Abstract
Variable Neighborhood Search (VNS) is a simple meta-heuristic that systematically changes the size and type of neighborhood during the search process in order to escape from local optima. In this paper, a variable-neighborhood-genetic-based-algorithm is proposed for the maximum satisfiability problem (MAX-SAT). Most of the work published earlier on VNS starts from the first neighborhood and moves on to higher neighborhoods without controlling and adapting the ordering of neighborhood structures. The order in which the neighborhood structures have been proposed in this work enables the genetic algorithm with a better mechanism for performing diversification and intensification. A set of benchmark problem instances is used to compare the effectiveness of the proposed algorithm against the standard genetic algorithm. This paper reports promising results when the proposed hybrid algorithm is compared with state-of-the art solvers.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Arcuri, A., & Briand, L. (2011). A Hitchhiker’s guide to statistical tests for assessing randomized algorithms in software engineering. Technical report, Simula research laboratory, number 13/2011.
Blum, C., & Roli, A. (2003). Meta-heuristics in combinatorial optimization: Overview and conceptual comparison. ACM Computing Surveys, 35(3), 268–308.
Bouhmala, N., & Oseland, M. (2017). Antelnd bradland. WalkSAT based-learning automata for MAX-SAT. In Advances in Intelligent Systems and Computing: Recent Advances in Soft Computing (MENDEL) (Vol. 576). Springer, Czech Republic.
Bouhmala, N. (2016). A simple and efficient variable neighborhood structure for the satisfiability problem. In Proceedings of 6th International Conference on Meta-heuristics and Nature (pp. 126–133), Marrakech.
Bouhmala, N. (2015). A multilevel learning automata for MAX-SAT. International Journal of Machine Learning & Cybernetics. Heidelberg: Springer. https://doi.org/10.1007/s13042-015-0355-4.
Bouhmala, N., Hjelmervik, K., & Øvergård, K. (2015). A generalized variable neighborhood search for combinatorial optimization problems. Electronic Notes in Discrete Mathematics, 47, 45–52.
Bouhmala, N., & Cai, X. (2009). A multilevel approach for the satisfiability problem. ISAST Transactions on Computers and Intelligent Systems, 2(1), 29–37.
Bouhmala. N. (2012). A multilevel memetic algorithm for large SAT-encoded problems. Evolutionary Computation, 20(4), 641–664.
Bouhmala, N., & Granmo, O. C. (2010). Stochastic learning for SAT-encoded graph coloring problems. International Journal of Applied Meta-heuristic Computing, 1(3), 1–19.
Bouhmala, N., & Granmo, O. C. (2010). Combining finite learning automata with GSAT for the satisfiability problem. Engineering Applications of Artificial Intelligence, 23(5), 715–726.
Cha, B., & Iwama, K. (1995). Performance tests of local search algorithms using new types of random CNF formula. In Proceedings of IJCAI95 (pp. 304–309). Morgan Kaufmann Publishers.
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Lawrence Erlbaum.
Cook, S. A. (1971). The complexity of theorem-proving procedures. In Proceedings of the Third ACM Symposium on Theory of Computing (pp. 151–158).
Frank, J. (1997). Learning short-term clause weights for GSAT. In Proceedings of IJCAI97 (pp. 384–389). Morgan Kaufmann Publishers.
Hansen, P., Jaumard, B., Mladenovic, N., & Parreira, A. D. (2000). Variable neighborhood search for maximum weighted satisfiability problem. Technical Report G-2000-62, Les Cahiers du GERAD, Group for Research in Decision Analysis.
Hansen, P., & Mladenovic, N. (1999). An introduction to variable neighborhood search. In S. Voss, S. Martello, I. H. Osman, & C. Roucairol (Eds.), Meta-heuristics: Advances and trends in local search paradigms for optimization (pp. 433–458). Boston: Kluwer.
Hoos, H. (2002). An adaptive noise mechanism for WalkSAT. In Proceedings of AAAI-2002 (pp. 655–660).
Hoos, H. (1999). On the run-time behavior of stochastic local search algorithms for SAT. In Proceedings of AAAI-99 (pp. 661–666).
Hu, B., & Raidl, R. (2006). Variable neighborhood descent with self-adaptive neighborhood-ordering. In C. Cotta, A. J. Fernandez, & J. E. Gallardo (Eds.), Proceedings of the 7th EU/MEeting on Adaptive, Self-Adaptive, and Multi-Level Meta-heuristics, Malaga, Spain.
Jin-Kao, H., Lardeux, F., & Saubion, F. (2003). Evolutionary computing for the satisfia-bility problem. In Applications of Evolutionary Computing, LNCS (Vol. 2611, pp. 258–267). England: University of Essex.
