写一个Matlab从配送中心出发多条线路连接其它点,每条线路不可连接超过6个节点并使路线长度之和最短
时间: 2024-03-02 09:49:15 浏览: 89
matlab 最短路径算法
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您的问题是一个典型的带约束条件的多旅行商问题(Constrained Multiple Traveling Salesman Problem,CMTSP)。该问题也是NP难问题,通常使用启发式算法求解。以下是一个使用遗传算法(Genetic Algorithm,GA)求解CMTSP的Matlab代码示例:
```matlab
% 配置参数
popSize = 50; % 种群大小
numCities = 30; % 城市数
maxGen = 500; % 进化代数
pc = 0.8; % 交叉概率
pm = 0.01; % 变异概率
maxNodes = 6; % 每条线路最大节点数
% 生成随机城市坐标
cities = rand(numCities, 2) * 100;
% 初始化种群
numRoutes = ceil(numCities/maxNodes);
pop = zeros(numCities+numRoutes-1, popSize);
for i = 1:popSize
idx = randperm(numCities);
for j = 1:numRoutes
startIdx = (j-1)*maxNodes + 1;
endIdx = min(j*maxNodes, numCities);
pop(startIdx:endIdx+(j<numRoutes), i) = idx(startIdx:endIdx);
end
end
% 进化过程
for gen = 1:maxGen
% 计算适应度值
dist = zeros(popSize, 1);
for i = 1:popSize
routes = cell(numRoutes, 1);
for j = 1:numRoutes
startIdx = (j-1)*maxNodes + 1;
endIdx = min(j*maxNodes, numCities);
route = pop(startIdx:endIdx+(j<numRoutes), i);
route(route==0) = [];
routes{j} = route;
end
% 计算路线长度
d = 0;
for j = 1:numRoutes
route = routes{j};
d = d + sum(sqrt(sum((cities(route, :) - circshift(cities(route, :), [1, 0])).^2, 2)));
end
dist(i) = d;
end
fitness = 1./dist;
fitness = fitness./sum(fitness);
% 种群选择
[val, idx] = sort(fitness, 'descend');
elite = pop(:, idx(1));
pop = pop(:, idx(1:popSize-1));
prob = cumsum(val);
prob = prob/prob(end);
for i = 1:popSize-1
a = find(rand() <= prob, 1);
b = find(rand() <= prob, 1);
if rand() <= pc
% 交叉
c = randi(numRoutes-1);
routeA = cell(numRoutes, 1);
routeB = cell(numRoutes, 1);
for j = 1:numRoutes
if j <= c
routeA{j} = routes{a}{j};
routeB{j} = routes{b}{j};
else
routeA{j} = routes{b}{j};
routeB{j} = routes{a}{j};
end
end
childA = [];
childB = [];
for j = 1:numRoutes
route = routeA{j};
for k = 1:length(route)
if sum(ismember(routeB{j}, route(k))) == 0
childA(end+1) = route(k);
end
end
missing = setdiff(routeB{j}, childA);
if length(missing) > 0
childA(end+1:end+length(missing)) = missing;
end
route = routeB{j};
for k = 1:length(route)
if sum(ismember(routeA{j}, route(k))) == 0
childB(end+1) = route(k);
end
end
missing = setdiff(routeA{j}, childB);
if length(missing) > 0
childB(end+1:end+length(missing)) = missing;
end
% 控制每条线路的节点数
if length(childA) > maxNodes
childA = childA(1:maxNodes);
end
if length(childB) > maxNodes
childB = childB(1:maxNodes);
end
end
childA = [childA, zeros(1, numCities-length(childA))];
childB = [childB, zeros(1, numCities-length(childB))];
pop(:, i) = childA;
pop(:, i+1) = childB;
else
% 复制
pop(:, i) = pop(:, a);
end
end
% 变异
for i = 2:popSize-1
if rand() <= pm
a = randi(numRoutes);
b = randi(numRoutes);
route = routes{a};
pos = randperm(length(route), 2);
route([pos(1), pos(2)]) = route([pos(2), pos(1)]);
if length(route) > maxNodes
route = route(1:maxNodes);
end
routes{a} = route;
pop(:, i) = zeros(numCities+numRoutes-1, 1);
for j = 1:numRoutes
startIdx = (j-1)*maxNodes + 1;
endIdx = min(j*maxNodes, numCities);
if j == a
pop(startIdx:endIdx+(j<numRoutes), i) = route;
else
pop(startIdx:endIdx+(j<numRoutes), i) = routes{j};
end
end
end
end
% 加入精英
pop(:, end) = elite;
end
% 输出最优解
routes = cell(numRoutes, 1);
for j = 1:numRoutes
startIdx = (j-1)*maxNodes + 1;
endIdx = min(j*maxNodes, numCities);
route = pop(startIdx:endIdx+(j<numRoutes), idx(1));
route(route==0) = [];
routes{j} = route;
end
d = 0;
for j = 1:numRoutes
route = routes{j};
d = d + sum(sqrt(sum((cities(route, :) - circshift(cities(route, :), [1, 0])).^2, 2)));
end
fprintf('最短路程长度:%f\n', d);
fprintf('最短路程路径:\n');
for j = 1:numRoutes
route = routes{j};
fprintf('[%d, %d, %d, %d, %d, %d]\n', route);
end
```
该代码使用遗传算法求解CMTSP问题,将城市坐标随机生成,通过进化过程逐步优化种群中的路线,并控制每条线路的节点数不超过6个。最终输出最短路程长度和路径。您可以根据实际情况进行参数调整和优化。
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