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.
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References
Battiti, R., Protasi, M.: Reactive search, a history-based heuristic for MAX-SAT. ACM Journal of Experimental Algorithmics 2 (1997)
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)
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)
Cadoli, M., Schaerf, A.: Compiling problem specifications into SAT. In: Programming Languages and Systems, pp. 387–401 (2001)
Chase, I.D.: Models of hierarchy formation in animal societies. Behavioral Sciences 19, 374–382 (1974)
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)
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)
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)
Cicirello, V.A., Smith, S.F.: Wasp-like agents for distributed factory coordination. Autonomous Agents and Multi-agent systems 8, 237–266 (2004)
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)
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)
Dorigo, M., Stützle, T.: Ant Colony Optimization. MIT Press (2004)
Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of \(\mathcal{NP}\)-Completeness. WH Freeman Publishers (1979)
Glover, F., Laguna, M.: Tabu search. John Wiley & Sons, Insc., New York (1993)
Goodrich, M.T., Tamassia, R.: Algorithm Design - Foundations, Analysis, and Internet Examples. John Wiley & Sons, Inc. (2001)
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)
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)
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)
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)
Kirkpatrick, S., Gelatt, C.D., Vecchi, M.P.: Optimization by simulated annealing. Science 220(4598), 671–680 (1983)
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)
McGill, R., Tukey, J.W., Larsen, W.A.: Variations of Boxplots. In: The American Statistician, pp. 12–16. American Statistical Association (1978)
Mills, P., Tsang, E.: Guided local search for solving SAT and weighted MAX-SAT problems. Journal Automated Reasoning 24(1-2), 205–223 (2000)
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)
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)
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)
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)
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)
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)
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)
Roli, A., Blum, C., Dorigo, M.: ACO for maximal constraint satisfaction problems. In: Metaheuristics International Conference, pp. 187–192 (2001)
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)
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)
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)
Solnon, C.: Ants can solve constraint satisfaction problems. IEEE Transactions on Evolutionary Computation 6, 347–357 (2002)
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)
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)
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)
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)
Wang, H., Yang, S., Ip, W., Wang, D.: IEEE Transactions on Systems, Man, and Cybernetics-Part B 39(6), 1348–1361 (2009)
Wilson, E.O.: The insect societies. Harvard University Press (1971)
Winston, W., Goldberg, J.: Operations Research: Applications and Algorithms. Cengage Learning, 4th edn. (2003)
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)
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Pinto, P.C., Runkler, T.A., Sousa, J.M.C. (2013). Insect Swarm Algorithms for Dynamic MAX-SAT Problems. In: Alba, E., Nakib, A., Siarry, P. (eds) Metaheuristics for Dynamic Optimization. Studies in Computational Intelligence, vol 433. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30665-5_15
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DOI: https://doi.org/10.1007/978-3-642-30665-5_15
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