Measuring the Searched Space to Guide Efficiency: The Principle and Evidence on Constraint Satisfaction
In this paper we present a new tool to measure the efficiency of evolutionary algorithms by storing the whole searched space of a run, a process whereby we gain insight into the number of distinct points in the state space an algorithm has visited as opposed to the number of function evaluations done within the run. This investigation demonstrates a certain inefficiency of the classical mutation operator with mutation-rate 1/l, where l is the dimension of the state space. Furthermore we present a model for predicting this inefficiency and verify it empirically using the new tool on binary constraint satisfaction problems.
KeywordsState Space Mutation Rate Evolutionary Algorithm Problem Instance Mutation Operator
Unable to display preview. Download preview PDF.
- 1.D. Achlioptas, L.M. Kirousis, E. Kranakis, D. Krizanc, M.S.O. Molloy, and Y.C. Stamatiou. Random constraint satisfaction a more accurate picture. In G. Smolka, editor, Principles and Practice of Constraint Programming— CP97, pages 107–120. Springer-Verlag, 1997.Google Scholar
- 2.T. Bäck. The interaction of mutation rate, selection, and self-adaptation within a genetic algorithm. In R. Manner and B. Manderick, editors, Parallel Problem Solving from Nature II, pages 85–94. Springer, 1992.Google Scholar
- 4.A.E. Eiben, E.H.L. Aarts, and K.M. Van Hee. Global convergence of genetic algorithms: an infinite markov chain analysis. In Proceedings of the First International Conference on Parallel Problem Solving from Nature, pages 4–12. Springer, Berlin, 1991.Google Scholar
- 6.E. Marchiori and A. Steenbeek. A genetic local search algorithm for random binary constraint satisfaction problems. In ACM Symposium on Applied Computing, pages 458–462, 2000.Google Scholar
- 7.H. Mühlenbein. How genetic algorithms really work: Mutation and hill-climbing. In R. Manner and B. Manderick, editors, Parallel Problem Solving from Nature II, pages 15–25. Springer, 1992.Google Scholar
- 8.E. Tsang. Foundations of Constraint Satisfaction. Academic Press, 1993.Google Scholar
- 9.J.I. van Hemert. Documentation of the RandomCsp library. Leiden University, randomcsp version 1. 5 edition, 2001. Available from http://www.liacs.nl/~jvhemert/randomcsp.
- 10.D. Whitley. The genitor algorithm and selection pressure: Why rank-based allocation of reproductive trials is best. In J. David Schaffer, editor, Proceedings of the Third International Conference on Genetic Algorithms (ICGA’89), pages 116–123, San Mateo, California, 1989. Morgan Kaufmann Publishers, Inc.Google Scholar