Abstract
This paper explores rule decomposition for solving the MAXSAT problem. Four approaches are proposed to steer a bee swarm optimization metaheuristic. Two decomposition methods are proposed: direct and indirect. The first one applies the Kmeans algorithm, while the second one transforms a MAXSAT instance into a transactional database before performing decomposition using the Apriori algorithm. Several experiments conducted on DIMACS benchmark instances, and some other hard and large SAT instances have been carried out. Results show clear improvement compared to the state-of-the-art MAXSAT algorithms in terms of the quality of the obtained solutions. They show that the proposed approaches are stable when dealing with hard instances such as Parity8 from DIMACS. Results also demonstrate the superiority of the proposed approaches for medium and large instances. The proposed approaches could be applied to other optimization problems such as the weighted MAXSAT problem, the MAXCSP and coloring problems. They may also be adapted for other metaheuristics and decomposition methods.
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References
Abrame A, Habet D (2014) Local max-resolution in branch and bound solvers for max-sat. In: Tools with artificial intelligence (ICTAI), 2014 IEEE 26th international conference on IEEE, pp 336–343
Abrame A, Habet D (2014) On the extension of learning for Max-SAT. In: STAIRS, pp 1–10
Agrawal R, Imielinski T, Swami A (1993) Mining association rules between sets of items in large databases. In: Acm sigmod record, vol 22(2). ACM, pp 207–216
Akbari R, Mohammadi A, Ziarati K (2010) A novel bee swarm optimization algorithm for numerical function optimization. Commun Nonlinear Sci Numer Simul 15(10):3142–3155
Ali HM, Ashrafinia S, Liu J, Lee D (2013) Broadband wireless network planning using evolutionary algorithms. In: Evolutionary computation (CEC), 2013 IEEE congress on IEEE, pp 1045–1052
Ali HM, Mitchell D, Lee DC (2014) MAX-SAT problem using evolutionary algorithms. In: Swarm intelligence (SIS), 2014 IEEE symposium on IEEE, pp 1–8
Ansetegui C, Gireldez-Cru J, Levy J (2012) The community structure of SAT formulas. In: International conference on theory and applications of satisfiability testing. Springer, Berlin, pp 410–423
Bouhmala N (2014) A variable neighborhood Walksat-based algorithm for MAX-SAT problems. Sci World J 2014. https://doi.org/10.1155/2014/798323
Bouhmala N (2015) A multilevel learning automata for MAX-SAT. Int J Mach Learn Cybernet 6(6):911–921
Cai S, Jie Z, Su K (2015) An effective variable selection heuristic in SLS for weighted Max-2-SAT. J Heuristics 21(3):433–456
Chen R, Santhanam R (2015) Improved algorithms for sparse MAX-SAT and MAX-k-CSP. In: International conference on theory and applications of satisfiability testing. Springer, pp 33–45
Chicano F, Sutton AM, Whitley LD, Alba E (2015) Fitness probability distribution of bit-flip mutation. Evol Comput 23(2):217–248
Davis M, Putnam H (1960) A computing procedure for quantification theory. J ACM (JACM) 7(3):201–215
Djeffal M, Drias H (2013) Multilevel bee swarm optimization for large satisfiability problem instances. In: Intelligent data engineering and automated learning IDEAL 2013. Springer, Berlin, pp 594–602
Djenouri Y, Drias H, Habbas Z (2014) Bees swarm optimisation using multiple strategies for association rule mining. Int J Bio-Inspired Comput 6(4):239–249
Djenouri Y, Drias H, Bendjoudi A (2014) Pruning irrelevant association rules using knowledge mining. Int J Bus Intelli Data Min 9(2):112–144
Djenouri Y, Habbas Z, Aggoune-Mtalaa W (2016) Bees swarm optimization metaheuristic guided by decomposition for solving MAX-SAT. In: Proceedings of the 8th international conference on agents and artificial intelligence, pp. 472–479
Djenouri Y, Habbas Z, Djenouri D (2017) Data mining-based decomposition for solving the MAXSAT problem: toward a new approach. IEEE Intell Syst 32(4):48–58
Drias H, Hireche C, Douib A (2013) Datamining techniques and swarm intelligence for problem solving: application to SAT. In: Nature and biologically inspired computing (NaBIC), 2013 World congress on IEEE, pp 200–206
Drias H, Sadeg S, Yahi S (2005) Cooperative bees swarm for solving the maximum weighted satisfiability problem. In: Computational intelligence and bioinspired systems, vol 3512. Springer, Heidelberg, pp 417–448
