Translating finite-domain integer constraint models to CP/SMT/ILP/PB/SAT solvers with CPMpy

2026-08-15

AI Summary

This study addresses the high cost and error-proneness of model refactoring caused by paradigm disparities among constraint solvers. We propose a modular automated translation framework based on CPMpy that employs a layered waterfall architecture to uniformly handle sub-expression negation and auxiliary variable generation while optimizing linearization strategies for nonlinear operators. This approach enables seamless translation from high-level models to low-level paradigms, including CP, SMT, and ILP. Experimental results demonstrate that the framework effectively eliminates manual rewriting and that its optimized linearization significantly enhances ILP and PB solving performance. Consequently, this work provides an efficient, flexible, and standardized solution for the automatic benchmarking of multi-paradigm solvers in combinatorial optimization.

Abstract

Constraint solving is a declarative approach for solving combinatorial satisfaction and optimization problems. The user specifies their problem through constraints and decision variables, and a generic solver is used to find a solution. Several constraint-solving technologies exist, and certain solvers perform well on certain problems. Therefore, it is useful to try different solvers given a particular application. However, each solving paradigm supports different types of constraints and decision variables. Our goal is to translate high-level constraint satisfaction and optimization problems into any lower-level formalism, including CP, SMT QF-LIA, ILP, PB and (Max)SAT. This allows for comparing different solving technologies for a particular problem, without requiring a user to manually remodel it for each solving paradigm. We define a high-level language of logical and arithmetic operations, and useful additional functions and constraints, which are known as global constraints in the CP community. We then present a modular framework for transforming our high-level modeling language to CP/SMT/ILP/PB and (Max)SAT solvers. While many transformations are partly described in the literature, we observe that they can be implemented through a modular waterfall of smaller components, where lower-level paradigms reuse the transformations of higher-level paradigms. Two recurring challenges are handling the negation of arbitrary subexpressions and avoiding the introduction of auxiliary variables. Additionally, we take special care linearizing non-linear operators for ILP, PB and SAT-solvers. The transformation waterfall is implemented and evaluated in the open-source CPMpy library. Our results show that constraint models significantly change throughout the transformations, and that optimizations to the linearization of constraints are essential for ILP and PB solvers.

Problem

• Constraint Solving
• Model Translation
• Solver Interoperability
• Combinatorial Optimization

Innovation

• Modular Transformation Waterfall
• CPMpy
• Non-linear Linearization
• Multi-solver Translation
• Auxiliary Variable Avoidance