Exploiting Semidefinite Relaxations in Constraint Programming

TL;DR

This paper explores integrating semidefinite relaxations into constraint programming to enhance search efficiency and pruning, demonstrating significant benefits on combinatorial problems like stable set and maximum clique.

Contribution

It introduces a novel approach that uses semidefinite relaxations to guide search and prune branches in constraint programming, improving performance on combinatorial problems.

Findings

Semidefinite relaxations effectively guide search tree traversal.

Using relaxations improves pruning and reduces computation time.

Experimental results show significant performance gains.

Abstract

Constraint programming uses enumeration and search tree pruning to solve combinatorial optimization problems. In order to speed up this solution process, we investigate the use of semidefinite relaxations within constraint programming. In principle, we use the solution of a semidefinite relaxation to guide the traversal of the search tree, using a limited discrepancy search strategy. Furthermore, a semidefinite relaxation produces a bound for the solution value, which is used to prune parts of the search tree. Experimental results on stable set and maximum clique problem instances show that constraint programming can indeed greatly benefit from semidefinite relaxations.