matlab代码 遗传算法解决tsp
时间: 2023-09-12 17:08:53 浏览: 47
以下是使用遗传算法解决TSP的MATLAB代码示例:
```
% TSP问题的遗传算法解决方案
% 定义TSP问题数据
cities = [0, 0; 1, 2; 3, 4; 5, 6; 7, 8];
nCities = size(cities, 1);
% 定义遗传算法参数
nGenerations = 100; % 迭代次数
nPopulation = 50; % 种群规模
mutationRate = 0.02; % 变异概率
% 初始化种群
population = zeros(nPopulation, nCities);
for i = 1:nPopulation
population(i, :) = randperm(nCities);
end
% 迭代遗传算法
for iGeneration = 1:nGenerations
% 计算适应度函数
fitness = zeros(nPopulation, 1);
for i = 1:nPopulation
fitness(i) = 1 / tspLength(population(i, :), cities);
end
% 选择父代
parentIndices = selection(fitness, nPopulation);
% 交叉
offspring = zeros(nPopulation, nCities);
for i = 1:2:nPopulation
[offspring(i, :), offspring(i+1, :)] = crossover(population(parentIndices(i), :), population(parentIndices(i+1), :));
end
% 变异
for i = 1:nPopulation
if rand < mutationRate
offspring(i, :) = mutation(offspring(i, :));
end
end
% 更新种群
population = offspring;
end
% 找到最佳路径
bestPath = population(1, :);
bestLength = tspLength(bestPath, cities);
for i = 2:nPopulation
length = tspLength(population(i, :), cities);
if length < bestLength
bestPath = population(i, :);
bestLength = length;
end
end
% 输出结果
disp('最佳路径:');
disp(bestPath);
disp(['路径长度:', num2str(bestLength)]);
% 计算路径长度
function length = tspLength(path, cities)
length = 0;
for i = 2:length(path)
length = length + norm(cities(path(i), :) - cities(path(i-1), :));
end
length = length + norm(cities(path(1), :) - cities(path(end), :));
end
% 轮盘赌选择
function indices = selection(fitness, n)
indices = zeros(n, 1);
for i = 1:n
r = rand;
index = 1;
while r > 0
r = r - fitness(index);
index = index + 1;
end
indices(i) = index - 1;
end
end
% 交叉
function [offspring1, offspring2] = crossover(parent1, parent2)
n = length(parent1);
point1 = randi(n);
point2 = randi(n);
if point1 > point2
[point1, point2] = deal(point2, point1);
end
offspring1 = parent1;
offspring2 = parent2;
offspring1(point1:point2) = parent2(point1:point2);
offspring2(point1:point2) = parent1(point1:point2);
end
% 变异
function offspring = mutation(parent)
n = length(parent);
point1 = randi(n);
point2 = randi(n);
offspring = parent;
offspring([point1, point2]) = offspring([point2, point1]);
end
```
这里,我们使用五个城市的TSP问题作为例子。首先我们定义了城市坐标,然后设置了遗传算法参数,包括迭代次数、种群规模和变异概率。接下来,我们初始化种群,并在每一代中进行选择、交叉和变异操作,更新种群。最后,我们找到最佳路径并输出结果。
需要注意的是,这个示例代码只是演示了如何使用遗传算法解决TSP问题,并不一定是最优解决方案。具体问题需要根据实际情况进行调整和优化。