Abstract
Evolutionary and genetic algorithms (EAs and GAs) are quite successful randomized function optimizers. This success is mainly based on the interaction of different operators like selection, mutation, and crossover. Since this interaction is still not well understood, one is interested in the analysis of the single operators. Jansen and Wegener (2001a) have described so-called real royal road functions where simple steady-state GAs have a polynomial expected optimization time while the success probability of mutation-based EAs is exponentially small even after an exponential number of steps. This success of the GA is based on the crossover operator and a population whose size is moderately increasing with the dimension of the search space. Here new real royal road functions are presented where crossover leads to a small optimization time, although the GA works with the smallest possible population size — namely 2.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Dietzfelbinger, M., Naudts, B., van Hoyweghen, C., and Wegener, I. (2002). The analysis of a recombinative hill-climber on H-IFF. Submitted for publication in IEEE Trans. on Evolutionary Computation.
Goldberg, D.E. (1989). Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley, Reading, Mass.
Holland, J.H. (1975). Adaptation in Natural and Artificial Systems. The Univ. of Michigan Press, Ann. Arbor, Mich.
Jansen, T. and Wegener, I. (2001a). Real royal road functions — where crossover provably is essential. Proc. of GECCO’2001, 375–382. Morgan Kaufmann, San Francisco, Calif.
Jansen, T. and Wegener, I. (2001b). On the utility of populations in evolutionary algorithms. Proc. of GECCO’2001, 1034–1041. Morgan Kaufmann, San Francisco, Calif.
Jansen, T. and Wegener, I. (2001c). Evolutionary algorithms — how to cope with plateaus of constant fitness and when to reject strings with the same fitness. IEEE Trans. on Evolutionary Computation 5, 589–599.
Mitchell, M. (1996). An Introduction to Genetic Algorithms. Chapter 4.2. MIT Press, Cambridge, Mass.
Mitchell, M., Forrest, S., and Holland, J.H. (1992). The royal road for genetic algorithms: Fitness landscapes and GA performance. Proc. of First European Conf. on Artificial Life. MIT Press, Cambridge, Mass.
Mitchell, M., Holland, J.H., and Forrest, S. (1994). When will a genetic algorithm outperform hill-climbing? Advances in NIPS 6, Morgan Kaufmann, San Mateo, Calif.
Motwani, R. and Raghavan, P. (1995). Randomized Algorithms. Cambridge Univ. Press.
Watson, R.A. and Pollack, J.B. (1999). Hierarchically-consistent test problems for genetic algorithms. Proc. of the Congress on Evolutionary Computation (CEC), 1406–1413. IEEE Press.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Storch, T., Wegener, I. (2003). Real Royal Road Functions for Constant Population Size. In: Cantú-Paz, E., et al. Genetic and Evolutionary Computation — GECCO 2003. GECCO 2003. Lecture Notes in Computer Science, vol 2724. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45110-2_14
Download citation
DOI: https://doi.org/10.1007/3-540-45110-2_14
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-40603-7
Online ISBN: 978-3-540-45110-5
eBook Packages: Springer Book Archive