写一个用遗传算法求一元函数最大值的matlab代码
时间: 2024-05-29 11:04:01 浏览: 97
好的,下面是代码:
function [bestX, bestY] = GeneticAlgorithmForFunctionMaximum(f, precision, limits, popSize, maxGenerations, eliteRate, mutationRate)
% 参数说明:
% f:一个句柄,表示要求解的一元函数;
% precision:一个数值,表示终止循环的精度,即当两代种群的最优值差小于此值时,终止循环;
% limits:一个二元向量,表示自变量 x 的取值范围;
% popSize:一个数值,表示种群大小;
% maxGenerations:一个数值,表示最大迭代次数;
% eliteRate:一个数值,表示精英个体的比例;
% mutationRate:一个数值,表示变异率。
% 初始化种群
popu = repmat(limits', popSize, 1) .* rand(popSize, length(limits));
fits = zeros(popSize, 1);
for i = 1:maxGenerations
% 计算个体适应度
for j = 1:popSize
fits(j) = f(popu(j, 1));
end
% 找出种群中的最优个体
[bestFit, bestIdx] = max(fits);
bestX = popu(bestIdx, 1);
bestY = bestFit;
% 判断是否满足终止条件
if i > 1 && abs(bestY - prevBestY) < precision
break;
end
prevBestY = bestY;
% 种群选择:锦标赛选择法
eliteNum = round(eliteRate * popSize);
idx = randperm(popSize);
elite = zeros(eliteNum, length(limits));
for j = 1:eliteNum
subIdx = idx(1:2);
if fits(subIdx(1)) > fits(subIdx(2))
elite(j, :) = popu(subIdx(1), :);
else
elite(j, :) = popu(subIdx(2), :);
end
idx = idx(3:end);
end
% 种群交叉:一点交叉
offspring = repmat(limits', popSize - eliteNum, 1) .* rand(popSize - eliteNum, length(limits));
crossoverPoints = round(rand(popSize - eliteNum, 1) * (length(limits) - 1)) + 1;
for j = 1:popSize - eliteNum
parent1 = popu(j, :);
parent2 = popu(mod(j, popSize) + 1, :);
offspring(j, 1:crossoverPoints(j)) = parent1(1:crossoverPoints(j));
offspring(j, crossoverPoints(j)+1:end) = parent2(crossoverPoints(j)+1:end);
end
% 种群变异:高斯变异
mutationNum = round(mutationRate * popSize * length(limits));
mutationIdx = randperm(popSize * length(limits), mutationNum);
offspring(mutationIdx) = offspring(mutationIdx) + randn(mutationNum, 1) .* limits(2) / 3;
offspring(offspring < limits(1)) = limits(1);
offspring(offspring > limits(2)) = limits(2);
% 更新种群
popu = [elite; offspring];
end
end
这是一个简单的遗传算法求解单一变量函数最大值的实现,应该能够满足你的需求。如果有其他问题,请随时提出。
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