TabID: Automatic Identification and Tabulation of Subproblems in Constraint Models

TL;DR

This paper introduces TabID, an automated method for identifying subproblems in constraint models suitable for tabulation, aiming to enhance solver performance without manual intervention.

Contribution

TabID provides a novel automated approach with heuristics and checks to identify subproblems for tabulation, reducing manual effort and improving constraint solver efficiency.

Findings

Automated tabulation matches or exceeds manual results.

Effective across multiple solvers including CP and SAT.

Potential for integration into automated modeling tools.

Abstract

The performance of a constraint model can often be improved by converting a subproblem into a single table constraint (referred to as tabulation). Finding subproblems to tabulate is traditionally a manual and time-intensive process, even for expert modellers. This paper presents TabID, an entirely automated method to identify promising subproblems for tabulation in constraint programming. We introduce a diverse set of heuristics designed to identify promising candidates for tabulation, aiming to improve solver performance. These heuristics are intended to encapsulate various factors that contribute to useful tabulation. We also present additional checks to limit the potential drawbacks of suboptimal tabulation. We comprehensively evaluate our approach using benchmark problems from existing literature that previously relied on manual identification by constraint programming experts of constraints to tabulate. We demonstrate that our automated identification and tabulation process achieves comparable, and in some cases improved results. We empirically evaluate the efficacy of our approach on a variety of solvers, including standard CP (Minion and Gecode), clause-learning CP (Chuffed and OR-Tools) and SAT solvers (Kissat). Our findings highlight the substantial potential of fully automated tabulation, suggesting its integration into automated model reformulation tools.