Experiments with Conflict Analysis in Mixed Integer Programming

TL;DR

This paper empirically evaluates two methods for conflict analysis in mixed integer programming, combining implications from infeasible subproblems and LP relaxations, to improve solver performance.

Contribution

It introduces a combined approach to conflict analysis in MIPs and a pool-based conflict management strategy, tested within the SCIP solver.

Findings

Combined conflict analysis methods improve MIP solving efficiency.

Pool-based conflict management outperforms traditional aging strategies.

Experiments on standard MIP benchmarks validate the proposed approaches.

Abstract

The analysis of infeasible subproblems plays an import 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. The first is to analyze the sequence of implications obtained by domain propagation that led to infeasibility. The result of the analysis are one or more sets of contradicting variable bounds from which so-called conflict constraints can be generated. This concept has its origin in solving satisfiability problems and is similarly used in constraint programming. The second is to analyze infeasible linear programming (LP) relaxations. The dual LP solution provides a set of multipliers that can be used to generate a single new globally valid linear constraint. The main contribution of this short paper is an empirical evaluation of two ways to combine these approaches. Experiments are carried out on general MIP instances from standard public test sets such as MIPLIB; the presented algorithms have been implemented within the non-commercial MIP solver SCIP. Moreover, we present a pool-based approach to manage conflicts which addresses the way a MIP solver traverses the search tree better than aging strategies known from SAT solving.