Exploiting Functional Constraints in Automatic Dominance Breaking for Constraint Optimization

Dominance breaking is a powerful technique in improving the solving efficiency of Constraint Optimization Problems (COPs) by removing provably suboptimal solutions with additional constraints. While dominance breaking is effective in a range of practical problems, it is usually problem specific and requires human insights into problem structures to come up with correct dominance breaking constraints. Recently, a framework is proposed to generate nogood constraints automatically for dominance breaking, which formulates nogood generation as solving auxiliary Constraint Satisfaction Problems (CSPs). However, the framework uses a pattern matching approach to synthesize the auxiliary generation CSPs from the specific forms of objectives and constraints in target COPs, and is only applicable to a limited class of COPs. This paper proposes a novel rewriting system to derive constraints for the auxiliary generation CSPs automatically from COPs with nested function calls, significantly generalizing the original framework. In particular, the rewriting system exploits functional constraints flattened from nested functions in a high-level modeling language. To generate more effective dominance breaking nogoods and derive more relaxed constraints in generation CSPs, we further characterize how to extend the system with rewriting rules exploiting function properties, such as monotonicity, commutativity, and associativity, for specific functional constraints. Experimentation shows significant runtime speedup using the dominance breaking nogoods generated by our proposed method. Studying patterns of generated nogoods also demonstrates that our proposal can reveal dominance relations in the literature and discover new dominance relations on problems with ineffective or no known dominance breaking constraints.