GA-easy and GA-hard constraint satisfaction problems
In this paper we discuss the possibilities of applying genetic algorithms (GA) for solving constraint satisfaction problems (CSP). We point out how the greediness of deterministic classical CSP solving techniques can be counterbalanced by the random mechanisms of GAs. We tested our ideas by running experiments on four different CSPs: N-queens, graph 3-colouring, the traffic lights and the Zebra problem. Three of the problems have proven to be GA-easy, and even for the GA-hard one the performance of the GA could be boosted by techniques familiar in classical methods. Thus GAs are promising tools for solving CSPs. In the discussion, we address the issues of non-solvable CSPs and the generation of all the solutions.
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References
- Adorf, H. M. and Johnston, M. D., A discrete stochastic neural network algorithm for constraint satisfaction problems, In Proc. of the International Joint Conference on Neural Networks, San Diego, CA 1990. Google Scholar
- Back, T., Khuri, A., An evolutionary heuristic for the maximum independent set problem, In Proc. of the First IEEE Conference on Evolutionary Computation, Orlando, Fl. 1994, pp 531–535. Google Scholar
- Brassard, G. and Bratley, P., Algorithmics — Theory and Practice, Prentice Hall, Englewood Cliffs, NJ, 1988. Google Scholar
- Cheeseman, P., Kenefsky, B. and Taylor, W. M., Where the really hard problems are, In Proc. of IJCAI-91, 1991, pp 331–337. Google Scholar
- Corcoran, A. L. and Wainwright, R. L., LibGA: A User Friendly Workbench for Order-Based Genetic Algorithm Research, In Proc. of Applied Computing: Sates of the Art and Practice-1993, 1993, pp 111–117. Google Scholar
- Crawford, K.D., Solving the n-queens problem using genetic algorithms, In Proc. ACM/SIGAPP Symposium on Applied Computing, Kansas City, Missouri, 1992, pp 1039–1047. Google Scholar
- Davenport, A., Tsang, E., Wang, C. J. and Zhu, K., GENET: A connnectionist architecture for solving constraint satisfaction problems by iterative improvement, In Proc. of AAAI'94. Google Scholar
- Davis, L., Handbook of Genetic Algorithms, Van Nostrand Reinhold, New York, 1991. Google Scholar
- Dechter, R., Enhancement schemes for constraint processing: Backjumping, learning, and cutset decomposition, Artificial Intelligence 41 1990, pp 273–312. Google Scholar
- Dozier, G., Bowen, J., Bahler, D., Solving small and large scale constraint satisfaction problems using a heuristic-based microgenetic agorithm, In Proc. of the First IEEE Conference on Evolutionary Computation, Orlando, Fl. 1994, pp 306–311. Google Scholar
- Dozier, G., Bowen, J., Bahler, D., Constraint processing using heuristic microgenetic algorithms, In Proc. of the ECAI'94 Workshop on Applied Genetic and Other Evolutionary Algorithms, Amsterdam, 1994. Google Scholar
- Eiben, A. E., Raué, P-E. and Ruttkay, Zs., Heuristic Genetic Algorithms for Constrained Problems, Part I: Principles, Technical Report IR-337, Dep. of Maths. and Comp. Sci., Free University Amsterdam, 1993. Google Scholar
- Eiben, A. E., Raué, P-E. and Ruttkay, Zs., Solving constraint satisfaction problems using genetic algorithms, In Proc. of the IEEE World Conf. on Comp. Intelligence, Orlando, 1994, pp 542–547. Google Scholar
- Eiben, A. E., Raué, P-E. and Ruttkay, Zs., Genetic algorithms with multi-parent reproduction, To appear in Proc. of the 3rd Parallel Problem Solving from Nature, LNCS Series, Springer-Verlag, 1994. Google Scholar
- Eiben, A. E., Raué, P-E. and Ruttkay, Zs., Repairing, adding constraints and learning as a means of improving GA performance on CSPs, In Proc. of the BENELEARN-94, Rotterdam, 1994. Google Scholar
- Forrest, S. and Mitchell, M., What makes a problem hard for a GA?, to appear in Machine Learning 1994. Google Scholar
- Fox, B. R. and McMahon, M.B., Genetic operators for sequencing problems, In Proc. of Foundations of Genetic Algorithms-90, Morgan Kaufman, 1991, pp 284–300. Google Scholar
- Freuder, E. C., A sufficient condition for backtrack-free search, Journal of the ACM 29, 1 1982. pp 24–32. Google Scholar
