基于MATLAB實現的改進遺傳算法（GA）用于有約束優化問題的代碼，包括處理非線性約束。此代碼通過引入懲罰函數和修復機制，有效處理約束條件，提高算法的魯棒性和收斂速度。

1. 定義優化問題

% 定義目標函數
function f = objectiveFunction(x)% 示例：非線性目標函數f = x(1)^2 + x(2)^2 + 10*sin(x(1)) + 5*cos(x(2));
end% 定義非線性約束函數
function [c, ceq] = nonlinearConstraints(x)% 示例：非線性約束c = [1.5 + x(1)*x(2) - x(1) - x(2)]; % 不等式約束 c(x) <= 0ceq = [x(1)^2 + x(2)^2 - 10]; % 等式約束 ceq(x) = 0
end

2. 定義改進遺傳算法

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; % 初始化種群obj.fitness = zeros(populationSize, 1);obj.bestSolution = [];obj.bestFitness = inf;endfunction [newPopulation, newFitness] = evolve(obj)% 評估適應度for i = 1:obj.populationSizeobj.fitness(i) = obj.evaluateFitness(obj.population(i, :));end% 選擇操作[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);% 變異操作mutated = obj.mutation(crossovered);% 合并精英和新種群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)% 目標函數值f = objectiveFunction(x);% 約束違反懲罰[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. 運行改進遺傳算法

% 參數設置
populationSize = 100;
numVariables = 2;
maxGenerations = 100;
mutationRate = 0.01;
crossoverFraction = 0.8;
penaltyFactor = 1000;% 初始化改進遺傳算法
ga = ImprovedGA(populationSize, numVariables, maxGenerations, mutationRate, crossoverFraction, penaltyFactor);% 進化過程
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% 輸出最佳解
disp('最佳解:');
disp(ga.bestSolution);
disp('最佳適應度:');
disp(ga.bestFitness);

參考代碼 改進的遺傳算法有約束優化，非線性約束也可解決 youwenfan.com/contentcsb/81359.html

說明

1. 定義優化問題：定義了目標函數和非線性約束函數。
2. 定義改進遺傳算法：實現了改進的遺傳算法，包括適應度評估、選擇、交叉和變異操作。
3. 運行改進遺傳算法：初始化算法參數，運行進化過程，并輸出最佳解和適應度。

改進

• 懲罰函數：通過引入懲罰函數處理約束條件，懲罰函數的值與約束違反程度成正比。
• 修復機制：在變異操作中，對違反約束的解進行修復，使其滿足約束條件。
• 精英策略：保留每代種群中的精英個體，加速算法收斂。