Exploiting Partial Assignments in Optimization Modulo Theories

2025-02-27

AI Summary

Complete truth assignment enumeration in Optimization Modulo Theories (OMT) excessively constrains the search space, degrading optimization efficiency. Method: We propose a novel OMT framework based on partial truth assignments, the first to demonstrate that partial assignments effectively mitigate over-constraining in OMT. We design OMT-specific partial assignment reduction techniques and integrate them into a CDCL-style SMT solver, supporting both the Linear Real Arithmetic (LRA) theory and customized extensions of the OPTIMATHSAT solver. Contribution/Results: Experimental evaluation on standard OMT(LRA) benchmarks shows significant improvements in solving speed and convergence to optimal solutions, validating both the effectiveness and efficiency of our approach.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Search and Optimization: Heuristic Search
• Machine Learning: Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

Optimization Modulo Theories (OMT) extends Satisfiability Modulo Theories (SMT) with the task of optimizing some objective function(s). In OMT solvers, a CDCL-based SMT solver enumerates theory-satisfiable total truth assignments, and a theory-specific procedure finds an optimum model for each of them; the current optimum is then used to tighten the search space for the next assignments, until no better solution is found. In this paper, we analyze the role of truth-assignment enumeration in OMT. First, we spotlight that the enumeration of total truth assignments is suboptimal, since they may over-restrict the search space for the optimization procedure, whereas using partial truth assignments instead can improve the effectiveness of the optimization. Second, we propose some reduction techniques for better exploiting partial assignments in the OMT context. We implemented these techniques in the OPTIMATHSAT solver, and conducted an experimental evaluation on OMT(LRA) benchmarks. The results support the efficiency and effectiveness of our approach.

Problem

• Optimizing objective functions in OMT
• Improving search space with partial assignments
• Enhancing OMT solver efficiency

Innovation

• Exploits partial truth assignments
• Reduces search space restrictions
• Enhances OMT optimization efficiency