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GRASP with Path-Relinking for the Weighted Maximum Satisfiability Problem

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Experimental and Efficient Algorithms (WEA 2005)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 3503))

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Abstract

A GRASP with path-relinking for finding good-quality solutions of the weighted maximum satisfiability problem (MAX-SAT) is described in this paper. GRASP, or Greedy Randomized Adaptive Search Procedure, is a randomized multi-start metaheuristic, where at each iteration locally optimal solutions are constructed, each independent of the others. Previous experimental results indicate its effectiveness for solving weighted MAX-SAT instances. Path-relinking is a procedure used to intensify the search around good-quality isolated solutions that have been produced by the GRASP heuristic. Experimental comparison of the pure GRASP (without path-relinking) and the GRASP with path-relinking illustrates the effectiveness of path-relinking in decreasing the average time needed to find a good-quality solution for the weighted maximum satisfiability problem.

AT&T Labs Research Technical Report TD-68QNGR. January 17, 2005. The research of Panos M. Pardalos is partially funded by NSF and CRDF grants.

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References

  1. Aiex, R.M., Binato, S., Resende, M.G.C.: Parallel GRASP with path-relinking for job shop scheduling. Parallel Computing 29, 393–430 (2003)

    Article  MathSciNet  Google Scholar 

  2. Aiex, R.M., Resende, M.G.C., Pardalos, P.M., Toraldo, G.: GRASP with path relinking for three-index assignment. INFORMS J. on Computing (2005) (In press)

    Google Scholar 

  3. Asano, T.: Approximation algorithms for MAX-SAT: Yannakakis vs. Goemans-Williamson. In: 5th IEEE Israel Symposium on the Theory of Computing and Systems, pp. 24–37 (1997)

    Google Scholar 

  4. Battiti, R., Protasi, M.: Reactive search, a history-sensitive heuristic for MAX-SAT. ACM Journal of Experimental Algorithms 2(2) (1997)

    Google Scholar 

  5. Battiti, R., Protasi, M.: Approximate algorithms and heuristics for the MAX-SAT. In: Du, D.Z., Pardalos, P.M. (eds.) Handbook of Combinatorial Optimization, vol. 1, pp. 77–148. Kluwer Academic Publishers, Dordrecht (1998)

    Google Scholar 

  6. Canuto, S.A., Resende, M.G.C., Ribeiro, C.C.: Local search with perturbations for the prize-collecting Steiner tree problem in graphs. Networks 38, 50–58 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  7. Chen, J., Friesen, D., Zheng, H.: Tight bound on johnson’s algorithm for MAX-SAT. In: Proceedings of the 12th Annual IEEE Conference on Computational Complexity, pp. 274–281 (1997)

    Google Scholar 

  8. Cook, S.A.: The complexity of theorem-proving procedures. In: Proceedings of the Third annual ACM Symposium on Theory of Computing, pp. 151–158 (1971)

    Google Scholar 

  9. Feige, U., Goemans, M.X.: Approximating the value of two proper proof systems, with applications to MAX-2SAT and MAX-DICUT. In: Proceeding of the Third Israel Symposium on Theory of Computing and Systems, pp. 182–189 (1995)

    Google Scholar 

  10. Feo, T.A., Resende, M.G.C., Smith, S.H.: A greedy randomized adaptive search procedure for maximum independent set. Operations Research 42, 860–878 (1994)

    Article  MATH  Google Scholar 

  11. Garey, M.R., Johnson, D.S.: Computers and intractability: A guide to the theory of NP-completeness. W.H. Freeman and Company, New York (1979)

    MATH  Google Scholar 

  12. Gent, I.P., Walsh, T.: Towards an understanding of hill-climbing procedures for SAT. In: Proceedings of the 11th National Conference on Artificial Intelligence, pp. 28–33 (1993)

    Google Scholar 

  13. Glover, F.: Tabu search and adaptive memory programming: Advances, applications and challenges. In: Barr, R.S., Helgason, R.V., Kennington, J.L. (eds.) Interfaces in Computer Science and Operations Research, pp. 1–75. Kluwer Academic Publishers, Dordrecht (1996)

    Google Scholar 

  14. Goemans, M.X., Williamson, D.P.: A new \(\frac{3}{4}\) approximation algorithm for the maximum satisfiability problem. SIAM Journal on Discrete Mathematics 7, 656–666 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  15. Goemans, M.X., Williamson, D.P.: Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming. Journal of Association for Computing Machinery 42(6), 1115–1145 (1995)

    MATH  MathSciNet  Google Scholar 

  16. Hansen, P., Jaumard, B.: Algorithms for the maximum satisfiability problem. Computing 44, 279–303 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  17. Hastad, J.: Some optimal inapproximability results. Journal of the ACM 48, 798–859 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  18. Johnson, D.S.: Approximation algorithms for combinatorial problems. Journal of Computer and System Sciences 9, 256–278 (1974)

