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… 

Improving the heuristic performance of Benders ’ decomposition

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

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

TLDR
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

TLDR
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

TLDR
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

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

A simulation-optimization approach for the stochastic discrete cost multicommodity flow problem

TLDR
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

TLDR
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

AHybridAlgorithmofAntColonyandBendersDecomposition for Large-Scale Mixed Integer Linear Programming

TLDR
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 artiˆcial intelligence.

References

SHOWING 1-10 OF 17 REFERENCES

Proximity search for 0-1 mixed-integer convex programming

TLDR
Promising computational results are presented, suggesting that proximity search can be quite effective in quickly refining a given feasible solution, particularly true when a sequence of similar MIPs has to be solved as, e.g., in a column-generation setting.

Partial Decomposition Strategies for Two-Stage Stochastic Integer Programs

We propose the concept of partial Benders decomposition, based on the idea of retaining a subset of scenario subproblems in the master formulation and develop a theory to support it that illustrates

Local branching

TLDR
This paper investigates the use of a generic MIP solver as a black-box ``tactical'' tool to explore effectively suitable solution subspaces defined and controlled at a ``strategic'' level by a simple external branching framework.

Strengthened Benders Cuts for Stochastic Integer Programs with Continuous Recourse

TLDR
It is demonstrated that using split cuts within the cut-and-project framework can significantly improve the performance of Benders decomposition and yield stronger relaxations in general when using multiple split disjunctions.

Progressive hedging‐based metaheuristics for stochastic network design

TLDR
A two‐stage stochastic programming formulation, where design decisions make up the first stage, while recourse decisions are made in the second stage to distribute the commodities according to observed demands, which is numerically shown to be computationally efficient and to yield high‐quality solutions under various problem characteristics and demand correlations.

The feasibility pump

TLDR
The outcome is that FP, in spite of its simple foundation, proves competitive with ILOG-Cplex both in terms of speed and quality of the first solution delivered.

Rounding and Propagation Heuristics for Mixed Integer Programming

TLDR
This paper focuses on primal heuristics that only employ computationally inexpensive procedures such as rounding and logical deductions (propagation), and introduces a new performance measure, the primal integral.

Using Constraint Programming and Local Search Methods to Solve Vehicle Routing Problems

TLDR
This work uses a local search method that is analogous to the shuffling technique of job-shop scheduling, and so meshes well with constraint programming technology, to solve vehicle routing problems.

Measuring the impact of primal heuristics

Accelerating Benders Decomposition by Local Branching

TLDR
This paper shows how local branching can be used to accelerate the classical Benders decomposition algorithm by applying local branching throughout the solution process, and shows how Benders feasibility cuts can be strengthened or replaced with local branching constraints.