# Proximity Benders: a decomposition heuristic for stochastic programs

@article{Boland2016ProximityBA, title={Proximity Benders: a decomposition heuristic for stochastic programs}, author={Natashia Boland and Matteo Fischetti and Michele Monaci and Martin W. P. Savelsbergh}, journal={Journal of Heuristics}, year={2016}, volume={22}, pages={181-198} }

In this paper we present a heuristic approach to two-stage mixed-integer linear stochastic programming models with continuous second stage variables. A common solution approach for these models is Benders decomposition, in which a sequence of (possibly infeasible) solutions is generated, until an optimal solution is eventually found and the method terminates. As convergence may require a large amount of computing time for hard instances, the method may be unsatisfactory from a heuristic point…

## 23 Citations

### Improving the heuristic performance of Benders ’ decomposition

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- 2018

A general enhancement of the Benders’ decomposition algorithm can be achieved through the improved use of large neighbourhood search heuristics within mixed-integer programming solvers. While…

### Large neighbourhood Benders ’ search

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A general enhancement of the Benders’ decomposition algorithm can be achieved through the improved use of large neighbourhood search heuristics within mixed-integer programming solvers. While…

### A Hybrid Algorithm of Ant Colony and Benders Decomposition for Large-Scale Mixed Integer Linear Programming

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- 2022

A low-workload, time-saving, and high-accuracy hybrid algorithm to solve MILP problems with a large amount of variables, which can be widely used in more commercial solvers and promote the utilization of the artificial intelligence.

### A Benders Decomposition Method for Two-Stage Stochastic Network Design Problems

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A Benders decomposition algorithm capable of efficiently solving large-scale instances of the well-known multi-commodity capacitated network design problem with demand uncertainty with numerical results confirm the superiority of the proposed algorithm over existing ones.

### Weighted proximity search

- Computer ScienceJ. Heuristics
- 2021

The concept of weighted Hamming distance is introduced that allows to design a new method called weighted proximity search, where low weights are associated with the variables whose value in the current solution is promising to change in order to find an improved solution, while high weights are assigned to variables that are expected to remain unchanged.

### Enhancing large neighbourhood search heuristics for Benders' decomposition

- BusinessJ. Heuristics
- 2021

A general enhancement of the Benders’ decomposition (BD) algorithm can be achieved through the improved use of large neighbourhood search heuristics within mixed-integer programming solvers. While…

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This article addresses a variant of the Discrete Cost Multicommodity Flow problem with random demands, where a penalty is incurred for each unrouted demand, and a simulation-optimization approach is developed to solve this challenging problem approximately.

### An Asynchronous Parallel Benders Decomposition Method

- Computer Science
- 2019

An asynchronous parallel BD method is introduced and it is shown that the proposed algorithm converges to the global optima and is suggested various acceleration strategies to enhance its performance.

### The Benders decomposition algorithm: A literature review

- Computer ScienceEur. J. Oper. Res.
- 2017

### AHybridAlgorithmofAntColonyandBendersDecomposition for Large-Scale Mixed Integer Linear Programming

- Computer Science
- 2022

A low-workload, time-saving, and high-accuracy hybrid algorithm to solve MILP problems with a large amount of variables, which can be widely used in more commercial solvers and promote the utilization of the articial intelligence.

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