- Freuder, E. C., A sufficient condition for backtrack-bounded search, Journal of the ACM 32, 4 1985. pp 775–761. Google Scholar
- Goldberg, D. E., Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley, 1989. Google Scholar
- Hao, J., Dorne, R., A new population-based method for satisfiability problems, In Proc. of ECAI'94, Amsterdam 1994, pp 135–139. Google Scholar
- Haralick, R. M., and Elliot, G. L., Increasing tree search efficiency for constraint satisfaction problems, Artificial Intelligence 14 1980, pp 263–313. Google Scholar
- Holland, J.H., Adaptation in Natural and Artificial Systems, Ann Arbor: Univ. of Michingan Press, 1992. Google Scholar
- Hower, W. and Jaboci, S., Parallel distributed constraint satisfaction, In Proc. of the Second International Workshop on Parallel Processing for Artificial Intelligence, IJCAI-93, Chambery, 1993, pp 65–68. Google Scholar
- Huang, W., Kao, C., Horng, J., A genetic algorithm approach for set covering problems, In Proc. of the First IEEE Conference on Evolutionary Computation, Orlando, Fl. 1994, pp 569–574. Google Scholar
- Johnson, D. S., Aragon, C. R., McGeoch, L. A. and Schevon, C., Optimization by simulated annealing: an experimental evaluation, Part II, Journal of Operations Research 39, 3 1991, pp 378–406. Google Scholar
- Khuri, S., Bäck, T. and Heitkötter, J., An evolutionary approach to combinatorial optimization problems, In Proceedings of CSC'94, Phoenix Arizona, 1994, ACM Press. Google Scholar
- Manderick, B. and Inayoshi, H., The weighted graph bi-partitioning problem: an analysis of GA performance, To appear in Proc. of the 3rd Parallel Problem Solving from Nature, Springer-Verlag, 1994. Google Scholar
- Mackworth, A.K., Concistency in networks of relations, Artificial Intelligence 8. 1977 pp 99–118. Google Scholar
- Meseguer, P., Constraint satisfactionproblems: an overview, AICOM, Vol. 2. no. 1 1989, pp 3–17. Google Scholar
- Michalewicz, Z. and Janikow, C. Z., Handling constraints in genetic algorithms, In Proc. of Int. Conference on Genetic Algorithms-91, Morgan Kaufman, 1991. Google Scholar
- Michalewicz, Z., Genetic Algorithms + Data Structures = Evolution Programs, Springer-Verlag, 1994. Google Scholar
- Minton, S., Johnston, M. D., Philips, A. and Laird, P., Minimizing conflicts: a heuristic repair method for constraint satisfaction and scheduling problems, Artificial Intelligence 58. 1992. pp 161–205. Google Scholar
- Mitchell, M., Forrest, S., and Holland, J., The royal road for genetic algorithms: fitness landscapes and GA performance, In Proc. of the First European Conference on Artificial Life, Cambridge, MA, MIT Press, 1991. Google Scholar
- Morris, P., On the density of solutions in equilibrium points for the n-queens problem, In Proc. AAAI-92, San Jose, CA 1992, pp 428–433. Google Scholar
- Paechter, B., Cumming, S., Luchian, H. and Petriuc, M., Two solutions for the general timetable problem using evolutionary methods, In Proc. of the First IEEE Conference on Evolutionary Computation, Orlando, Fl. 1994, pp 300–305. Google Scholar
- Paredis, J., Exploiting constraints as background knowledge for a case-study for scheduling, In Proc. Parallel Problem Solving from Nature, 1992, Elsevier. Google Scholar
- Sosic, R., Gu, J., A polynomial time algorithm for the n-queens problem, SIGART 1 (3), 1990, pp 7–11. Google Scholar
- Starkweather, T., Mc Daniel, S., Mathias, K., Whitley, D. and Whitley, C., A comparison of genetic sequenceing operators, In Proc. of Int. Conference on Genetic Algorithms-91, 1991, pp 69–76. Google Scholar
- Tsang, E. P. K. and Warwick, T., Applying genetic algorithms to constraint satisfaction optimization problems, In Proc. of ECAI-90, 1990, pp 649–654. Google Scholar
- Yamada, T. and Nakano, R., A genetic algorithm applicable to large-scale job-shop problems, In Proc. Parallel Problem Solving from Nature, 1992, Elsevier, pp 281–290. Google Scholar
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Authors and Affiliations
- Dept. of Mathematics and Computer Science, Vrije Universiteit Amsterdam, De Boelelaan 1081a, 1081, HV Amsterdam, The Netherlands Ágoston Eiben, Paul-Erik Raué & Zsófia Ruttkay
- Ágoston Eiben