Escoffier B, Paschos VT, Tourniaire E (2014) Approximating Max Sat by moderately exponential and parameterized algorithms. Theoret Comput Sci 560:147–157
Folino G, Pizzuti C, Spezzano G (2001) Parallel hybrid method for SAT that couples genetic algorithms and local search. Evolut Comput IEEE Trans 5(4):323–334
Fontaine M, Loudni S, Boizumault P (2011) Guiding VNS with tree decomposition. In: Tools with artificial intelligence (ICTAI), 2011 23rd IEEE international conference on IEEE, pp 505–512
Fukunaga AS (2004) Evolving local search heuristics for SAT using genetic programming. In: Genetic and evolutionary computation conference. Springer, Berlin, pp 483–494
Jabbour S, Sais L, Salhi Y (2013) Boolean satisfiability for sequence mining. In: Proceedings of the 22nd ACM international conference on conference on information and knowledge management. ACM, pp 649–658
Jabbour S, Sais L, Salhi Y (2015) Decomposition based SAT encodings for itemset mining problems. In: Advances in knowledge discovery and data mining. Springer, Berlin, pp 662–674
Kanazawa K, Maruyama T (2014) FPGA acceleration of SAT/Max-SAT solving using variable-way cache. In: Field programmable logic and applications (FPL), 2014 24th international conference on IEEE, pp 1–4
Kashan MH, Nahavandi N, Kashan AH (2012) DisABC: a new artificial bee colony algorithm for binary optimization. Appl Soft Comput 12(1):342–352
Kolokolov A, Adelshin A, Yagofarova D (2013) Analysis and solving SAT and MAX-SAT problems using an L-partition approach. J Math Modell Algorithms Oper Res 12(2):201–212
Kumar V (1992) Algorithms for constraint-satisfaction problems: a survey. AI Mag 13(1):32
Lardeux F, Saubion F, Hao JK (2006) GASAT: a genetic local search algorithm for the satisfiability problem. Evol Comput 14(2):223–253
Li CM, Anbulagan A (1997) Heuristics based on unit propagation for satisfiability problems. In: Proceedings of the 15th international joint conference on artificial intelligence, vol 1. Morgan Kaufmann Publishers Inc, pp 366–371
Luo C, Cai S, Wu W, Jie Z, Su K (2015) CCLS: an efficient local search algorithm for weighted maximum satisfiability. IEEE Trans Comput 64(7):1830–1843
MacQueen J (1967) Some methods for classification and analysis of multivariate observations. In: Proceedings of the fifth Berkeley symposium on mathematical statistics and probability, vol 1(14), pp 281–297
Molnar B, Ercsey-Ravasz M (2014) Analog dynamics for solving max-SAT problems. In: 2014 IEEE symposium on IEEE
Park TJ, Van Gelder A (2000) Partitioning methods for satisfiability testing on large formulas. Inf Comput 162(1–2):179–184
Poli R, Langdon WB, Holland O (2005) Extending particle swarm optimisation via genetic programming. In: European conference on genetic programming. Springer, Berlin, pp 291–300
Poloczek M, Williamson DP, van Zuylen A (2014) On some recent approximation algorithms for MAX SAT. In Latin American symposium on theoretical informatics. Springer, Berlin, pp 598–609
Sabar NR, Kendall G (2015) Population based Monte Carlo tree search hyper-heuristic for combinatorial optimization problems. Inf Sci 314:225–239
Sadowski KL, Bosman PA, Thierens D (2013) On the usefulness of linkage processing for solving MAX-SAT. In: Proceedings of the 15th annual conference on genetic and evolutionary computation. ACM, pp 853–860
Sakai T, Seto K, Tamaki S (2015) Solving sparse instances of max SAT via width reduction and greedy restriction. Theory Comput Syst 57(2):426–443
Selman B, Kautz H (1993) Domain-independent extensions to GSAT: solving large structured satisfiability problems. In: IJCAI. vol 93, pp 290–295
Tompkins DA, Hoos HH (2004) UBCSAT: an implementation and experimentation environment for SLS algorithms for SAT and MAX-SAT. In: International conference on theory and applications of satisfiability testing. Springer, Berlin, pp 306–320
Wu X, Kumar V, Quinlan JR, Ghosh J, Yang Q, Motoda H, Zhou ZH (2008) Top 10 algorithms in data mining. Knowl Inf Syst 14(1):1–37
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Djenouri, Y., Habbas, Z., Djenouri, D. et al. Bee swarm optimization for solving the MAXSAT problem using prior knowledge. Soft Comput 23, 3095–3112 (2019). https://doi.org/10.1007/s00500-017-2956-1
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DOI: https://doi.org/10.1007/s00500-017-2956-1