带约束的PSO算法的matlab代码

下面是一段使用带约束的PSO算法解决有约束的优化问题的 MATLAB 代码示例：

% 定义适应度函数
function f = fitness(x)
    % 目标函数
    f = x(1)^2 + x(2)^2;
    % 约束条件
    g1 = x(1) + x(2) - 2;
    g2 = -x(1) - x(2) - 2;
    % 惩罚项
    penalty = max(0, g1)^2 + max(0, g2)^2;
    % 计算适应度函数值
    f = f + penalty;
end

% 定义带约束的PSO算法
function [gbest, gbest_fitness] = cpspso(fitness, n, max_iter, xmin, xmax, v_max, c1, c2, w)
    % 初始化粒子群
    x = rand(n, length(xmin)) .* (xmax - xmin) + xmin;
    v = rand(n, length(xmin)) .* (2 * v_max) - v_max;
    pbest = x;
    pbest_fitness = arrayfun(fitness, pbest);
    [gbest_fitness, gbest_index] = min(pbest_fitness);
    gbest = pbest(gbest_index, :);
    % 迭代更新粒子
    for i = 1:max_iter
        % 更新粒子速度和位置
        v = w * v + c1 * rand(n, length(xmin)) .* (pbest - x) + c2 * rand(n, length(xmin)) .* (gbest - x);
        x = x + v;
        % 修正不满足约束条件的粒子
        for j = 1:n
            for k = 1:length(xmin)
                if x(j, k) > xmax(k)
                    x(j, k) = xmax(k);
                    v(j, k) = -v_max(k);
                end
                if x(j, k) < xmin(k)
                    x(j, k) = xmin(k);
                    v(j, k) = v_max(k);
                end
            end
        end
        % 更新粒子的最优解和全局最优解
        pbest_fitness_new = arrayfun(fitness, pbest);
        update = find(pbest_fitness_new < pbest_fitness);
        pbest(update, :) = x(update, :);
        pbest_fitness(update) = pbest_fitness_new(update);
        [gbest_fitness_new, gbest_index_new] = min(pbest_fitness);
        if gbest_fitness_new < gbest_fitness
            gbest = pbest(gbest_index_new, :);
            gbest_fitness = gbest_fitness_new;
        end
        % 输出迭代结果
        fprintf('Iteration: %d, GBest Fitness: %f\n', i, gbest_fitness);
    end
end

% 测试带约束的PSO算法
xmin = [-5, -5];
xmax = [5, 5];
n = 50;
max_iter = 100;
v_max = 0.5 .* (xmax - xmin);
c1 = 2;
c2 = 2;
w = 0.7;
[gbest, gbest_fitness] = cpspso(@fitness, n, max_iter, xmin, xmax, v_max, c1, c2, w);
fprintf('Optimal Solution: (%f, %f)\n', gbest(1), gbest(2));
fprintf('Optimal Fitness: %f\n', gbest_fitness);

在上述代码中，我们使用了带约束的PSO算法来解决一个有约束的优化问题，其中目标函数为x1^2 + x2^2，约束条件为x1 + x2 <= 2和-x1 - x2 <= 2。我们在算法中使用了惩罚项来惩罚不满足约束条件的解，并使用了修正方式将粒子的位置限制在合法范围内。最终，我们得到了最优解和最优适应度函数值。