    Article  MATH  MathSciNet  Google Scholar 

  19. Johnson, D.S., Trick, M.A. (eds.): Cliques, coloring, and Satisfiability: Second DIMACS Implementation Challenge. DIMACS Series in Discrete Mathematics and Theoretical Computer Science. American Mathematical Society, Providence (1996)

    MATH  Google Scholar 

  20. Karloff, H., Zwick, U.: A \(\frac{7}{8}\)-approximation algorithm for MAX-3SAT. In: Proceedings of the 38th Annual IEEE Symposium on Foundations of Computer Science, pp. 406–415 (1997)

    Google Scholar 

  21. Laguna, M., Martí, R.: GRASP and path relinking for 2-layer straight line crossing minimization. INFORMS Journal on Computing 11, 44–52 (1999)

    Article  MATH  Google Scholar 

  22. Resende, M.G.C., Feo, T.A.: A GRASP for Satisfiability. In: Johnson, D.S., Trick, M.A. (eds.) Cliques, coloring, and Satisfiability: Second DIMACS Implementation Challenge, 26th edn. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, pp. 499–520. American Mathematical Society, Providence (1996)

    Google Scholar 

  23. Resende, M.G.C., Pitsoulis, L.S.: Greedy randomized adaptive search procedures. In: Pardalos, P.M., Resende, M.G.C. (eds.) Handbook of Applied Optimization, pp. 168–183. Oxford University Press, Oxford (2002)

    Google Scholar 

  24. Resende, M.G.C., Pitsoulis, L.S., Pardalos, P.M.: Approximate solutions of weighted MAX-SAT problems using GRASP. In: Du, D.-Z., Gu, J., Pardalos, P.M. (eds.) Satisfiability Problem: Theory and Applications, pp. 393–405. American Mathematical Society, Providence (1997)

    Google Scholar 

  25. Resende, M.G.C., Pitsoulis, L.S., Pardalos, P.M.: Fortran subroutines for computing approximate solutions of weighted MAX-SAT problems using GRASP. Discrete Applied Mathematics 100, 95–113 (2000)

    Article  MATH  Google Scholar 

  26. Resende, M.G.C., Ribeiro, C.C.: A GRASP with path-relinking for private virtual circuit routing. Networks 41, 104–114 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  27. Resende, M.G.C., Ribeiro, C.C.: GRASP and path-relinking: Recent advances and applications. In: Ibaraki, T., Nonobe, K., Yagiura, M. (eds.) Metaheuristics: Progress as Real Problem Solvers, pp. 29–63. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  28. Ribeiro, C.C., Uchoa, E., Werneck, R.F.: A hybrid GRASP with perturbations for the Steiner problem in graphs. INFORMS Journal on Computing 14, 228–246 (2002)

    Article  MathSciNet  Google Scholar 

  29. Selman, B., Levesque, H., Mitchell, D.: A new method for solving hard satisfiability instances. In: Proceedings of the 10th National Conference on Artificial Intelligence, pp. 440–446 (1992)

    Google Scholar 

  30. Spears, W.M.: Simulated annealing for hard satisfiability problems. In: Johnson, D.S., Trick, M.A. (eds.) Cliques, coloring, and Satisfiability: Second DIMACS Implementation Challenge. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 26, pp. 533–555. American Mathematical Society, Providence (1996)

    Google Scholar 

  31. Trevisan, L.: Approximating satisfiable satisfiability problems. Algorithmica 28(1), 145–172 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  32. Yannakakis, M.: On the approximation of maximum Satisfiability. In: Proceedings of the Third ACM-SIAM Symposium on Discrete Algorithms, pp. 1–9 (1992)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics and Applications, University of Napoli Federico II, Compl. MSA, Via Cintia, 80126, Napoli, Italy

    Paola Festa

  2. Department of Industrial and Systems Engineering, University of Florida, 303 Weil Hall, Gainesville, FL, 32611, USA

    Panos M. Pardalos

  3. Department of Mathematical and Physical Sciences, School of Engineering, Aristotle University of Thessaloniki, Thessaloniki, GR54124, Greece

    Leonidas S. Pitsoulis

  4. Internet and Network Systems Research Center, AT&T Labs Research, 180 Park Avenue, Room C241, Florham Park, NJ, 07932, USA

    Mauricio G. C. Resende

Authors
  1. Paola Festa
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  2. Panos M. Pardalos
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  3. Leonidas S. Pitsoulis
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  4. Mauricio G. C. Resende
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Editor information

Editors and Affiliations

  1. CTI and Univ. of Patras, Greece

    Sotiris E. Nikoletseas

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© 2005 Springer-Verlag Berlin Heidelberg

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Festa, P., Pardalos, P.M., Pitsoulis, L.S., Resende, M.G.C. (2005). GRASP with Path-Relinking for the Weighted Maximum Satisfiability Problem. In: Nikoletseas, S.E. (eds) Experimental and Efficient Algorithms. WEA 2005. Lecture Notes in Computer Science, vol 3503. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11427186_32

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  • DOI: https://doi.org/10.1007/11427186_32

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-25920-6

  • Online ISBN: 978-3-540-32078-4

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