Automatic generation of dominance breaking nogoods for a class of constraint optimization problems

Abstract

Constraint Optimization Problems (COPs) ask for an assignment of values to variables in order to optimize an objective subject to constraints that restrict the value combinations in the assignment. They are usually solved by the classical Branch and Bound (B&B) search algorithm. Dominance breaking is an important technique in B&B to prune assignments that are subordinate to others concerning the objective value and/or the satisfiability of constraints. In practice, the addition of constraints for dominance breaking can drastically speed up the B&B search for solving many COPs. However, identification of suboptimal assignments in COPs and derivation of useful constraints for dominance breaking are usually problem-specific and require sophisticated human insights on the problem structure.This paper proposes the first theoretical and practical framework for automatic generation of dominance breaking constraints for a class of COPs consisting of efficiently checkable objectives and constraints. In particular, the framework focuses on generating nogood constraints representing incompatible value assignments and formulates nogood generation as solving auxiliary constraint satisfaction problems. The proposed method can generate nogoods of varying strengths for dominance breaking by controlling the number of involved variables. Experimentation on various benchmarks demonstrates the effectiveness of the proposal in both efficiency and ease of use. The superior performance is also supported by a theoretical analysis to compare the relative strength of automatically generated nogoods with manually derived dominance breaking constraints in the literature.