Insect Swarm Algorithms for Dynamic MAX-SAT Problems

  • Pedro C. Pinto
  • Thomas A. Runkler
  • João M. C. Sousa
Part of the Studies in Computational Intelligence book series (SCI, volume 433)

Abstract

The satisfiability (SAT) problem and the maximum satisfiability problem (MAX-SAT) were among the first problems proven to be \(\mathcal{N P}\)-complete. While only a limited number of theoretical and real-world problems come as instances of SAT or MAX-SAT, many combinatorial problems can be encoded into them. This puts the study of MAX-SAT and the development of adequate algorithms to address it in an important position in the field of computer science. Among the most frequently used optimization methods for the MAX-SAT problem are variations of the greedy hill climbing algorithm. This chapter studies the application to dynamic MAX-SAT (i.e. MAX-SAT problems with structures that change over time) of the swarm based metaheuristics ant colony optimization and wasp swarm optimization algorithms, which are based in the real life behavior of ants and wasps, respectively. The algorithms are applied to several sets of static and dynamic MAX-SAT instances and are shown to outperform the greedy hill climbing and simulated annealing algorithms used as benchmarks.

Keywords

Local Search Tabu Search Constraint Satisfaction Problem High Quality Solution Stage Duration 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Battiti, R., Protasi, M.: Reactive search, a history-based heuristic for MAX-SAT. ACM Journal of Experimental Algorithmics 2 (1997)Google Scholar
  2. 2.
    Blum, C., Dorigo, M.: The hyper-cube framework for ant colony optimization. IEEE Transactions on Systems, Man, and Cybernetics-Part B 34(2), 1161–1172 (2004)CrossRefGoogle Scholar
  3. 3.
    Branke, J., Schmeck, H.: Designing evolutionary algorithms for dynamic optimization problems. In: Advances in Evolutionary Computing: Theory and Applications, pp. 239–262. Springer-Verlag New York, Inc., New York (2003)Google Scholar
  4. 4.
    Cadoli, M., Schaerf, A.: Compiling problem specifications into SAT. In: Programming Languages and Systems, pp. 387–401 (2001)Google Scholar
  5. 5.
    Chase, I.D.: Models of hierarchy formation in animal societies. Behavioral Sciences 19, 374–382 (1974)CrossRefGoogle Scholar
  6. 6.
    Cheeseman, P., Kanefsky, B., Taylor, W.M.: Where the really hard problems are. In: Proceedings of the 12th International Joint Conference on Artificial Intelligence, Sidney, Australia, pp. 331–337 (1991)Google Scholar
  7. 7.
    Cicirello, V.A., Smith, S.F.: Ant colony for autonomous decentralized shop floor routing. In: Proceedings of the 5th International Symposium on Autonomous Decentralized Systems, pp. 383–390 (2001)Google Scholar
  8. 8.
    Cicirello, V.A., Smith, S.F.: Wasp nests for self-configurable factories. In: Agents 2001, Proceedings of the 5th International Conference on Autonomous Agents, pp. 473–480. ACM Press (2001)Google Scholar
  9. 9.
    Cicirello, V.A., Smith, S.F.: Wasp-like agents for distributed factory coordination. Autonomous Agents and Multi-agent systems 8, 237–266 (2004)CrossRefGoogle Scholar
  10. 10.
    Cook, S.A.: The complexity of theorem-proving procedures. In: Proceedings of the Third Annual ACM Symposium on Theory of Computing, pp. 151–158. ACM, New York (1971)CrossRefGoogle Scholar
  11. 11.
    Dorigo, M., Maniezzo, V., Colorni, A.: Ant system: Optimization by a colony of cooperating agents. IEEE Transactions on Systems, Man, and Cybernetics-Part B 26(1), 29–41 (1996)CrossRefGoogle Scholar
