Local Rapid Learning for Integer Programs

Berthold, Timo; Stuckey, Peter J.; Witzig, Jakob

doi:10.1007/978-3-030-19212-9_5

Cited by 4 publications

(5 citation statements)

References 32 publications

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“…The combination of two measures that we introduced in this paper fulfills that role and captures the impact of dual degeneracy well, as we demonstrated in our analysis. It has already been successfully applied to improve the hybrid branching rule (Achterberg and Berthold 2009) of SCIP, see Berthold et al (2019a), and in recent work on local rapid learning (Berthold et al 2019b).…”

Section: Discussionmentioning

confidence: 99%

“…Multiple ways to exploit degeneracy in different algorithmic components of the MIP solver Gurobi are discussed by Achterberg (2018). Finally, the authors of this paper investigated branching improvements obtained by exploiting dual degeneracy and the knowledge of multiple optimal LP solutions (Berthold and Salvagnin 2013;Berthold et al 2019a).…”

Section: Fig 1 Illustration Of Primal and Dual Degenerate Solutionsmentioning

confidence: 99%

“…Therefore, we will use this method for a deeper analysis of the effects of dual degeneracy in MIP models in the following. More practical methods to sample alternative LP optima are discussed by Berthold et al (2019a).…”

Section: The Effect Of Dual Degeneracy On Lp Solution Valuesmentioning

confidence: 99%

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An exploratory computational analysis of dual degeneracy in mixed-integer programming

Gamrath

Berthold²,

Salvagnin³

2020

EURO Journal on Computational Optimization

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Dual degeneracy, i.e., the presence of multiple optimal bases to a linear programming (LP) problem, heavily affects the solution process of mixed integer programming (MIP) solvers. Different optimal bases lead to different cuts being generated, different branching decisions being taken and different solutions being found by primal heuristics. Nevertheless, only a few methods have been published that either avoid or exploit dual degeneracy. The aim of the present paper is to conduct a thorough computational study on the presence of dual degeneracy for the instances of well-known public MIP instance collections. How many instances are affected by dual degeneracy? How degenerate are the affected models? How does branching affect degeneracy: Does it increase or decrease by fixing variables? Can we identify different types of degenerate MIPs? As a tool to answer these questions, we introduce a new measure for dual degeneracy: the variable–constraint ratio of the optimal face. It provides an estimate for the likelihood that a basic variable can be pivoted out of the basis. Furthermore, we study how the so-called cloud intervals—the projections of the optimal face of the LP relaxations onto the individual variables—evolve during tree search and the implications for reducing the set of branching candidates.

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Section: Discussionmentioning

confidence: 99%

Section: Fig 1 Illustration Of Primal and Dual Degenerate Solutionsmentioning

confidence: 99%

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An exploratory computational analysis of dual degeneracy in mixed-integer programming

Gamrath

Berthold²,

Salvagnin³

2020

EURO Journal on Computational Optimization

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“…We plan to implement NLPbased conflict analysis into the academic constraint integer programming solver SCIP and to study its impact on solver behavior. As in the MIP case, infeasibility information might be used in several other contexts, consider hybrid branching [3], conflict-driven diving heuristics [54], and also rapid learning [7,9].…”

Section: Outlook and Theoretical Thoughtsmentioning

confidence: 99%

A Status Report on Conflict Analysis in Mixed Integer Nonlinear Programming

Witzig

Berthold²,

Stefan³

2019

Integration of Constraint Programming, Artificial Intelligence, and Operations Research

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Mixed integer nonlinear programs (MINLPs) are arguably among the hardest optimization problems, with a wide range of applications. MINLP solvers that are based on linear relaxations and spatial branching work similar as mixed integer programming (MIP) solvers in the sense that they are based on a branch-and-cut algorithm, enhanced by various heuristics, domain propagation, and presolving techniques. However, the analysis of infeasible subproblems, which is an important component of most major MIP solvers, has been hardly studied in the context of MINLPs. There are two main approaches for infeasibility analysis in MIP solvers: conflict graph analysis, which originates from artificial intelligence and constraint programming, and dual ray analysis.The main contribution of this short paper is twofold. Firstly, we present the first computational study regarding the impact of dual ray analysis on convex and nonconvex MINLPs. In that context, we introduce a modified generation of infeasibility proofs that incorporates linearization cuts that are only locally valid. Secondly, we describe an extension of conflict analysis that works directly with the nonlinear relaxation of convex MINLPs instead of considering a linear relaxation. This is work-in-progress, and this short paper is meant to present first theoretical considerations without a computational study for that part.

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“…In this paper, we mostly follow the concepts and the notation of [2]. Followup publications suggested methods to use conflict information for variable selection in branching [3,34], to tentatively generate conflicts before branching [6,8,11], and to analyze infeasibility detected in primal heuristics [9,10,51]. Besides, instead of simply analyzing infeasibility that is derived more or less coincidentally, methods were introduced to generate additional conflict information explicitly [21,51].…”

Section: Introductionmentioning

confidence: 99%

Computational aspects of infeasibility analysis in mixed integer programming

Witzig

Berthold²,

Stefan³

2021

Math. Prog. Comp.

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The analysis of infeasible subproblems plays an important role in solving mixed integer programs (MIPs) and is implemented in most major MIP solvers. There are two fundamentally different concepts to generate valid global constraints from infeasible subproblems: conflict graph analysis and dual proof analysis. While conflict graph analysis detects sets of contradicting variable bounds in an implication graph, dual proof analysis derives valid linear constraints from the proof of the dual LP’s unboundedness. The main contribution of this paper is twofold. Firstly, we present three enhancements of dual proof analysis: presolving via variable cancellation, strengthening by applying mixed integer rounding functions, and a filtering mechanism. Further, we provide a comprehensive computational study evaluating the impact of every presented component regarding dual proof analysis. Secondly, this paper presents the first combined approach that uses both conflict graph and dual proof analysis simultaneously within a single MIP solution process. All experiments are carried out on general MIP instances from the standard public test set Miplib 2017; the presented algorithms have been implemented within the non-commercial MIP solver and the commercial MIP solver .

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Local Rapid Learning for Integer Programs

Cited by 4 publications

References 32 publications

An exploratory computational analysis of dual degeneracy in mixed-integer programming

An exploratory computational analysis of dual degeneracy in mixed-integer programming

A Status Report on Conflict Analysis in Mixed Integer Nonlinear Programming

Computational aspects of infeasibility analysis in mixed integer programming

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