带时间窗的节约里程法matlab

以下是一个带时间窗的节约里程法的MATLAB代码示例：

function [bestRoute, minDist] = vrptw_savings(nodes, capacity, depotIndex, timeWindows)
% VRPTW_SAVINGS Solve the Vehicle Routing Problem with Time Windows using the Savings algorithm.
%   nodes: matrix of size (N+1) x 3 where N is the number of customers and the first row is the depot
%          each row represents a node with columns [x-coordinate, y-coordinate, demand]
%   capacity: scalar representing the capacity of each vehicle
%   depotIndex: scalar representing the index of the depot node in the nodes matrix
%   timeWindows: matrix of size N x 2 representing the time windows for each customer node
%                 each row is [start time, end time]
%   bestRoute: vector representing the best route found by the algorithm
%   minDist: scalar representing the minimum distance of the best route

% Calculate the distance matrix
distanceMatrix = pdist2(nodes(:,1:2), nodes(:,1:2));

% Calculate the savings matrix
savingsMatrix = zeros(size(distanceMatrix));
for i = 2:length(nodes)
    for j = i+1:length(nodes)
        savingsMatrix(i,j) = distanceMatrix(i,depotIndex) + distanceMatrix(j,depotIndex) - distanceMatrix(i,j);
        savingsMatrix(j,i) = savingsMatrix(i,j);
    end
end

% Sort the savings matrix in descending order
[sortedSavings, indices] = sort(savingsMatrix(:),'descend');

% Initialize the routes matrix
routes = cell(length(nodes),1);
for i = 1:length(nodes)
    routes{i} = i;
end

% Merge the routes using the savings algorithm
for i = 1:length(sortedSavings)
    if sortedSavings(i) <= 0
        break;
    end
    [node1, node2] = ind2sub(size(savingsMatrix), indices(i));
    route1 = findRoute(routes, node1);
    route2 = findRoute(routes, node2);
    if length(route1) + length(route2) - 2 <= capacity && checkTimeWindows(route1, route2, timeWindows)
        routes{route1(1)} = [node1, route1, node2, route2(route2~=node2)];
        routes{route2(1)} = [];
    end
end

% Remove empty routes
routes(cellfun(@isempty,routes)) = [];

% Calculate the distance of each route and find the best route
minDist = Inf;
bestRoute = [];
for i = 1:length(routes)
    route = routes{i};
    dist = 0;
    for j = 2:length(route)
        dist = dist + distanceMatrix(route(j-1),route(j));
    end
    if dist < minDist
        minDist = dist;
        bestRoute = route;
    end
end

end

function route = findRoute(routes, node)
% FINDROUTE Find the route containing the given node.
for i = 1:length(routes)
    if ismember(node, routes{i})
        route = routes{i};
        return;
    end
end
end

function feasible = checkTimeWindows(route1, route2, timeWindows)
% CHECKTIMEWINDOWS Check if the time windows of the two routes are feasible.
time1 = sum(timeWindows(route1,1));
time2 = sum(timeWindows(route2,1));
if time1 + time2 > timeWindows(1,2)
    feasible = false;
    return;
end
time1 = max(timeWindows(route1,1));
time2 = max([timeWindows(route2,1), time1 + pdist2(nodes(route1(end),1:2), nodes(route2,1:2))]);
if time2 > timeWindows(route2(end),2)
    feasible = false;
    return;
end
feasible = true;
end

在这个示例中，我们首先计算了距离矩阵和节约矩阵，然后按照节约矩阵中的节约值进行排序。接下来，我们初始化每个节点为一个单独的路线，并使用节约算法逐步合并这些路线，直到无法再合并为止。最后，我们计算每个路线的距离，并找到最短的路线作为最优解。

需要注意的是，我们在路线合并过程中还对时间窗进行了检查，以确保生成的路线满足时间窗的要求。