7 votes

Is Benders decomposition and the L-shaped method the same algorithm?

In the paper that proposed L-shaped method, you can find In section 2, an algorithm which is essentially the same as the algorithm developed by Benders[3] is described and a geometric interpretation ...
Penghui Guo's user avatar
4 votes
Accepted

How to pass the values of a variable of the first model to a parameter of the second model?

First of all, I assume that the mentioned model is just to reflect what you want to do otherwise, it needs more attention as the problem is infeasible. To capture a variable value and store that into ...
A.Omidi's user avatar
  • 8,717
3 votes

Tips for implementing Benders Decomposition in C++?

Recent versions of CPLEX (12.7 or later) have built in support for Benders. You can let CPLEX decide what to put in the master problem and what goes in the subproblems, or you can use annotations to ...
prubin's user avatar
  • 38.8k
2 votes

Deriving a lower bound for a two-stage stochastic problem

The following is a valid lower bound for the stochastic programming problem. \begin{align} \mathbb{E}_{\mathbb{\xi} \in \varOmega} \min \limits_{x\in X} \left( c^\top x + \mathcal{Q}(x, \xi) \right) \...
Penghui Guo's user avatar
1 vote

Benchmark problems for Benders Decomposition

Some collections of testing instances for Stochastic Programming which can be solved by the Benders Decomposition / L-shaped / SDDP: MSPLib-Library https://github.com/bonnkleiford/MSPLib-Library ...
Penghui Guo's user avatar
1 vote

Recommendations to understand stochastic version of Benders?

Not in C++, but SDDP.jl implements Benders for two-stage stochastic programming (as well as SDDP for multi-stage). There are a few tutorials which work though the algorithm: https://sddp.dev/stable/...
Oscar Dowson's user avatar
1 vote

Tips for implementing Benders Decomposition in C++?

For example, If your problem is two-stages stochastic programming, then you can separate your problem into master problem and sub-problem by your hands. Then you can use CPLEX to model both stages in ...
ytsao's user avatar
  • 366
1 vote
Accepted

Deriving a lower bound for a two-stage stochastic problem

It's a while since I asked this question. I have now came across the answer which is as follows: Yes, if the stochastic problem is solved through the horizon based on the realized scenario, it ...
Mostafa's user avatar
  • 2,104

Only top scored, non community-wiki answers of a minimum length are eligible