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

TL;DR

This work analyzes state-of-the-art methods for solving Pseudo-Boolean problems within the SCIP framework and its parallel variant FiberSCIP. It introduces and integrates PB-specific enhancements—RLT cuts for AND constraints, Flower inequalities, symmetry handling, robust numerical strategies, large-integer heuristics, and cut-based PB conflict analysis—into SCIP/FiberSCIP. PB24 competition results show SCIP-based solvers achieved top performance across multiple categories, with post-competition refinements yielding additional solved instances and faster runtimes, and an emphasis on the pivotal role of symmetry handling. The findings underscore the practical viability and effectiveness of a SCIP-based approach for diverse PB problem classes in both single- and multi-threaded settings.

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.

Figures (1)

• Figure 1: Running time for each solved instance