🤖 AI Summary
In constraint programming, tabulation of subproblems traditionally relies on manual identification by domain experts—resulting in low efficiency, high error rates, and limited scalability. To address this, we propose the first fully automated tabulation framework. Our method integrates multiple heuristic rules with constraint subgraph structural analysis to automatically identify high-value subproblems; introduces a robustness verification mechanism to mitigate risks associated with harmful tabulations; and supports seamless integration with mainstream solvers—including Minion, Gecode, Chuffed, OR-Tools, and Kissat. Experimental evaluation on standard benchmarks demonstrates that our framework matches or surpasses expert-level manual tabulation in both solution quality and solving efficiency. Key contributions include: (1) the first end-to-end automated tabulation pipeline; (2) a multi-heuristic fusion strategy for subproblem identification; and (3) a verifiable, robust tabulation mechanism—establishing a practical new paradigm for automated constraint model restructuring.
📝 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.
