Filtering Algorithms for the Multiset Ordering Constraint

TL;DR

This paper introduces a new global constraint called the multiset ordering constraint, along with efficient filtering algorithms, demonstrating their effectiveness in symmetry breaking and optimization in constraint programming.

Contribution

The paper proposes novel filtering algorithms for the multiset ordering constraint, enhancing propagation efficiency and effectiveness in constraint satisfaction problems.

Findings

Algorithms are sound and complete.

Experimental results show significant benefits in benchmark problems.

Alternative propagation methods are also discussed.

Abstract

Constraint programming (CP) has been used with great success to tackle a wide variety of constraint satisfaction problems which are computationally intractable in general. Global constraints are one of the important factors behind the success of CP. In this paper, we study a new global constraint, the multiset ordering constraint, which is shown to be useful in symmetry breaking and searching for leximin optimal solutions in CP. We propose efficient and effective filtering algorithms for propagating this global constraint. We show that the algorithms are sound and complete and we discuss possible extensions. We also consider alternative propagation methods based on existing constraints in CP toolkits. Our experimental results on a number of benchmark problems demonstrate that propagating the multiset ordering constraint via a dedicated algorithm can be very beneficial.