利用梯度下降算法对PSO进行优化.zip

% 定义一个粒子群优化（PSO）算法函数 % 输入参数包括问题实例、粒子群大小、最大迭代次数 % 输出最优位置与最优适应度 function [bestPosition, bestFitness] = PSO(problem, swarmSize, maxIterations, inertiaWeight_out, cognitiveWeight_out, socialWeight_out) global inertiaWeight cognitiveWeight socialWeight; inertiaWeight = inertiaWeight_out; cognitiveWeight = cognitiveWeight_out; socialWeight = socialWeight_out; % 初始化粒子群 swarm = initializeSwarm(problem, swarmSize); % 初始化最佳位置和最佳适应度 [bestFitness, site] = min(swarm(1).fitness); bestPosition = swarm(site).position; % 主循环 for iteration = 1:maxIterations % 更新粒子的位置和速度 swarm = updateParticles(swarm, bestPosition,problem); % 评估每个粒子的适应度 swarm = evaluateFitness(swarm, problem); % 更新最佳位置和适应度 for i = 1:swarmSize if swarm(i).fitness < bestFitness bestPosition = swarm(i).position; bestFitness = swarm(i).fitness; end end end end % 初始化粒子群 function swarm = initializeSwarm(problem, swarmSize) swarm(swarmSize) = struct('position', [], 'velocity', [], 'fitness', [], 'bestPosition', [], 'bestFitness', []); for i = 1:swarmSize % 随机生成粒子的初始位置 swarm(i).position = rand(1, problem.dimension) .* (problem.upperBound - problem.lowerBound) + problem.lowerBound; swarm(i).bestPosition = swarm(i).position; % 初始化粒子的速度为零向量 swarm(i).velocity = zeros(1, problem.dimension); % 计算粒子的初始适应度 swarm(i).fitness = problem.fitnessFunction(swarm(i).position); swarm(i).bestFitness = swarm(i).fitness; end end % 更新粒子的位置和速度，并考虑边界影响 function swarm = updateParticles(swarm, bestPosition, problem) global inertiaWeight % 惯性权重 global cognitiveWeight % 认知权重 global socialWeight % 社会权重 for i = 1:length(swarm) % 更新粒子的速度 swarm(i).velocity = inertiaWeight * swarm(i).velocity ... + cognitiveWeight * rand(1) * (swarm(i).bestPosition - swarm(i).position) ... + socialWeight * rand(1) * (bestPosition - swarm(i).position); % 更新粒子的位置 swarm(i).position = swarm(i).position + swarm(i).velocity; % 考虑边界影响 % 限制粒子的位置在问题定义的边界内 swarm(i).position = max(swarm(i).position, problem.lowerBound); swarm(i).position = min(swarm(i).position, problem.upperBound); end end % 评估每个粒子的适应度 function swarm = evaluateFitness(swarm, problem) for i = 1:length(swarm) % 计算粒子的适应度 swarm(i).fitness = problem.fitnessFunction(swarm(i).position); [swarm(i).position, swarm(i).fitness] = gradient_descent(problem.fitnessFunction, swarm(i).position, 1e-3, 1e-6, 200, problem.upperBound, problem.lowerBound); % 更新粒子的最佳位置和适应度 if swarm(i).fitness < swarm(i).bestFitness swarm(i).bestPosition = swarm(i).position; swarm(i).bestFitness = swarm(i).fitness; end end end