Automatic Algorithm Selection for Pseudo-Boolean Optimization with Given Computational Time Limits

TL;DR

This paper presents an anytime meta-solver for Pseudo-Boolean Optimization that predicts the best solver within time limits, significantly improving over Gurobi in finding feasible solutions for hard instances.

Contribution

The study introduces a novel anytime meta-solver for PBO, demonstrating substantial empirical improvements over the single best solver Gurobi in challenging problem instances.

Findings

Meta-solver finds feasible solutions for 47% of instances Gurobi fails to solve.

Significant performance gains over Gurobi in time-constrained scenarios.

Effective for NP-hard Pseudo-Boolean Optimization problems.

Abstract

Machine learning (ML) techniques have been proposed to automatically select the best solver from a portfolio of solvers, based on predicted performance. These techniques have been applied to various problems, such as Boolean Satisfiability, Traveling Salesperson, Graph Coloring, and others. These methods, known as meta-solvers, take an instance of a problem and a portfolio of solvers as input. They then predict the best-performing solver and execute it to deliver a solution. Typically, the quality of the solution improves with a longer computational time. This has led to the development of anytime selectors, which consider both the instance and a user-prescribed computational time limit. Anytime meta-solvers predict the best-performing solver within the specified time limit. Constructing an anytime meta-solver is considerably more challenging than building a meta-solver without the "anytime" feature. In this study, we focus on the task of designing anytime meta-solvers for the NP-hard optimization problem of Pseudo-Boolean Optimization (PBO), which generalizes Satisfiability and Maximum Satisfiability problems. The effectiveness of our approach is demonstrated via extensive empirical study in which our anytime meta-solver improves dramatically on the performance of Mixed Integer Programming solver Gurobi, which is the best-performing single solver in the portfolio. For example, out of all instances and time limits for which Gurobi failed to find feasible solutions, our meta-solver identified feasible solutions for 47% of these.