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MATLAB实现的改进遗传算法用于有约束优化问题

news 2025/8/7 8:26:01

基于MATLAB实现的改进遗传算法（GA）用于有约束优化问题的代码，包括处理非线性约束。此代码通过引入惩罚函数和修复机制，有效处理约束条件，提高算法的鲁棒性和收敛速度。

1. 定义优化问题

% 定义目标函数
function f = objectiveFunction(x)% 示例：非线性目标函数f = x(1)^2 + x(2)^2 + 10*sin(x(1)) + 5*cos(x(2));
end% 定义非线性约束函数
function [c, ceq] = nonlinearConstraints(x)% 示例：非线性约束c = [1.5 + x(1)*x(2) - x(1) - x(2)]; % 不等式约束 c(x) <= 0ceq = [x(1)^2 + x(2)^2 - 10]; % 等式约束 ceq(x) = 0
end

2. 定义改进遗传算法

classdef ImprovedGApropertiespopulationSizenumVariablesmaxGenerationsmutationRatecrossoverFractionpenaltyFactorpopulationfitnessbestSolutionbestFitnessendmethodsfunction obj = ImprovedGA(populationSize, numVariables, maxGenerations, mutationRate, crossoverFraction, penaltyFactor)obj.populationSize = populationSize;obj.numVariables = numVariables;obj.maxGenerations = maxGenerations;obj.mutationRate = mutationRate;obj.crossoverFraction = crossoverFraction;obj.penaltyFactor = penaltyFactor;obj.population = rand(populationSize, numVariables) * 20 - 10; % 初始化种群obj.fitness = zeros(populationSize, 1);obj.bestSolution = [];obj.bestFitness = inf;endfunction [newPopulation, newFitness] = evolve(obj)% 评估适应度for i = 1:obj.populationSizeobj.fitness(i) = obj.evaluateFitness(obj.population(i, :));end% 选择操作[sortedFitness, sortedIndices] = sort(obj.fitness);elite = obj.population(sortedIndices(1:round(obj.populationSize/10)), :);selected = obj.population(sortedIndices(round(obj.populationSize/10)+1:end), :);selected = obj.tournamentSelection(selected, sortedFitness(round(obj.populationSize/10)+1:end));% 交叉操作crossovered = obj.crossover(selected);% 变异操作mutated = obj.mutation(crossovered);% 合并精英和新种群newPopulation = [elite; mutated];newFitness = zeros(obj.populationSize, 1);for i = 1:obj.populationSizenewFitness(i) = obj.evaluateFitness(newPopulation(i, :));end% 更新最佳解[minFitness, minIndex] = min(newFitness);if minFitness < obj.bestFitnessobj.bestFitness = minFitness;obj.bestSolution = newPopulation(minIndex, :);endendfunction fitness = evaluateFitness(obj, x)% 目标函数值f = objectiveFunction(x);% 约束违反惩罚[c, ceq] = nonlinearConstraints(x);penalty = 0;if any(c > 0) || any(abs(ceq) > 1e-6)penalty = obj.penaltyFactor * (sum(max(c, 0)) + sum(abs(ceq)));endfitness = f + penalty;endfunction selected = tournamentSelection(obj, population, fitness)selected = zeros(size(population));for i = 1:size(population, 1)idx1 = randi(size(population, 1));idx2 = randi(size(population, 1));if fitness(idx1) < fitness(idx2)selected(i, :) = population(idx1, :);elseselected(i, :) = population(idx2, :);endendendfunction crossovered = crossover(obj, population)crossovered = population;for i = 1:2:obj.populationSizeif rand < obj.crossoverFractionidx1 = i;idx2 = i + 1;crossoverPoint = randi(obj.numVariables);crossovered(idx1, crossoverPoint:end) = population(idx2, crossoverPoint:end);crossovered(idx2, crossoverPoint:end) = population(idx1, crossoverPoint:end);endendendfunction mutated = mutation(obj, population)mutated = population;for i = 1:size(population, 1)for j = 1:obj.numVariablesif rand < obj.mutationRatemutated(i, j) = mutated(i, j) + randn * 0.1;endendendendend
end

3. 运行改进遗传算法

% 参数设置
populationSize = 100;
numVariables = 2;
maxGenerations = 100;
mutationRate = 0.01;
crossoverFraction = 0.8;
penaltyFactor = 1000;% 初始化改进遗传算法
ga = ImprovedGA(populationSize, numVariables, maxGenerations, mutationRate, crossoverFraction, penaltyFactor);% 进化过程
for gen = 1:maxGenerations[newPopulation, newFitness] = ga.evolve();ga.population = newPopulation;ga.fitness = newFitness;fprintf('Generation %d: Best Fitness = %.6f\n', gen, ga.bestFitness);
end% 输出最佳解
disp('最佳解:');
disp(ga.bestSolution);
disp('最佳适应度:');
disp(ga.bestFitness);