cplex求解固定车场的车辆路径问题MATLAB代码

以下是使用MATLAB调用CPLEX求解固定车场的车辆路径问题的示例代码：

function [X, objval] = solve_vrp(n, m, q, c, d)
% n: 客户数量
% m: 车辆数量
% q: 车辆容量
% c: 客户的坐标
% d: 客户之间的距离矩阵

% 定义问题
cplex = Cplex('vrp');
cplex.Model.sense = 'minimize';

% 添加变量
x = {};
for i = 1:n+1
    for j = 1:n+1
        if i ~= j
            x{end+1} = sprintf('x_%d_%d', i, j);
        end
    end
end
cplex.addCols(zeros(length(x), 1), [], x);

% 添加约束
Aeq = {};
beq = zeros(n+m, 1);
lb = zeros(length(x), 1);
ub = ones(length(x), 1);
for i = 1:n
    Aeq{end+1} = sparse(1:length(x), find(strcmp(x, sprintf('x_%d_%d', i, 1))), 1, 1, length(x));
    Aeq{end+1} = sparse(1:length(x), find(strcmp(x, sprintf('x_%d_%d', 1, i))), 1, 1, length(x));
end
for j = 1:m
    Aeq{end+1} = sparse(1:length(x), find(strcmp(x, sprintf('x_%d_%d', n+j, 1))), 1, 1, length(x));
    Aeq{end+1} = sparse(1:length(x), find(strcmp(x, sprintf('x_%d_%d', 1, n+j))), 1, 1, length(x));
end
for k = 1:n
    Aeq{end+1} = sparse(1:length(x), find(strcmp(x, sprintf('x_%d_%d', k, 1))), 1, 1, length(x));
    Aeq{end+1} = sparse(1:length(x), find(strcmp(x, sprintf('x_%d_%d', 1, k))), 1, 1, length(x));
    Aeq{end+1} = sparse(1:length(x), find(strcmp(x, sprintf('x_%d_%d', k, n+1))), 1, 1, 1, length(x));
    Aeq{end+1} = sparse(1:length(x), find(strcmp(x, sprintf('x_%d_%d', n+1, k))), 1, 1, 1, length(x));
end
for i = 2:n
    beq(i-1) = 1;
    Aeq{end+1} = sparse(1:length(x), find(strcmp(x, sprintf('x_%d_%d', i, 1))), 1, 1, length(x));
    Aeq{end+1} = sparse(1:length(x), find(strcmp(x, sprintf('x_%d_%d', 1, i))), 1, 1, length(x));
end
for j = 1:m
    beq(n+j) = -q;
    for i = 2:n
        Aeq{end+1} = sparse(1:length(x), find(strcmp(x, sprintf('x_%d_%d', i, n+j))), 1, 1, length(x));
        Aeq{end+1} = sparse(1:length(x), find(strcmp(x, sprintf('x_%d_%d', n+j, i))), 1, 1, length(x));
    end
end
cplex.addRows(beq, Aeq, beq, [], []);

for i = 1:n+1
    for j = 1:n+1
        if i ~= j
            lb(find(strcmp(x, sprintf('x_%d_%d', i, j)))) = 0;
            ub(find(strcmp(x, sprintf('x_%d_%d', i, j)))) = 1;
        end
    end
end
cplex.Model.lb = lb;
cplex.Model.ub = ub;

% 添加目标函数
obj = zeros(length(x), 1);
for i = 1:n+1
    for j = 1:n+1
        if i ~= j
            obj(find(strcmp(x, sprintf('x_%d_%d', i, j)))) = d(i, j);
        end
    end
end
cplex.Model.obj = obj;

% 求解问题
cplex.solve();

% 输出结果
X = zeros(n+1, n+1);
for i = 1:n+1
    for j = 1:n+1
        if i ~= j
            X(i, j) = cplex.Solution.x(find(strcmp(x, sprintf('x_%d_%d', i, j)))));
        end
    end
end
objval = cplex.Solution.objval;
end

其中，`n`是客户数量，`m`是车辆数量，`q`是车辆容量，`c`是客户的坐标矩阵，`d`是客户之间的距离矩阵。约束条件包括每个客户被恰好访问一次、每个车辆出发和返回都必须在仓库、每个车辆的容量不能超过限制。目标函数为最小化总行驶距离。