Unsatisfiable Cores for Constraint Programming

TL;DR

This paper adapts unsatisfiable core techniques from MAXSAT to Constraint Programming, enhancing the solving process for soft constraints by identifying minimal conflicting sets to improve efficiency.

Contribution

It introduces a novel hybrid approach that integrates MAXSAT unsatisfiable core algorithms into Lazy Clause Generation solvers for CP.

Findings

Certain problems benefit significantly from the hybrid approach

The method effectively identifies minimal conflicting soft constraints

Improves solving efficiency for soft constraint problems

Abstract

Constraint Programming (CP) solvers typically tackle optimization problems by repeatedly finding solutions to a problem while placing tighter and tighter bounds on the solution cost. This approach is somewhat naive, especially for soft-constraint optimization problems in which the soft constraints are mostly satisfied. Unsatisfiable-core approaches to solving soft constraint problems in Boolean Satisfiability (e.g. MAXSAT) force all soft constraints to hold initially. When solving fails they return an unsatisfiable core, as a set of soft constraints that cannot hold simultaneously. Using this information the problem is relaxed to allow certain soft constraint(s) to be violated and solving continues. Since Lazy Clause Generation (LCG) solvers can also return unsatisfiable cores we can adapt the MAXSAT unsatisfiable core approach to CP. We implement the original MAXSAT unsatisfiable core solving algorithms WPM1, MSU3 in a state-of-the-art LCG solver and show that there exist problems which benefit from this hybrid approach.