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Algorithms for the maximum satisfiability problem

Algorithmen für das maximale Erfüllbarkeitsproblem

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Abstract

Old and new algorithms for the Maximum Satisfiability problem are studied. We first summarize the different heuristics previously proposed, i.e., the approximation algorithms of Johnson and of Lieberherr for the general Maximum Satisfiability problem, and the heuristics of Lieberherr and Specker, Poljak and Turzik for the Maximum 2-Satisfiability problem. We then consider two recent local search algorithmic schemes, the Simulated Annealing method of Kirkpatrick, Gelatt and Vecchi and the Steepest Ascent Mildest Descent method, and adapt them to the Maximum Satisfiability problem. The resulting algorithms, which avoid being blocked as soon as a local optimum has been found, are shown empirically to be more efficient than the heuristics previously proposed in the literature.

Zusammenfassung

Es werden bekannte und neue Algorithmen für das maximale Erfüllbarkeitsproblem untersucht. Zunächst geben wir eine Übersicht über verschiedene bisher vorgeschlagene Heuristiken wie z.B. die Approximationsalgorithmen von Johnson und von Lieberherr für das allgemeine maximale Erfüllbarkeitsproblem und die Heuristiken von Lieberherr und Specker, sowie von Poljak und Turzik für das maximale 2-Erfüllbarkeitsproblem. Sodann beachten wir zwei neuere lokale Suchverfahren, wie die Simulated Annealing Methode von Kirkpatrick, Gelatt und Vecchi sowie die Methods des steilsten Anstieges und flachsten Abstieges und adaptieren diese Verfahren für das maximale Erfüllbarkeitsproblem. Es zeigt sich, daß diese Verfahren, die nicht in einem lokalen Optimum stehen bleiben, empirisch effizienter sind als die bisher in der Literatur vorgeschlagenen Heuristiken.

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Authors and Affiliations

  1. Rutcor, Hill Center for Mathematical Sciences, Rutgers University, 08903, New Brunswick, NY, U.S.A.

    Pierre Hansen

  2. Département de Mathématiques Appliquées, Gérad and École Polytechnique, Succ. A., C.P. 6079, H3C 3A7, Montréal, Québec, Canada

    Brigitte Jaumard

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  1. Pierre Hansen
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  2. Brigitte Jaumard
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Additional information

Research of the first author was supported by Air Force Office of Scientific Research Grant # AFOSR-0271 to Rutgers University. Research of the second author was carried out while visiting the CAIP Center, Rutgers University.

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Hansen, P., Jaumard, B. Algorithms for the maximum satisfiability problem. Computing 44, 279–303 (1990). https://doi.org/10.1007/BF02241270

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