  12. 12.
    Dorigo, M., Stützle, T.: Ant Colony Optimization. MIT Press (2004)Google Scholar
  13. 13.
    Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of \(\mathcal{NP}\)-Completeness. WH Freeman Publishers (1979)Google Scholar
  14. 14.
    Glover, F., Laguna, M.: Tabu search. John Wiley & Sons, Insc., New York (1993)Google Scholar
  15. 15.
    Goodrich, M.T., Tamassia, R.: Algorithm Design - Foundations, Analysis, and Internet Examples. John Wiley & Sons, Inc. (2001)Google Scholar
  16. 16.
    Grasse, P.: La reconstruction du nid et les coordinations inter-individuelles chez bellicositermes natalensis et cubitermes sp. la theorie de la stigmergie: Essai d’interpretation du comportement des termites constructeurs. Insectes Sociaux 6, 41–81 (1959)CrossRefGoogle Scholar
  17. 17.
    Hartmann, S.A., Runkler, T.A.: Online optimization of a color sorting assembly buffer using ant colony optimization. In: Proceedings of the Operations Research Conference, pp. 415–420 (2007)Google Scholar
  18. 18.
    Hoos, H.H., O’Neill, K.: Stochastic local search methods for dynamic SAT - an initial investigation. In: Leveraging Probability and Uncertainty in Computation, Austin, Texas, pp. 22–26. AAAI Press (2000)Google Scholar
  19. 19.
    Hoos, H.H., Stützle, T.: Local search algorithms for SAT: an empirical evaluation. In: Journal of Automated Reasoning, special Issue ” SAT 2000”, pp. 421–481 (1999)Google Scholar
  20. 20.
    Kirkpatrick, S., Gelatt, C.D., Vecchi, M.P.: Optimization by simulated annealing. Science 220(4598), 671–680 (1983)MathSciNetMATHCrossRefGoogle Scholar
  21. 21.
    Liu, J., Zhong, W., Jiao, L.: A multiagent evolutionary algorithm for constraint satisfaction problems. IEEE Transactions on Systems, Man, and Cybernetics-Part B 36(1), 54–73 (2006)CrossRefGoogle Scholar
  22. 22.
    McGill, R., Tukey, J.W., Larsen, W.A.: Variations of Boxplots. In: The American Statistician, pp. 12–16. American Statistical Association (1978)Google Scholar
  23. 23.
    Mills, P., Tsang, E.: Guided local search for solving SAT and weighted MAX-SAT problems. Journal Automated Reasoning 24(1-2), 205–223 (2000)MathSciNetMATHCrossRefGoogle Scholar
  24. 24.
    Mitchell, D., Selman, B., Levesque, H.: Hard and easy distributions of SAT problems. In: 10th National Conference on Artificial Intelligence, San Jose, CA, pp. 459–465 (1992)Google Scholar
  25. 25.
    Tamura, N., Taga, A., Kitagawa, S., Banbara, M.: Compiling Finite Linear CSP into SAT. In: Benhamou, F. (ed.) CP 2006. LNCS, vol. 4204, pp. 590–603. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  26. 26.
    Pimont, S., Solnon, C.: A generic ant algorithm for solving constraint satisfaction problems. In: 2th International Workshop on Ant Algorithms, Brussels, Belgium, pp. 100–108 (2000)Google Scholar
  27. 27.
    Pinto, P., Runkler, T.A., Sousa, J.M.C.: Wasp swarm optimization of logistic systems. In: Ribeiro, et al. (eds.) Adaptive and Natural Computing Algorithms, 7th International Conference on Adaptive and Natural Computing Algorithms, Coimbra, Portugal, pp. 264–267. Springer, NewYork (2005)Google Scholar
  28. 28.
    Pinto, P., Runkler, T.A., Sousa, J.M.C.: Ant colony optimization and its application to regular and dynamic MAX-SAT problems. In: Advances in Biologically Inspired Information Systems: Models, Methods, and Tools, pp. 283–302 (2007)Google Scholar
  29. 29.
    Pinto, P.C., Runkler, T.A., Sousa, J.M.C.: Wasp Swarm Algorithm for Dynamic MAX-SAT Problems. In: Beliczynski, B., Dzielinski, A., Iwanowski, M., Ribeiro, B. (eds.) ICANNGA 2007. LNCS, vol. 4431, pp. 350–357. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  30. 30.
