C ++中的多模型构建（迭代）（具有多个场景的Benders分解）

Question

I'm trying to write a Benders Decomposition code in C++ to solve a facility location problem. It is a two stage stochastic programming example and the demand parameters depend on the scenarios. I wrote a similar code in AMPL before and it's run file was starting as follows:

option solver cplexamp;

option omit_zero_rows 1;
option display_eps .000001;
option solver_msg 0;
option show_boundto1 0;

problem Master: r, y, theta,
                Master_Cost, Cut_Defn, Open_Facilities_Facility_Capacity, Number_of_Facilities_Per_Node;

problem Sub{s in 1..NSec}:
    {k in 1..K, (i,j) in LINKS} x[k,s,i,j],
    {k in 1..K, i in 1..nnodes} z[k,s,i],
    {k in 1..K, i in 1..nnodes} w[k,s,i],
    BSP_Cost[s],
    {i in 1..nnodes, k in 1..K} Flow_Conservation[i,k,s],
    {(i,j) in LINKS} Arc_Capacity[i,j,s];

let nCUT := 0;
let {s in 1..NSec} theta[s] := 0;
let {k in 1..K, i in 1..nnodes} R[k,i] := 0;

param GAP default Infinity;
param newGAP;

However, in C++ I don't know how to construct subproblems (build models) with respect to scenarios. (I should construct a model for every scenario indexed by s )

Below is the subproblem generation part of my code (s number of models); however, I realized this is wrong because it is only adding constraints to a one large problem instead of s subproblems.

IloModel model_sub(env);

    IloObjective Objective_sub(env);

    model_sub.add(Objective_sub);

    for (int s=0; s<S; s++){
        for (int i=0; i<I; i++){
                for (int j=0; j<J; j++){
                    model_sub.add(MU[i][s] + Beta[j][s] <= c[j][i]);   
                }
        }
    }

    IloCplex cplex_sub(model_sub);

Any help is appreciated, thanks a lot.

Note: This link has a code that is working with only a single subproblem (a single scenario). This is basically what I'm trying to replicate (or base my code on), if anyone is interested. If you also have a link or a file of a multi-scenario Benders code, that'd also be amazingly generous.

Thanks again.

Answer 1

您可以有一个IloModel每个方案或有一个IloModel为您的子问题，但修改每一个需要解决的一个问题特定场景时间。