Abstract
The maximum satisfiability problem (MAX-SAT) refers to the task of finding a variable assignment that satisfies the maximum number of clauses (or the sum of weight of satisfied clauses) in a Boolean Formula. Most local search algorithms including tabu search rely on the 1-flip neighbourhood structure. In this work, we introduce a tabu search algorithm that makes use of the multilevel paradigm for solving MAX-SAT problems. The multilevel paradigm refers to the process of dividing large and difficult problems into smaller ones, which are hopefully much easier to solve, and then work backward towards the solution of the original problem, using a solution from a previous level as a starting solution at the next level. This process aims at looking at the search as a multilevel process operating in a coarse-to-fine strategy evolving from k-flip neighbourhood to 1-flip neighbourhood-based structure. Experimental results comparing the multilevel tabu search against its single level variant are presented.
Highlights
IntroductionComplete [1] plays a central role problem in many applications in the fields of VLSI Computer-Aided design, Computing Theory, and Artificial Intelligence
The satisfiability problem which is known to be NP-complete [1] plays a central role problem in many applications in the fields of VLSI Computer-Aided design, Computing Theory, and Artificial Intelligence
We introduce a tabu search algorithm that makes use of the multilevel paradigm for solving maximum satisfiability problem (MAX-SAT) problems
Summary
Complete [1] plays a central role problem in many applications in the fields of VLSI Computer-Aided design, Computing Theory, and Artificial Intelligence. Efficient methods that can solve large and hard instances of MAX-SAT are eagerly sought Due to their combinatorial explosion nature, large and complex MAX-SAT problems are hard to solve using systematic algorithms based on branch and bound techniques [2]. This work is motivated by the recent results presented in [5] where the multilevel paradigm was capable of improving the asymptotic convergence of memetic algorithms dramatically on large industrial instances. To this end, the focus is restricted to formulas in which all the weights are equal to 1 i.e. unweighted MAX-SAT) using a offset of industrial problem instances.
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