Abstract
We present a genetic-based approach to solve SAT problem and NP-complete problems. The main idea of the approach presented here is to exploit the fact that, although all NP-complete problems are equally difficult in a general computational sense, some have much better genetic representations than others, leading to much more successful use of genetic-based algorithm on some NP-complete problems than on others. Since any NP-complete problem can be mapped into any other one in polynomial time by a transformation, the approach described here consists of identifying and finding a canonical or generic NP-complete problem on which genetic algorithm work well, and solving other NP-complete problems indirectly by translating them onto the canonical problem. We presented some initial results where we have the Boolean Satisfiability Problem (SAT) as a canonical problem, and results on Hamiltonian Circuit problem which represent a family of NP-complete problems, it can be solved efficiently by mapping them first onto SAT problems.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Rudolf F. Albrecht, Colin R. Reeves, and Nigel C. Steele, editors. Artificial neural nets and genetic algorithms. Springer, April 14–16 1993. ANNGA 93, International Conference on Artificial Neural Networks & Genetic Algorithms.
Back, Eiben, and Vink. A superior evolutionary algorithm for 3-SAT. In International Conference on Evolutionary Programming, in cooperation with IEEE Neural Networks Council. LNCS, 1998.
Eiben and van der Hauw. Solving 3-SAT by (gas) adapting constraint weights. In Proceedings of The IEEE Conference on Evolutionary Computation, World Congress on Computational Intelligence, 1997.
J. Grefenstette and al. Genetic algorithms fot the traveling salesman problem. In Conference on Intelligent Systems and Machines, 1984.
Chris Gathercole. An investigation of supervised learning in genetic programming. In Ph.D. thesis. Department of Electronics and Electrical Engineering. University of Edinburg, 1998, 1998.
M. Garey and D. Johnsond. Computers and intractability: A guide to the theory of np-completeness. In W. H. Freeman and Company, CA., 1979.
D. Goldberg and Robert Lingle. Alleles, loci, and the traveling salesman problem. In Conference on Intelligent Systems and Machines 161–165, 1985.
D. Goldberg. Genetic algorithms in search, optmization and machine learning. In Addison Wesley Pubslishing, ISBN:0-201-15767-5, 1989.
Gerald Smith H. Adaptive genetic algorithms and the boolean satisfiability problem. In Conference on genetic algorithm, 1979.
J. H. Holland. Adaptation in natural and artificial systems. In The university of Michigan Press, 1975.
J.R. Koza. Genetic Programming. MIT Press, 1992.
William B. Langdon. Data structures and genetic programming. In Ph.D. thesis. University College, London, 1998.
H. Levesque, B. Selman, and D. Mitchell. A new method for solving hard satisfiability problems. In Proceeding of AAAI, pages 440-446, 1992.
Gregory J. E. Rawlins, editor. Foundations of Genetic Algorithms, San Mateo, California, 1991. Morgan Kaufmann.
Günter Rudolph. Convergence analysis of canonical genetic algorithms. IEEE Trans. Neural Networks, Special Issue on Evolutionary Computation, 5(1):96–101, 1994.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Tounsi, M. (2002). A Genetic-Based Approach for Satisfiability Problems. In: Calmet, J., Benhamou, B., Caprotti, O., Henocque, L., Sorge, V. (eds) Artificial Intelligence, Automated Reasoning, and Symbolic Computation. AISC Calculemus 2002 2002. Lecture Notes in Computer Science(), vol 2385. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45470-5_20
Download citation
DOI: https://doi.org/10.1007/3-540-45470-5_20
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-43865-6
Online ISBN: 978-3-540-45470-0
eBook Packages: Springer Book Archive