Solution Dominance over Constraint Satisfaction Problems

TL;DR

This paper introduces a formal framework called solution dominance for reasoning about preferred solutions in CSPs, extending MiniZinc with dominance nogoods to facilitate flexible and comparative solving of diverse dominance-based problems.

Contribution

It formalizes solution dominance in CSPs as Constraint Dominance Problems, extends MiniZinc with dominance nogoods, and provides a generic incremental solving method compatible with existing solvers.

Findings

Framework captures various CSP variants including optimization and multi-objective problems.

Extended MiniZinc to incorporate dominance relations via dominance nogoods.

Proposed solving method supports experimentation with different dominance relations.

Abstract

Constraint Satisfaction Problems (CSPs) typically have many solutions that satisfy all constraints. Often though, some solutions are preferred over others, that is, some solutions dominate other solutions. We present solution dominance as a formal framework to reason about such settings. We define Constraint Dominance Problems (CDPs) as CSPs with a dominance relation, that is, a preorder over the solutions of the CSP. This framework captures many well-known variants of constraint satisfaction, including optimization, multi-objective optimization, Max-CSP, minimal models, minimum correction subsets as well as optimization over CP-nets and arbitrary dominance relations. We extend MiniZinc, a declarative language for modeling CSPs, to CDPs by introducing dominance nogoods; these can be derived from dominance relations in a principled way. A generic method for solving arbitrary CDPs incrementally calls a CSP solver and is compatible with any existing solver that supports MiniZinc. This encourages experimenting with different solution dominance relations for a problem, as well as comparing different solvers without having to modify their implementations.