Exact and approximate determination of the Pareto set using minimal correction subsets

TL;DR

This paper advances methods for solving multi-objective Boolean optimization by ensuring MCSs correspond to Pareto-optimal solutions and introduces algorithms that efficiently approximate the Pareto frontier with guarantees.

Contribution

It demonstrates that MCS enumeration can be adapted to always find Pareto-optimal solutions and proposes two algorithms for guaranteed approximation of the Pareto frontier.

Findings

New algorithms outperform state-of-the-art in approximating Pareto frontiers.

Guaranteed approximation ratios achieved in multiple benchmark sets.

Method ensures MCSs directly correspond to Pareto-optimal solutions.

Abstract

Recently, it has been shown that the enumeration of Minimal Correction Subsets (MCS) of Boolean formulas allows solving Multi-Objective Boolean Optimization (MOBO) formulations. However, a major drawback of this approach is that most MCSs do not correspond to Pareto-optimal solutions. In fact, one can only know that a given MCS corresponds to a Pareto-optimal solution when all MCSs are enumerated. Moreover, if it is not possible to enumerate all MCSs, then there is no guarantee of the quality of the approximation of the Pareto frontier. This paper extends the state of the art for solving MOBO using MCSs. First, we show that it is possible to use MCS enumeration to solve MOBO problems such that each MCS necessarily corresponds to a Pareto-optimal solution. Additionally, we also propose two new algorithms that can find a (1 + {\varepsilon})-approximation of the Pareto frontier using MCS enumeration. Experimental results in several benchmark sets show that the newly proposed algorithms allow finding better approximations of the Pareto frontier than state-of-the-art algorithms, and with guaranteed approximation ratios.