KhudaBukhsh, A. R., Xu, L., Hoos, H., & Leyton-Brown, K. (2009). SATenstein: automatically building local search SAT solvers from components. In Proceedings of the 25th International Joint Conference on Artificial Intelligence (IJCAI-09).
Lardeux, F., Saubion, F., & Hao, J. K. (2006). GASAT: A genetic local search algorithm for the satisfibility problem. Evolutionary Computation, 14(2), 223–253.
Li, C. M., & Huang, W. Q. (2005). Diversification and determinism in local search for satisfiability. In Proceedings of the Eighth International Conference on Theory and Applications of Satisfiability Testing (SAT-05), Lecture Notes in Computer Science (Vol. 3569, pp. 158–172).
Li, C. M., Wei, W., & Zhang, H. (2007). Combining adaptive noise and look-ahead in local search for SAT. In Lecture notes in computer science (Vol. 4501, pp. 121–131).
Lozano, M., Herrera, F., & Cano, R. (2008). Replacement strategies to preserve useful diversity in steady-state genetic algorithms. Information Sciences, 178(23), 4421–4433.
Mazure, B., \(Sa\ddot{i}s\), L., & \(Gr\acute{e}goire\), E. (1997). Tabu search for SAT. In Proceedings of the Fourteenth National Conference on Artificial Intelligence (AAAI-97) (pp. 281–285).
McAllester, D., Selman, B., & Kautz, H. (1997). Evidence for invariants in local search. In Proceedings of the Fourteenth National Conference on Artificial Intelligence (AAAI-97) (pp. 321–326).
Mladenović, N., & Hansen, P. (1997). Variable neighborhood search. Computer and Operations Research, 24, 1097–1100.
Mooney, C. Z., & Duval, R. D. (1993). Bootstrapping—A nonparametric approach to statistical inference. Sage University Press.
Selman, B., Kautz, H. A., & Cohen, B. (1994). Noise strategies for improving local search. In Proceedings of AAAI’94 (pp. 337–343). MIT Press.
Selman, B., Levesque, H., & Mitchell, D. (1992). A new method for solving hard satisfiability problems. In Proceedings of AAA92 (pp. 440–446). MIT Press.
Spears, W. (1995). Adapting crossover in evolutionary algorithms. In Proceedings of the Fourth Annual Conference on Evolutionary Programming (pp. 367–384). MIT Press.
Talbi, E. G. (2009). Meta-heuristics: From design to implementation. Wiley.
Vargha, A., & Delaney, H. D. (2000). A critique and improvement of the CL common language effect size statistics of McGraw and Wong. Journal of Educational and Behavioral Statistics, 25(2), 101–132.
Vrajitoru, D. (1999). Genetic programming operators applied to genetic algorithms. In Proceedings of the Genetic and Evolutionary Computation Conference, Orlando (FL) (pp. 686–693). Morgan Kaufmann Publishers.
Wong, Y., Lee, Y., Leung, K., & Ho, C. (2003). A novel approach in parameter adaptation and diversity maintenance for genetic algorithms. Soft Computing, 7, 506–515.
Xu, L., Hutter, F., Hoos, H., & Leyton-Brown, K. (2008). SATzilla: Portfolio-based algorithm selection for SAT. Journal of Artificial Intelligence Research (JAIR), 32, 565–606.
Yang, X. S., & Gandomi, A. H. (2012). Bat algorithm: A novel approach for global engineering optimization. Engineering Computations, 29(5), 464–483.
Yang, X. S., & Deb, S. (2010). Eagle strategy using \(L\acute{e}vy\) work and firefly algorithms for stochastic optimization. In Nature Inspired Cooperative Strategies for Optimization (NICSO2010) (pp. 101–111). Springer.
Yagiura, M., & Ibaraki, T. (2001). Efficient 2 and 3-flip neighborhood search algorithms for the MAX SAT: Experimental evaluation. Journal of Heuristics, 7, 423–442.
Zhipeng, L., & Jin-Kao, H. (2012). Adaptive memory-based local search for MAX-SAT. Applied Soft Computing.
Acknowledgements
We would like to address a particular warm thank to the members of the organizing committee and scientific committee for making the First EAI International Conference on Computer Science and Engineering, NOVEMBER 11–12, 2016, PENANG, MALAYSIA a great success.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this chapter
Cite this chapter
Bouhmala, N., Øvergård, K.I. (2018). Combining Genetic Algorithm with Variable Neighborhood Search for MAX-SAT. In: Zelinka, I., Vasant, P., Duy, V., Dao, T. (eds) Innovative Computing, Optimization and Its Applications. Studies in Computational Intelligence, vol 741. Springer, Cham. https://doi.org/10.1007/978-3-319-66984-7_5
Download citation
DOI: https://doi.org/10.1007/978-3-319-66984-7_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-66983-0
Online ISBN: 978-3-319-66984-7
eBook Packages: EngineeringEngineering (R0)