Abstract
The Max Sat problem is very known problem in computer science. It aims to find the best assignment for a set of Boolean variables that gives the maximum of verified clauses in a Boolean formula. Unfortunately, this problem was showed NP-Hard if the number of variable per clause is higher than 3. In this article, we propose a new iterative stochastic approach called QSAT based on a hybrid algorithm of Quantum Evolutionary Algorithm QEA and Local Search Algorithm LSA. QSAT is based on a basic core defined by a suitable quantum representation and an adapted quantum evolutionary dynamic enhanced by Local Search procedure. The obtained results are encouraging and prove the feasibility and the effectiveness of our approach. QSAT is distinguished by a reduced population size and a reasonable number of iterations to find the best assignment, thanks to the principles of quantum computing.
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References
Cook, S.A.: The Complexity of Theorem Proving Procedures. In: Proc. 3rd Ann. ACM Symp. On Theory of Computing, Association for Computing Machinery, pp. 151–158 (1971)
Alsinet, T., Manya, F., Planes, J.: Improved Branch and Bound Algorithms for Max-2-SAT and Weighted Max-2-SAT. In: Proceedings of Sixth Catalan Conference on Artificial Intelligence (CCIA 2003) (October 2003)
Marchiori, E., Rossi, C.: A Flipping Genetic Algorithm for Hard 3-SAT Problems. In: Proc. of the Genetic and Evolutionary Computation Conference, vol. 1, pp. 393–400 (1999)
Marques-Silva, J.P., Sakallah, K.A.: GRASP: A Search Algorithm for Propositional Satisfiability. IEEE Transactions on Computers 48(5), 506–521 (1999)
Holger, H., Stützle, T.: Local search algorithms for SAT: An empirical evaluation. Journal of Automated Reasoning 24(4), 421–481 (2000)
Williams, C.P., Clearwater, S.H.: Explorations in quantum computing. Springer, Berlin (1998)
Han, K.H., Kim, J.H.: Quantum-inspired Evolutionary Algorithms with a New Termination Criterion, Hε Gate, and Two Phase Scheme. IEEE Transactions on Evolutionary Computation 8(2), 156–169 (2004)
Layeb, A., Saidouni, D.E.: Quantum Genetic Algorithm for Binary Decision Diagram Ordering Problem. The proceeding of International Journal of Computer Science and Network Security 7(9), 130–135 (2007)
Layeb, A., Meshoul, S., Batouhe, M.: Multiple Sequence Alignment by Quantum Genetic Algorithm. In: The 7th International Workshop on Parallel and Distributed Scientific and Engineering Computing of the 20th International Parallel and Distributed Processing Symposium, Greece, pp. 1–8 (April 2006)
Asahiro, Y., Iwama, K., Miyano, E.: Random Generation of Test Instanzes with Controlled Attributes. In: Johnson, D.S., Trick, M.A. (eds.) Cliques, Coloring, and Satisfiability: The Second DIMACS Implementation Challenge. DIMACS Series on Discr. Math. and Theor. Comp. Sci, vol. 26, pp. 377–394 (1996), http://www.cs.ubc.ca/~hoos/SATLIB/Benchmarks/SAT/DIMACS/AIM/descr.html
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Layeb, A., Saidouni, DE. (2008). A New Quantum Evolutionary Local Search Algorithm for MAX 3-SAT Problem. In: Corchado, E., Abraham, A., Pedrycz, W. (eds) Hybrid Artificial Intelligence Systems. HAIS 2008. Lecture Notes in Computer Science(), vol 5271. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87656-4_22
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DOI: https://doi.org/10.1007/978-3-540-87656-4_22
Publisher Name: Springer, Berlin, Heidelberg
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