如何解决铁路线路规划问题?

Question

我正在写关于铁路客运线路规划问题的论文。我想看看计算铁路网络中鲁棒性的不同方法。由于我没有OPL经验，因此在解决模型时遇到了一些问题。我的主管帮不了我，我拼命地寻找可以帮助我正确建模的人。该模型应确定要暗示哪些线路，以及火车的频率和车厢数量，同时将成本保持在最低水平。

我有以下两个问题： 我有一组边 (E) 和一组潜在的线 (L)。例如，我如何告诉 OPL，第 1 行由边 1 和 2 组成。我发现很难将这些变量联系起来。

我正在使用一个二元决策变量 x[L][F][C]，它分别表示线路、线路频率和车厢数量。如何告诉模型一个值只乘以 F 的值。例如第三个约束，我想将 F 和 C 的值乘以 capC。

int nv = ...;
range V = 1..nv;            //set of stations.
int ne =...;
range E =1..ne;                 //set of edges.
int nf = ...;
range F = 1..nf;            //set of possible frequencies.
int nc = ...;   
range C = 1..nc;            //set of possible carriages.
int nl = ...;
range L = 1..nl;            //set of potential lines.
//Parameters
int capC = ...;             //Capacity per carriage
int w[L] = ...;             //cost for using line l
int fmin[E] = ...;          //min freq per line l 
int fmax[E] = ...;          //max freq per line l
int h[E] = ...;             //Demand edge e
//Decision variable
dvar boolean x[L][F][C];                        
//Objective function
minimize sum(l in L, f in F, c in C) w[l] * x[l][f][c]; 
//Constraints
subject to {
forall (e in E)
sum(l in L, f in F, c in C) x[l][f][c] >= fmin[e];        //Min edge freq
forall (e in E)
sum(l in L, f in F, c in C) x[l][f][c] <= fmax[e];        //Max edge freq 
forall (e in E)
sum(l in L, f in F, c in C) x[l][f][c] * capC >= h[e];  //Transfer all passengers
forall (l in L)
sum(f in F, c in C) x[l][f][c] <= 1;              //Per line at most 1

Answer 1

关于"我想将 F 和 C 的值乘以 capC"，您是否尝试过转向

forall (e in E) sum(l in L, f in F, c in C) x[l][f][c] * capC >= h[e]; //Transfer all passengers

到

forall (e in E) sum(l in L, f in F, c in C) f*c*x[l][f][c] * capC >= h[e]; //Transfer all passengers

？