Dynamic Initial Weight Assignment for MaxSAT

Abdelraouf Ishtaiwi,Qasem Abu Al-Haija

doi:10.3390/a14040115

Abstract

The Maximum Satisfiability (Maximum Satisfiability (MaxSAT)) approach is the choice, and perhaps the only one, to deal with most real-world problems as most of them are unsatisfiable. Thus, the search for a complete and consistent solution to a real-world problem is impractical due to computational and time constraints. As a result, MaxSAT problems and solving techniques are of exceptional interest in the domain of Satisfiability (Satisfiability (SAT)). Our research experimentally investigated the performance gains of extending the most recently developed SAT dynamic Initial Weight assignment technique (InitWeight) to handle the MaxSAT problems. Specifically, we first investigated the performance gains of dynamically assigning the initial weights in the Divide and Distribute Fixed Weights solver (DDFW+Initial Weight for Maximum Satisfiability (DDFW+InitMaxSAT)) over Divide and Distribute Fixed Weights solver (DDFW) when applied to solve a wide range of well-known unweighted MaxSAT problems obtained from DIMACS. Secondly, we compared DDFW+InitMaxSAT’s performance against three known state-of-the-art SAT solving techniques: YalSAT, ProbSAT, and Sparrow. We showed that the assignment of dynamic initial weights increased the performance of DDFW+InitMaxSAT against DDFW by an order of magnitude on the majority of problems and performed similarly otherwise. Furthermore, we showed that the performance of DDFW+InitMaxSAT was superior to the other state-of-the-art algorithms. Eventually, we showed that the InitWeight technique could be extended to handling partial MaxSAT with minor modifications.

Highlights

Maximum Satisfiability (MaxSAT) is a general optimization NP-hard [1] form of the well-known NP-complete propositional Satisfiability (SAT) [2]
We conducted this research in three steps as follows: (1) a survey of the structural information of the problem sets, (2) an investigation of the distribution of clauses weights, and (3) an experimental comparison of the InitWeight mechanism implemented in Divide and Distribute Fixed Weights solver (DDFW) against the state-of-the-art YalSAT, Sparrow, and ProbSAT
The pigeon hole problem set’s encoding is as follows: assuming there are i number of holes and j number of pigeons that must be placed in i, n + 1 number of clauses are generated to ensure a pigeon is put in some hole, and a group of clauses is added to ensure a pigeon can be put in one single hole only

Summary

Introduction

Maximum Satisfiability (MaxSAT) is a general optimization NP-hard [1] form of the well-known NP-complete propositional Satisfiability (SAT) [2]. Given a propositional SAT encoded problem in Conjunctive Normal Form (CNF), where CNF consists of a set of conjunctive clauses and each clause consists of a set of disjunctive literals (propositional variables) or their negations, a solution to a MaxSAT problem is the one with the maximum number of satisfied clauses. Handling real-world problems by employing MaxSAT methods is more practical, as many, if not most, real-world problems are unsatisfiable (an assignment that satisfies all the clauses does not exist). Instead of searching for a completely optimal solution, MaxSAT solving methods aim to find the assignments with the maximum number of satisfied clauses. MaxSAT is of exceptional interest to researchers in the SAT community, as finding a general-purpose solver that could find near-optimum solutions to MaxSAT is an open research area with significant potentials

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Conclusion