State-of-the-art Methods for Pseudo-Boolean Solving with SCIP

TL;DR

This paper reviews the top-performing SCIP-based methods for Pseudo-Boolean problems, highlighting recent enhancements and algorithmic innovations that led to success in the 2024 competition.

Contribution

It introduces new algorithmic ideas and improvements to SCIP's Pseudo-Boolean solving capabilities based on recent competition results.

Findings

SCIP-based solvers won five of six categories in the 2024 competition.

SCIP solved 759 out of 1,207 instances, while FiberSCIP solved 776.

Enhanced SCIP's algorithms led to improved performance in Pseudo-Boolean problem solving.

Abstract

The Pseudo-Boolean problem deals with linear or polynomial constraints with integer coefficients over Boolean variables. The objective lies in optimizing a linear objective function, or finding a feasible solution, or finding a solution that satisfies as many constraints as possible. In the 2024 Pseudo-Boolean competition, solvers incorporating the SCIP framework won five out of six categories it was competing in. From a total of 1,207 instances, SCIP successfully solved 759, while its parallel version FiberSCIP solved 776. Based on the results from the competition, we further enhanced SCIP's Pseudo-Boolean capabilities. This article discusses the results and presents the winning algorithmic ideas.