Certifying Pareto-Optimality in Multi-Objective Maximum Satisfiability

2025-01-29

AI Summary

This work addresses the challenge of trustworthy verification of Pareto-optimal solutions for the multi-objective maximum satisfiability (MO-MaxSAT) problem. Methodologically, it introduces the first verifiable proof logging mechanism based on the VeriPB format—without modifying the VeriPB standard or existing proof checkers—by formalizing multi-objective dominance relations via preordered logic, thereby enabling automatic generation and machine-checkable certification of Pareto-optimality proofs. Key contributions include: (i) the first rigorous, lightweight, and integrable verifiability framework for MO-MaxSAT; (ii) end-to-end implementation within state-of-the-art solvers; and (iii) empirical evaluation demonstrating strong scalability and bounded runtime overhead. The approach significantly enhances the reliability and trustworthiness of automated reasoning tools in multi-objective optimization settings.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Search and Optimization: Metareasoning and Metaheuristics
• Knowledge Representation and Reasoning: Preferences

Application Category

• Web Mining and Content Analysis: Web data provenance, reliability, and authenticity
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

Due to the wide employment of automated reasoning in the analysis and construction of correct systems, the results reported by automated reasoning engines must be trustworthy. For Boolean satisfiability (SAT) solvers - and more recently SAT-based maximum satisfiability (MaxSAT) solvers - trustworthiness is obtained by integrating proof logging into solvers, making solvers capable of emitting machine-verifiable proofs to certify correctness of the reasoning steps performed. In this work, we enable for the first time proof logging based on the VeriPB proof format for multi-objective MaxSAT (MO-MaxSAT) optimization techniques. Although VeriPB does not offer direct support for multi-objective problems, we detail how preorders in VeriPB can be used to provide certificates for MO-MaxSAT algorithms computing a representative solution for each element in the non-dominated set of the search space under Pareto-optimality, without extending the VeriPB format or the proof checker. By implementing VeriPB proof logging into a state-of-the-art multi-objective MaxSAT solver, we show empirically that proof logging can be made scalable for MO-MaxSAT with reasonable overhead.

Problem

• Multi-objective MaxSAT
• Automated Reasoning
• Reliability

Innovation

• VeriPB
• Multi-objective MaxSAT
• Solution Verification