Solving multiobjective discrete optimization problems with propositional minimal model generation

Abstract

We propose a propositional logic based approach to solve MultiObjective Discrete Optimization Problems (MODOPs). In our approach, there exists a one-to-one correspondence between a Pareto front point of MODOP and a P -minimal model of the CNF formula obtained from MODOP. This correspondence is achieved by adopting the order encoding as CNF encoding for multiobjective functions. Finding the Pareto front is done by enumerating all P-minimal models. The beauty of the approach is that each Pareto front point is blocked by a single clause that contains at most one literal for each objective function. We evaluate the effectiveness of our approach by empirically contrasting it to a state-of-the-art MODOP solving technique.