Adaptive Algorithmic Behavior for Solving Mixed Integer Programs Using Bandit Algorithms

Hendel, Gregor; Miltenberger, Matthias; Witzig, Jakob

doi:10.1007/978-3-030-18500-8_64

Cited by 7 publications

(1 citation statement)

References 7 publications

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“…Adaptive algorithm selection may also be beneficial in other parts of the solver where the choice between similar methods largely affects the overall performance. In a recent article [42], promising results are presented for diving heuristics, and for dynamic switching between different pricing strategies of the dual simplex procedure to maximize the node throughput during the search. Second, we hope that the software design of the introduced ALNS framework proves useful as a development platform for incorporating novel LNS-related heuristic ideas and algorithmic enhancements into SCIP more easily in the future.…”

Section: Discussionmentioning

confidence: 99%

Adaptive large neighborhood search for mixed integer programming

Hendel

2021

Math. Prog. Comp.

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Large Neighborhood Search (LNS) heuristics are among the most powerful but also most expensive heuristics for mixed integer programs (MIP). Ideally, a solver adaptively concentrates its limited computational budget by learning which LNS heuristics work best for the MIP problem at hand. To this end, this work introduces Adaptive Large Neighborhood Search (ALNS) for MIP, a primal heuristic that acts as a framework for eight popular LNS heuristics such as Local Branching and Relaxation Induced Neighborhood Search (RINS). We distinguish the available LNS heuristics by their individual search spaces, which we call auxiliary problems. The decision which auxiliary problem should be executed is guided by selection strategies for the multi armed bandit problem, a related optimization problem during which suitable actions have to be chosen to maximize a reward function. In this paper, we propose an LNS-specific reward function to learn to distinguish between the available auxiliary problems based on successful calls and failures. A second, algorithmic enhancement is a generic variable fixing prioritization, which ALNS employs to adjust the subproblem complexity as needed. This is particularly useful for some LNS problems which do not fix variables by themselves. The proposed primal heuristic has been implemented within the MIP solver SCIP. An extensive computational study is conducted to compare different LNS strategies within our ALNS framework on a large set of publicly available MIP instances from the MIPLIB and Coral benchmark sets. The results of this simulation are used to calibrate the parameters of the bandit selection strategies. A second computational experiment shows the computational benefits of the proposed ALNS framework within the MIP solver SCIP.

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Section: Discussionmentioning

confidence: 99%

Adaptive large neighborhood search for mixed integer programming

Hendel

2021

Math. Prog. Comp.

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Online Learning for Scheduling MIP Heuristics

Chmiela

Gleixner

Lichocki

et al. 2023

Lecture Notes in Computer Science

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Machine learning augmented branch and bound for mixed integer linear programming

Scavuzzo,

Aardal,

Lodi

et al. 2024

Math. Program.

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Mixed Integer Linear Programming (MILP) is a pillar of mathematical optimization that offers a powerful modeling language for a wide range of applications. The main engine for solving MILPs is the branch-and-bound algorithm. Adding to the enormous algorithmic progress in MILP solving of the past decades, in more recent years there has been an explosive development in the use of machine learning for enhancing all main tasks involved in the branch-and-bound algorithm. These include primal heuristics, branching, cutting planes, node selection and solver configuration decisions. This article presents a survey of such approaches, addressing the vision of integration of machine learning and mathematical optimization as complementary technologies, and how this integration can benefit MILP solving. In particular, we give detailed attention to machine learning algorithms that automatically optimize some metric of branch-and-bound efficiency. We also address appropriate MILP representations, benchmarks and software tools used in the context of applying learning algorithms.

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Adaptive Algorithmic Behavior for Solving Mixed Integer Programs Using Bandit Algorithms

Cited by 7 publications

References 7 publications

Adaptive large neighborhood search for mixed integer programming

Adaptive large neighborhood search for mixed integer programming

Online Learning for Scheduling MIP Heuristics

Machine learning augmented branch and bound for mixed integer linear programming

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