MATLAB实现的改进遗传算法用于有约束优化问题

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

matlab 复制代码

% 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) <= 0
    ceq = [x(1)^2 + x(2)^2 - 10]; % 等式约束 ceq(x) = 0
end

2. 定义改进遗传算法

matlab 复制代码

classdef ImprovedGA
    properties
        populationSize
        numVariables
        maxGenerations
        mutationRate
        crossoverFraction
        penaltyFactor
        population
        fitness
        bestSolution
        bestFitness
    end

    methods
        function 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;
        end

        function [newPopulation, newFitness] = evolve(obj)
            % 评估适应度
            for i = 1:obj.populationSize
                obj.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.populationSize
                newFitness(i) = obj.evaluateFitness(newPopulation(i, :));
            end

            % 更新最佳解
            [minFitness, minIndex] = min(newFitness);
            if minFitness < obj.bestFitness
                obj.bestFitness = minFitness;
                obj.bestSolution = newPopulation(minIndex, :);
            end
        end

        function 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)));
            end
            fitness = f + penalty;
        end

        function 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, :);
                else
                    selected(i, :) = population(idx2, :);
                end
            end
        end

        function crossovered = crossover(obj, population)
            crossovered = population;
            for i = 1:2:obj.populationSize
                if rand < obj.crossoverFraction
                    idx1 = i;
                    idx2 = i + 1;
                    crossoverPoint = randi(obj.numVariables);
                    crossovered(idx1, crossoverPoint:end) = population(idx2, crossoverPoint:end);
                    crossovered(idx2, crossoverPoint:end) = population(idx1, crossoverPoint:end);
                end
            end
        end

        function mutated = mutation(obj, population)
            mutated = population;
            for i = 1:size(population, 1)
                for j = 1:obj.numVariables
                    if rand < obj.mutationRate
                        mutated(i, j) = mutated(i, j) + randn * 0.1;
                    end
                end
            end
        end
    end
end

3. 运行改进遗传算法

matlab 复制代码

% 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);

参考代码改进的遗传算法有约束优化，非线性约束也可解决 youwenfan.com/contentcsb/81359.html

说明

定义优化问题：定义了目标函数和非线性约束函数。
定义改进遗传算法：实现了改进的遗传算法，包括适应度评估、选择、交叉和变异操作。
运行改进遗传算法：初始化算法参数，运行进化过程，并输出最佳解和适应度。

改进

惩罚函数：通过引入惩罚函数处理约束条件，惩罚函数的值与约束违反程度成正比。
修复机制：在变异操作中，对违反约束的解进行修复，使其满足约束条件。
精英策略：保留每代种群中的精英个体，加速算法收敛。