    Resende, M.G.C., Pitsoulis, L.S., Pardalos, P.M.: Approximate solution of weighted MAX-SAT problems using GRASP. In: Satisfiability Problem: Theory and Applications. DIMACS Series on Discrete Mathematics and Theoretical Computer Science, vol. 35, pp. 393–405. American Mathematical Society (1997)Google Scholar
  31. 31.
    Roli, A., Blum, C., Dorigo, M.: ACO for maximal constraint satisfaction problems. In: Metaheuristics International Conference, pp. 187–192 (2001)Google Scholar
  32. 32.
    Silva, C.A., Runkler, T.A., Sousa, J.M.C., Sá da Costa, J.M.G.: Distributed supply chain management using ant colony optimization. European Journal of Operational Research 199(2), 349–358 (2009)MathSciNetMATHCrossRefGoogle Scholar
  33. 33.
    Silva, C.A., Sousa, J.M.C., Runkler, T.A., Sá da Costa, J.: Distributed optimization of logistic systems and its suppliers using ant colony optimization. International Journal of Systems Science 37(8), 503–512 (2006)MathSciNetMATHCrossRefGoogle Scholar
  34. 34.
    Smyth, K., Hoos, H., Stützle, T.: Iterated Robust Tabu Search for MAX-SAT. In: Xiang, Y., Chaib-draa, B. (eds.) Canadian AI 2003. LNCS (LNAI), vol. 2671, pp. 129–144. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  35. 35.
    Solnon, C.: Ants can solve constraint satisfaction problems. IEEE Transactions on Evolutionary Computation 6, 347–357 (2002)CrossRefGoogle Scholar
  36. 36.
    Stützle, T., Hoos, H.H.: The max-min ant system and local search for the traveling salesman problem. In: Proceedings of the 4th International Conference on Evolutionary Computation, vol. 8, pp. 308–313. IEEE Press (1997)Google Scholar
  37. 37.
    Stützle, T., López-Ibánez, M., Dorigo, M.: A Concise Overview of Applications of Ant Colony Optimization. In: Wiley Encyclopedia of Operations Research and Management Science. John Wiley & Sons (2011)Google Scholar
  38. 38.
    Theraulaz, G., Goss, S., Gervet, J., Deneubourg, J.L.: Task differentiation in polistes wasps colonies: A model for self-organizing groups of robots. In: From Animals to Animats: Proceedings of the 1st International Conference on Simulation of Adaptive Behavior, pp. 346–355. MIT Press (1991)Google Scholar
  39. 39.
    Stützle, T., Hoos, H., Roli, A.: A review of the literature on local search algorithms for MAX-SAT. Technical report aida-01-02. Technical report, Technische Universität Darmstadt (2006)Google Scholar
  40. 40.
    Wang, H., Yang, S., Ip, W., Wang, D.: IEEE Transactions on Systems, Man, and Cybernetics-Part B 39(6), 1348–1361 (2009)CrossRefGoogle Scholar
  41. 41.
    Wilson, E.O.: The insect societies. Harvard University Press (1971)Google Scholar
  42. 42.
    Winston, W., Goldberg, J.: Operations Research: Applications and Algorithms. Cengage Learning, 4th edn. (2003)Google Scholar
  43. 43.
    Zhang, W.: Phase Transitions and Backbones of 3-SAT and Maximum 3-SAT. In: Walsh, T. (ed.) CP 2001. LNCS, vol. 2239, pp. 153–167. Springer, Heidelberg (2001)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Pedro C. Pinto
    • 1
  • Thomas A. Runkler
    • 2
  • João M. C. Sousa
    • 3
  1. 1.Department T3RBayern Chemie GmbH, MBDA DeutschlandAschau am InnGermany
  2. 2.Intelligent Systems and Control, CT T IAT ISCSiemens AG, Corporate TechnologyMunichGermany
  3. 3.Instituto Superior Técnico, Dep. of Mechanical Engineering, IDMEC-LAETATechnical University of LisbonLisbonPortugal

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