Questions tagged [benders-decomposition]

For questions related to Benders decomposition, a type of optimization algorithm in which certain variables are optimized in a "master problem," the values of those variables are fixed, the remaining variables are optimized in a "subproblem," cuts are generated to be added to the master problem, and the method repeats.

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Ill-conditioned LP in Benders decomposition

I have implemented a Benders decomposition for a constrained network flow but the LP solver (Gurobi) warns me of the ill-conditioning of the subproblem dual LP. As you can see below, the coefficients ...
Mauricio Zambon's user avatar
6 votes
0 answers
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Benders decomposition for a dense MILP

I am trying to solve a large MILP, but it seems like dense problems can be very difficult for moderns solvers. I tried to solve the problem described below considering only constraints (1) and (2) ...
Enthusiast's user avatar
2 votes
1 answer
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Implementing Logic-based Benders decomposition on a single search tree

Currently, I am working on a scheduling problem and trying to approach it by the logic-based Benders decomposition method. Theoretically, I have everything, i.e., the master and sub problem(s), the ...
Amir Hosseini's user avatar
2 votes
0 answers
100 views

Automated Benders Using Annotations

I'm trying to solve an optimization model using Automated Benders with annotations using CPLEX library in C++. I've defined a master problem and N (number of supply nodes in my model's network) ...
Vala's user avatar
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Benders with MINLP subproblem as the pricing problem of Dantzig Wolfe

I have a convex MINLP that after a Dantzig-Wolfe reformulation, passes most of the difficulty onto the pricing problem, which becomes a convex MINLP itself. The pricing problem should be solvable with ...
J. Dionisio's user avatar
2 votes
0 answers
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Two-stage stochastic with non-linear recourse

I am working on a two-stage facility location problem as I described in this question. I am solving it with the L-shaped method (Benders decomposition). The cost value between each $(i,j)$ is a ...
mars's user avatar
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2 votes
0 answers
265 views

About combinatorial Benders Cuts

I am solving an OR scheduling problem where I assign the patient to (day,OR) tuple in Master Problem. Once the assignment is made, a subproblem can be solved for each (day,OR) tuple independently ...
Amogh Bhosekar's user avatar
1 vote
0 answers
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CPLEX gets stuck in "Performing restart"

During solving my problem using generic lazy cuts (in Benders decomposition fashion), the solver gets stuck logging out "Performing restart 2" for several hours (while the time limit is 30 ...
Amir Hossein Hosseini's user avatar
1 vote
1 answer
60 views

Fast Algorithms for Min-cost Multicommodity Flow Problem with Most Arcs Having 0 cost

I have a min-cost multicommodity flow problem with the following characteristics: Flows can be fractional (integer flows not required) Set of commodity types is $K$, set of demand nodes is $\\{ d_k : ...
graphtheory123's user avatar
1 vote
0 answers
41 views

Is there a way to calcuate the maximum number of cuts in a Benders decomposition?

Since the benders algorithm is finite, there a maximum number of cuts that could theoretically be added. The worst case is that I add cuts for all extreme points and all extreme rays that are part of ...
Arctic_Skill's user avatar
1 vote
0 answers
82 views

Weird behavior when using Automatic Benders Decomposition in CPLEX

I've encountered some weird behavior when using the Automatic Benders Decomposition in CPLEX. I initially solved the MIP without BD and then I compared the results against the Full, Workers and User ...
CHE's user avatar
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1 vote
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Seeking Assistance with Applying Benders Technique for Bilinear Problem Solving

I have two specific types of bilinear terms in the problem. The first type involves the multiplication of an integer variable and a continuous variable, while the second type involves the ...
Samira Fallah's user avatar
1 vote
0 answers
708 views

How to eliminate large matrix coefficients and large RHS warning in Gurobi

I'm solving a large network flow problem using Gurobi to do Benders decomposition in Python. The imported .csvs contain values that typically fall in either zero, the range of [20,200], or with a ...
Emma Kuttler's user avatar
1 vote
0 answers
113 views

Benders Decomposition Problem

$$r_{m_h,s}(n)=\frac B{m_hb_\ell s}\log_2(1+\gamma_{m_h,s}(n))$$ How to deal with multiple subproblems in Benders decomposition when the original objective function is in product form of an integer ...
Sheikh Salman Hassan's user avatar