自适应遗传算法是一种改进的遗传算法，它可以根据当前种群的状态动态调整参数，如交叉概率和变异概率。这样可以提高算法在不同阶段的性能。以下是一个基本的MATLAB实现示例，用于演示如何构建自适应遗传算法：
- % 自适应遗传算法示例
- % 问题参数设置
- populationSize = 100; % 种群规模
- chromosomeLength = 50; % 染色体长度
- maxGenerations = 100; % 最大代数
- % 遗传算法参数
- initialCrossoverRate = 0.7;
- initialMutationRate = 0.01;
- % 创建初始种群
- population = randi([0, 1], populationSize, chromosomeLength);
- % 主循环
- for generation = 1:maxGenerations
- % 计算适应度
- fitness = evaluateFitness(population);
-
- % 自适应调整：根据适应度调整交叉率和变异率
- averageFitness = mean(fitness);
- maxFitness = max(fitness);
-
- crossoverRate = initialCrossoverRate + (maxFitness - averageFitness) / maxFitness;
- mutationRate = initialMutationRate * (1 - averageFitness / maxFitness);
-
- % 选择（轮盘赌选择）
- selectedIndices = rouletteWheelSelection(fitness, populationSize);
- selectedPopulation = population(selectedIndices, :);
-
- % 交叉
- newPopulation = zeros(size(population));
- for i = 1:2:populationSize
- parent1 = selectedPopulation(i, :);
- parent2 = selectedPopulation(i+1, :);
- if rand < crossoverRate
- [child1, child2] = crossover(parent1, parent2);
- newPopulation(i, :) = child1;
- newPopulation(i+1, :) = child2;
- else
- % 不进行交叉
- newPopulation(i, :) = parent1;
- newPopulation(i+1, :) = parent2;
- end
- end
-
- % 变异
- for i = 1:populationSize
- newPopulation(i, :) = mutate(newPopulation(i, :), mutationRate);
- end
-
- % 更新种群
- population = newPopulation;
-
- % 输出当前代信息
- fprintf('Generation %d: Max Fitness = %f\n', generation, maxFitness);
- end
- % 辅助函数
- function fitness = evaluateFitness(population)
- % 适应度评估函数（示例：简单求和）
- fitness = sum(population, 2);
- end
- function selectedIndices = rouletteWheelSelection(fitness, numSelected)
- % 轮盘赌选择
- totalFitness = sum(fitness);
- selectionProb = fitness / totalFitness;
- cumulativeProb = cumsum(selectionProb);
- selectedIndices = zeros(numSelected, 1);
- for i = 1:numSelected
- r = rand;
- selectedIndices(i) = find(cumulativeProb >= r, 1, 'first');
- end
- end
- function [child1, child2] = crossover(parent1, parent2)
- % 单点交叉
- point = randi(length(parent1) - 1);
- child1 = [parent1(1:point), parent2(point+1:end)];
- child2 = [parent2(1:point), parent1(point+1:end)];
- end
- function mutatedChild = mutate(child, mutationRate)
- % 基因突变
- mutationMask = rand(size(child)) < mutationRate;
- mutatedChild = xor(child, mutationMask);
- end
### 解释：
- **适应度评估**：`evaluateFitness` 函数用于评估每个个体的适应度。
- **选择过程**：使用轮盘赌选择方法，从种群中选择适应度较高的个体。
- **交叉和变异**：通过 `crossover` 和 `mutate` 函数实现个体间的基因交叉和突变操作。
- **自适应调整**：根据当前种群的适应度，动态调整交叉率和变异率来优化算法性能。
### 注意：
- 在实际应用中，请根据问题具体需求和特性进一步优化适应度函数和参数调整策略。
- 此代码中的适应度函数和其他参数均为示例设置，需根据具体问题进行调整。
--- 光学专家Gpt |
