matlab代码 遗传算法解决tsp
时间: 2023-09-12 12:08:52 浏览: 31
以下是一个基本的MATLAB代码,用遗传算法解决TSP问题:
```matlab
% 初始化城市坐标
x = [0.5454 0.1076 0.2658 0.5584 0.2861];
y = [0.5497 0.0082 0.8143 0.1254 0.6324];
% 初始化遗传算法参数
popSize = 50;
numGen = 100;
mutationRate = 0.02;
tournamentSize = 5;
elite = 1;
% 创建初始种群
n = length(x);
pop = zeros(popSize, n);
for i = 1:popSize
pop(i,:) = randperm(n);
end
% 遗传算法主程序
for i = 1:numGen
% 计算种群中每个个体的适应度
fitness = zeros(popSize,1);
for j = 1:popSize
fitness(j) = tspFitness(pop(j,:), x, y);
end
% 选择下一代
newPop = zeros(popSize, n);
for j = 1:popSize
% 选择两个个体进行竞争
tournament = randperm(popSize, tournamentSize);
[maxFitness, idx] = max(fitness(tournament));
winner = tournament(idx);
% 复制胜者到下一代
newPop(j,:) = pop(winner,:);
end
% 交叉操作
for j = 1:2:popSize
% 随机选择两个个体
parent1 = randperm(popSize, 1);
parent2 = randperm(popSize, 1);
% 生成交叉点
crossPoint1 = randi(n-1);
crossPoint2 = randi([crossPoint1+1, n]);
% 生成子代
child1 = zeros(1,n);
child2 = zeros(1,n);
child1(crossPoint1:crossPoint2) = pop(parent1, crossPoint1:crossPoint2);
child2(crossPoint1:crossPoint2) = pop(parent2, crossPoint1:crossPoint2);
for k = crossPoint2+1:n
% 查找第一个不在子代1中的城市
if ~ismember(pop(parent2,k), child1)
child1(k) = pop(parent2,k);
end
% 查找第一个不在子代2中的城市
if ~ismember(pop(parent1,k), child2)
child2(k) = pop(parent1,k);
end
end
% 更新种群
newPop(j,:) = child1;
newPop(j+1,:) = child2;
end
% 变异操作
for j = 1:popSize
if rand < mutationRate
% 随机选择两个城市进行交换
swapPoint1 = randi(n);
swapPoint2 = randi(n);
temp = newPop(j,swapPoint1);
newPop(j,swapPoint1) = newPop(j,swapPoint2);
newPop(j,swapPoint2) = temp;
end
end
% 精英保留
[~, idx] = sort(fitness, 'descend');
elitePop = pop(idx(1:elite),:);
newPop(1:elite,:) = elitePop;
% 更新种群
pop = newPop;
end
% 输出结果
[bestFitness, idx] = max(fitness);
bestPath = pop(idx,:);
fprintf('最短路径长度: %f\n', bestFitness);
fprintf('最短路径: ');
fprintf('%d ', bestPath);
fprintf('\n');
% 计算适应度函数
function fitness = tspFitness(path, x, y)
n = length(path);
fitness = 0;
for i = 1:n-1
fitness = fitness + sqrt((x(path(i+1))-x(path(i)))^2 + (y(path(i+1))-y(path(i)))^2);
end
fitness = fitness + sqrt((x(path(n))-x(path(1)))^2 + (y(path(n))-y(path(1)))^2);
fitness = 1/fitness;
end
```
这段代码实现了一个简单的遗传算法,用于解决TSP问题。它使用随机生成的初始种群,并使用交叉和变异操作来生成新的个体。在每一代中,它选择下一代的个体,用精英保留来保留最好的个体,并使用适应度函数来评估每个个体的适应度。最终,它输出找到的最短路径及其长度。