群智能优化算法 matlab

### 群智能优化算法 MATLAB 实现教程 #### 遗传算法 MATLAB 实现 遗传算法通过模拟自然选择过程来进行全局搜索。下面是一个简单的遗传算法MATLAB实现示例： ```matlab function [bestIndividual, bestFitness] = geneticAlgorithm(fitnessFunction, numVars, populationSize, mutationRate, maxGenerations) % 初始化种群 population = rand(populationSize, numVars); for generation = 1:maxGenerations % 计算适应度 fitnessValues = arrayfun(@(indiv) fitnessFunction(indiv), population); % 选择操作 [~, sortedIndices] = sort(fitnessValues, 'descend'); selectedPopulation = population(sortedIndices(1:populationSize/2), :); % 交叉操作 children = crossover(selectedPopulation); % 变异操作 mutatedChildren = mutate(children, mutationRate); % 更新种群 population = [selectedPopulation; mutatedChildren]; % 打印当前最佳解 [~, bestIndex] = max(fitnessValues); fprintf('Generation %d Best Fitness: %.4f\n', generation, fitnessValues(bestIndex)); end % 返回最优个体及其适应度 [~, bestIndex] = max(arrayfun(@(indiv) fitnessFunction(indiv), population)); bestIndividual = population(bestIndex, :); bestFitness = fitnessFunction(bestIndividual); function offspring = crossover(parents) % 进行单点交叉 numParents = size(parents, 1); numOffspring = floor(numParents / 2); offspring = zeros(numOffspring, numVars); for i = 1:numOffspring parentA = parents(i,:); parentB = parents(mod(i,numParents)+1,:); crossPoint = ceil(rand * (numVars - 1)); %#ok<CELS> offspring(i,:) = [parentA(1:crossPoint), parentB(crossPoint+1:end)]; end end function mutant = mutate(child, rate) % 对染色体进行随机变异 mask = rand(size(child)) < rate; mutant = child; mutant(mask) = rand(sum(mask), 1); end end ``` 此代码展示了如何创建一个基本的遗传算法框架，包括初始化、评估、选择、交叉和变异等主要组件[^1]。 #### 蚂蚁群算法 MATLAB 实现 蚂蚁群算法模仿了蚂蚁觅食过程中释放的信息素机制来解决路径规划等问题。这里给出一段简化版的蚂蚁群算法MATLAB代码片段: ```matlab % 参数设置 m = 50; % 蚂蚁数量 n = length(D); % 城市数目 alpha = 1; % 信息启发因子 beta = 5; % 启发式因子 rho = 0.1; % 信息素蒸发系数 Q = 100; % 增加的信息量常数 tau = ones(n,n); % 初始信息浓度矩阵 eta = 1./D; % 启发函数（距离倒数） iter_max = 200; for iter = 1:iter_max path = cell(m, n); % 存储各只蚂蚁走过的路线 delta_tau = zeros(n,n);% 当前迭代产生的增量信息素分布表 for k = 1:m % m只蚂蚁循环 visited = false(1,n); current_city = randi([1,n]); visited(current_city)=true; path{k}(1) = current_city; for j=2:n % 构建一条完整的环路 p = calculateProbability(tau, eta, alpha, beta, ~visited); next_city = randsample(find(~visited), 1,'Weights',p); visited(next_city) = true; path{k}(j) = next_city; end L(k) = calPathLength(path{k}, D); % 计算该条路径长度 delta_tau = updateDeltaTau(delta_tau, Q/L(k), path{k}); end tau = (1-rho)*tau + delta_tau;%更新信息素浓度 end function prob = calculateProbability(tau, eta, alpha, beta, available_cities) numerators = power(tau(:,available_cities).*eta(:,available_cities)', alpha.*beta)'; denominator = sum(numerators(:)); prob = numerators ./ denominator; end function dT = updateDeltaTau(dT, qL, route) cities_pairs = combnk(route, 2); for pair=cities_pairs' dT(pair{1},pair{2}) = dT(pair{1},pair{2}) + qL; dT(pair{2},pair{1}) = dT(pair{2},pair{1}) + qL; end end ``` 上述程序实现了标准ACO模型的核心逻辑，并针对旅行商问题进行了具体化处理. #### 大鼠群优化器(RSO) MATLAB 实现 大鼠群优化器是一种新颖的群体智能方法，它受到老鼠寻找食物的行为模式所启发。以下是RSO的一个简单版本在MATLAB上的编码方式： ```matlab function [gbestPosition, gBestScore] = RSO(objectiveFunc, lb, ub, swarmSize, iterations) dimension = numel(lb); positions = bsxfun(@plus,lb,(ub-lb).*rand(swarmSize,dimension)); velocities = zeros(swarmSize,dimension); personalBestPositions = positions; scores = arrayfun(@(pos)objectiveFunc(pos),positions); [~,idx]=min(scores); globalBestPosition = positions(idx,:); wMax = 0.9; wMin = 0.4; c1 = 2; c2 = 2; for t=1:iterations w=wMax-(wMax-wMin)*(t/iterations); for i=1:length(positions) r1=rand(); r2=rand(); velocities(i,:)=... w*velocities(i,:)+c1*r1*(personalBestPositions(i,:)-positions(i,:)); positions(i,:)=positions(i,:)+velocities(i,:); positions(i,:)=(max(min(positions(i,:),ub),lb)); score=objectiveFunc(positions(i,:)); if(score<scores(i)) personalBestPositions(i,:)=positions(i,:); scores(i)=score; if(score<gBestScore) globalBestPosition=positions(i,:); gBestScore=score; end end end end end ``` 这段脚本定义了一个名为`RSO`的功能，用于执行大鼠群优化过程并返回找到的最佳位置以及对应的得分值[^2].