超详细 | 差分进化算法原理及其实现(Matlab/Python)

function [best_y, best_x] = de_optim(objective_func, nvars, bounds, popsize, max_iter, display_progress)
    % 差分进化优化算法示例
    % objective_func: 目标函数句柄
    % nvars: 变量数量
    % bounds: 变量的上下界，例如: bounds = [lb, ub];
    % popsize: 种群大小
    % max_iter: 最大迭代次数
    % display_progress: 是否显示进度
 
    % 初始化种群和参数
    pop = initializega(nvars, popsize, bounds);
    F  = zeros(popsize, 1);
    CR = 0.7; % 交叉率
    F  = de_eval(pop, objective_func);
    [best_fit, best_index] = min(F);
    best_x = pop(:, best_index);
    best_y = best_fit;
 
    for t = 1:max_iter
        % 选择操作
        pop = select(pop, F);
        % 交叉操作
        pop = cross(pop, CR);
        % 变异操作
        pop = mut(pop, nvars, 0.1);
        % 评估新种群
        F = de_eval(pop, objective_func);
        % 更新最佳个体
        [best_fit, best_index] = min(F);
        best_x = pop(:, best_index);
        best_y = best_fit;
        if display_progress
            disp(['Iteration: ', num2str(t), ' Best Fitness: ', num2str(best_fit)]);
        end
    end
end
 
function pop = initializega(nvars, popsize, bounds)
    % 初始化种群
    pop = rand(nvars, popsize) * (bounds(:, 2) - bounds(:, 1)) + repmat(bounds(:, 1), nvars, 1);
end
 
function F = de_eval(pop, objective_func)
    % 评估种群
    [~, nvars] = size(pop);
    F = zeros(nvars, 1);
    for i = 1:nvars
        F(i) = objective_func(pop(:, i));
    end
end
 
function pop = select(pop, F)
    % 选择操作
    nvars = size(pop, 2);
    for i = 1:nvars
        if rand() < 0.9
            pop(:, i) = best(pop, F, i);
        end
    end
end
 
function pop = cross(pop, CR)
    % 交叉操作
    [~, nvars] = size(pop);
    for i = 1:2:nvars-1
        if rand() < CR
            r = randperm(nvars);
            pop(:, [i, i+1]) = pop(:, [r(1), r(2)]);
        end
    end
end
 
function pop = mut(pop, nvars, F)
    % 变异操作
    for i = 1:nvars
        if rand() < F
            r = randperm(nvars);
            pop(:, i) = pop(:, r(1));
        end
    end
end
 
function x = best(pop, F, index)
    % 返回当前最佳个体
    [~, nvars] = size(pop);
    best_index = find(F == min(F));
    if index ~= best_index
        x = pop(:, best_index);
    else
        x = pop(:, index);
    end
end

这个代码实例提供了一个简化的差分进化算法框架，包括初始化、选择、交叉和变异操作。在这个框架中，我们使用Matlab语言实现了一个简单的差分进化优化过程。这个例子展示了如何使用Matlab进行基本的差分进化优化，并