A Multilevel Tabu Search for the Maximum Satisfiability Problem ()

Noureddine Bouhmala, Sirar Salih

Department of Information and Communication Technology, University of Agder, Grimstad, Norway.

Department of Maritime Technology and Innovation, Vestfold University College, Horten, Norway.

**DOI: **10.4236/ijcns.2012.510068
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Department of Information and Communication Technology, University of Agder, Grimstad, Norway.

Department of Maritime Technology and Innovation, Vestfold University College, Horten, Norway.

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.

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N. Bouhmala and S. Salih, "A Multilevel Tabu Search for the Maximum Satisfiability Problem," *International Journal of Communications, Network and System Sciences*, Vol. 5 No. 10, 2012, pp. 661-670. doi: 10.4236/ijcns.2012.510068.

Conflicts of Interest

The authors declare no conflicts of interest.

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