = randperm(popsize);
    index = find (r ~= i);
    rn = r(index(1:3));
    r0 = rn(1); r1 = rn(2); r2 = rn(3);%     fprintf('i = %d, r0 = %d, r1 = %d, r2 = %d\n', i, r0, r1, r2);

    mutationpop(i,:) = pop(r0,:) + F .* (pop(r1,:) - pop(r2,:));endend

function crossoverpop = crossover(pop, mpop, cr)% 交叉% pop           input  种群% mpop          input  变异后的种群% cr            input  交叉概率% crossoverpop  output 交叉后的种群[popsize, chromlength] = size(pop);crossoverpop = mpop;r = rand(popsize, chromlength);index = find (r > cr);crossoverpop(index) = pop(index);jrand = randi(chromlength, 1, popsize);crossoverpop(sub2ind(size(crossoverpop), [1:popsize], jrand)) ...
    = mpop(sub2ind(size(mpop), [1:popsize], jrand));end

function newpop = constrictboundary(pop, xl, xu)% 约束边界（边界吸收）% pop       input  种群% xl        input  自变量最小值（包含）% xu        input  自变量最大值（包含）% newpop    output 约束边界后的种群newpop = pop;newpop(newpop < xl) = xl;newpop(newpop > xu) = xu;end

function newpop = selection(pop, npop)% 选择（小值优化）% pop           input  种群1（原始种群）% pop           input  种群2（变异-交叉种群）% newpop        output 选择后的种群newpop = pop;index = find(calobj(npop) <= calobj(pop));newpop(index, :) = npop(index, :);end

clc;clear;NP  = 20;       % 种群规模D   = 2;        % 参数个数G   = 30;       % 最大进化代数F   = 0.5;      % 缩放因子Cr  = 0.8;      % 交叉因子xl  = -4;       % x下限（也是y下限）xu  = 4;        % x上限（也是y上限）bestvalue = zeros(3, G);% 优化gen = 0;pop = initpop(NP, D, xl, xu);objvalue = calobj(pop);while gen < G
    mpop = mutation(pop, F);                    % 变异
    cpop = crossover(pop, mpop, Cr);            % 交叉
    cpop = constrictboundary(cpop, xl, xu);     % 约束边界
    pop = selection(pop, cpop);                 % 选择
    objvalue = calobj(pop);
    gen = gen + 1;

    % 记录最优
    [~, index] = min(objvalue);
    bestvalue(1:2, gen) = pop(index,:)';
    bestvalue(3,gen) = objvalue(index);endfprintf('bestX = %f, bestY = %f, bestZ = %f\n', ...
    bestvalue(1,end), bestvalue(2,end), bestvalue(3,end));% 绘图figure(1);x = [-4:0.1:4]; y = [-4:0.1:4];[X, Y] = meshgrid(x, y);Z = 3 * cos(X .* Y) + X + Y;surf(X, Y, Z);hold on;scatter3(bestvalue(1,:), bestvalue(2,:), bestvalue(3,:), ...
    'MarkerEdgeColor','k', 'MarkerFaceColor',[0 .75 .75]);xlabel('x'); ylabel('y'); zlabel('z'); title('函数图');hold off;figure(2);plot(bestvalue(3,:));xlabel('进化代数'); ylabel('最优目标函数值'); title('目标函数值变化图');