Abstract
Satisfiability (SAT) Problem is an NP-Complete problem which means no deterministic algorithm is able to solve it in a polynomial time. Simulated Annealing (SA) can find very good solutions of SAT instances if its control parameters are correctly tuned. SA can be tuned experimentally or by using a Markov approach; the latter has been shown to be the most efficient one. Moreover Golden Ratio (GR) is an unconventional technique used to solve many problems. In this paper a new algorithm named Golden Ratio for Simulated Annealing (GRSA) is presented; it is tuned for three different cooling schemes. GRSA uses GR to dynamically decrease the SA temperature and a Markov Model to tune its parameters. Two SA tuned versions are compared in this paper: GRSA and a classical SA. Experimentation shows that the former is much more efficient than the latter.
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References
Garey, M.R., Johnson, D.S.: Computers and Intractability: A guide to the theory of NP-Completeness. W.H. Freeman, New York (1979)
Cook, S.A.: The complexity of theorem proving procedures. In: Proceedings of 3rd Annual ACM symposium on the Theory of Computing, pp. 151–158. ACM, New York (1971)
Papadimitriou, C.H.: Computational Complexity. Addison Wesley Longman, Redwood City (1995)
Gu, J.: Multispace search for satisfiability and NP-hard problems. In: Satisfiability Problem: Theory and Applications: Proceedings of a DIMACS Workshop. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 35, pp. 407–517 (1996)
Creignou, N.: The class of problems that are linearly equivalent to satisfiability or a uniform method for proving NP-completeness. In: Martini, S., Börger, E., Kleine Büning, H., Jäger, G., Richter, M.M. (eds.) CSL 1992. LNCS, vol. 702, pp. 115–133. Springer, Heidelberg (1993)
Edmons, J.: Minimum partition of a matroid into independent subset. J. Res. Nat. Bur. Standards Sect. B 69, 67–72 (1965)
Cook, S.: Computational Complexity of Higher Type Functions. In: Proc. International Congress of Mathematicians, Kyoto, Japan, pp. 51–69. Springer, Heidelberg (1991)
Bertzekas, D.P.: Network Optimization: Continuos and Discrete Models. Athena Scientific (1998)
Bazaraa, M.S., Sherali, H.D., Shetty, C.M.: Non Linear Programming: Theory and Algorithms, 2nd edn. Wiley, Chichester (1993)
Olivetti the Fianca, F., Von Zuben, F.J., Nunes de Castro, L.: An Artificial Immune Network for Multimodal Function Optimization on Dynamic Environments. In: GECCO 2005, Washington DC, USA, June 25-29 (2005)
Livio, M.: The Golden Ratio: The Story of Phi, The World’s Most Astonishing Number. Broadway Books, New York (2002)
Cook, S., Mithchel, D.G.: Finding Hard Instances of the Satisfiability Problem: A Survey. In: Satisfibility Problem Theory and Applications. Dimacs Series Discrete Mathematics and Theoretical Computer Sciences, pp. 1–17 (1997)
Gu, J., Purdom, P., Franco, J., Wah, B.: Algorithms for the satisfaibility (SAT) problem: A Survey. In: Satisfibility Problem Theory and Applications. Dimacs Series Discrete Mathematics and Theoretical Computer Sciences, pp. 19–151 (1997)
Cerny, V.: A Thermodynamical Approach to the Traveling Salesman Problem: An efficient Simulation Algorithm, Report, Comenius University, Bratislava, Czechoslovakia (1982)
Cerny, V.: Thermodynamical approach to the traveling salesman problem: An efficient simulation algorithm. Journal of Optimization Theory and Applications 45, 41–51 (1985)
Kirkpatrick, S., Gelatt, C.D., Vecchi, M.P.: Optimization by Simulated Annealing. Science (4598) 220, 671–680 (1983)
Aarts, E., y Korst, E.: Simulated annealing and Boltzman machines: A stochastic approach to combinatorial optimization and neural computing. John Wiley & Sons, Great Bretain (1989)
Frausto, J., Sanvicente, H., Imperial, F.: ANDYMARK: An analytical Method to Establish Dynamically the Length of the Markov Chian in Simulated Annealing for the Satisfiablity Problem. Springer, Heidelberg (2006)
Ingber, L.: Simulated Annealing; Practice Versus Theory. J. MATHL. Comput. Modeling 18(11), 29–57 (1993)
Mezard, M., Parisi, G., Zecchina, R.: Analytic and algorithmic solution of random satisfiability problems. Science, June 27 (2002)
SATLIB - The Satisfiability Library, http://www.cs.ubc.ca/~hoos/SATLIB/index-ubc.html
Horie, S., Watanabe, O.: Hard instance generation for SAT, Technical Report TR97-0007, Dept. of Computer Science, Tokyo Inst. of Tech. (Available from CS Dept. TR Archive); the extended abstract appeared in Proc. ISAAC 1997. LNCS, vol. 1350. Springer, Heidelberg (1997)
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Frausto-Solis, J., Martinez-Rios, F. (2008). Golden Ratio Annealing for Satisfiability Problems Using Dynamically Cooling Schemes. In: An, A., Matwin, S., Raś, Z.W., Ślęzak, D. (eds) Foundations of Intelligent Systems. ISMIS 2008. Lecture Notes in Computer Science(), vol 4994. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68123-6_24
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