Conflict-Driven Heuristics for Mixed Integer Programming

TL;DR

This paper introduces novel conflict-driven heuristics for mixed-integer programming that integrate conflict analysis with diving strategies, improving solver performance on benchmark problems.

Contribution

It combines conflict analysis and diving heuristics in MIP solving, creating two new methods that enhance search efficiency and solution quality.

Findings

Both heuristics improve solving times on benchmark sets.

Conflict-driven diving outperforms traditional methods in certain instances.

Enhanced search strategies lead to better dual bounds.

Abstract

Two essential ingredients of modern mixed-integer programming (MIP) solvers are diving heuristics that simulate a partial depth-first search in a branch-and-bound search tree and conflict analysis of infeasible subproblems to learn valid constraints. So far, these techniques have mostly been studied independently: primal heuristics under the aspect of finding high-quality feasible solutions early during the solving process and conflict analysis for fathoming nodes of the search tree and improving the dual bound. Here, we combine both concepts in two different ways. First, we develop a diving heuristic that targets the generation of valid conflict constraints from the Farkas dual. We show that in the primal this is equivalent to the optimistic strategy of diving towards the best bound with respect to the objective function. Secondly, we use information derived from conflict analysis to enhance the search of a diving heuristic akin to classical coefficient diving. The computational performance of both methods is evaluated using an implementation in the source-open MIP solver SCIP. Experiments are carried out on publicly available test sets including Miplib 2010 and Cor@l.

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