Abstract
In this paper we continue our earlier studies [13, 14] on boundary operators for constrained parameter optimization problems. The significance of this line of research is based on the observation that usually the global solution for many optimization problems lies on the boundary of the feasible region. Thus, for many constrained numerical optimization problems it might be beneficial to search just the boundary of the search space defined by a set of constraints (some other algorithm might be used for searching the interior of the search space, if activity of a constraint is not certain). We discuss one particular class of boundary operators — sphere operators — and discuss their applicability to some constrained problems (with convex feasible search spaces) through a mapping between the boundary of the feasible region of the search space and a sphere. We provide also with some experimental evaluation of these transformations.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
S. Baluja,. An empirical comparison of seven iterative and evolutionary function optimization heuristics. Technical Report CMU-CS-95-193, School of Computer Science, Carnegie Mellon University, 1995.
C.A. Floudas and P.M. Pardalos. Recent Advances in Global Optimization. Princeton Series in Computer Science, Princeton University Press, Princeton, NJ, 1992.
C. M. Fonseca and P. J. Fleming. On the performance assessment and comparison of stochastic multiobjective optimizers. In H.-M. Voigt, W. Ebeling, I. Rechenberg, and H.-P. Schwefel, editors, Proceedings of the 4 th Conference on Parallel Problems Solving from Nature, number 1141 in LNCS, pages 584–593. Springer Verlag, Sept. 1996.
N. Hansen, A. Ostermeier, and A. Gawelczyk. On the adaptation of arbitrary normal mutation distributions in evolution strategies: The generating set adaptation. In L. J. Eshelman, editor, Proceedings of the 6 th International Conference on Genetic Algorithms, pages 57–64. Morgan Kaufmann, 1995.
A. Keane. Genetic Algorithms Digest. V8n16. (1994, May 19).
S. Koziel. Homomorphous mappings in numerical optimization with constraints using genetic algorithms. Technical University of Gdańsk, Technichal Report, 1997.
C. Margerin. Une introduction à la géométrie. Course at ENSTA — Palaiseau — France, 1990.
Z. Michalewicz, T.D. Logan, and S. Swaminathan. Evolutionary Operators for Continuous Convex Parameter Spaces. In Proceedings of the 3 rd Annual Conference on Evolutionary Programming, pages 84–97, 1994.
Z. Michalewicz and M. Schoenauer. Evolutionary Algorithms for Constrained parameter Optimization Problems. Evolutionary Computation, Vol. 4, No.1, 1996, pp. 1–32.
Z. Michalewicz, G. Nazhiyath, and M. Michalewicz. A note on usefulness of geometrical crossover for numerical optimization problems. In L. J. Fogel, P. J Angeline, and T. Bäck, editors, Proceedings of the 5 th Annual Conference on Evolutionary Programming, pages 305–312. MIT Press, 1996.
N. J. Radcliffe. Equivalence class analysis of genetic algorithms. Complex Systems, 5:183–20, 1991.
I. Rechenberg. Evolutionstrategie: Optimierung Technisher Systeme nach Prinzipien des Biologischen Evolution. Stuttgart: Fromman-Holzboog Verlag, 1973.
M. Schoenauer and Z. Michalewicz. Evolutionary Computation at the Edge of Feasibility. In H.-M. Voigt, W. Ebeling, I. Rechenberg, and H.-P. Schwefel, editors, Proceedings of the 4 th Parallel Problem Solving from Nature, Springer-Verlag, LNCS 1141, pp.245–254, 1996.
M. Schoenauer and Z. Michalewicz. Boundary Operators for Constrained Parameter Optimization Problems. In T. Bäck, editor, Proceedings of the 7 th International Conference on Genetic Algorithms, pages 322–329. Morgan Kaufmann, 1997.
M. Schoenauer and Z. Michalewicz. Boundary Operators for Evolutionary Algorithms. In preparation.
H.-P. Schwefel. Evolution and Optimum Seeking. John Wiley, Chichester, UK 1995.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1998 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Schoenauer, M., Michalewicz, Z. (1998). Sphere operators and their applicability for constrained parameter optimization problems. In: Porto, V.W., Saravanan, N., Waagen, D., Eiben, A.E. (eds) Evolutionary Programming VII. EP 1998. Lecture Notes in Computer Science, vol 1447. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0040777
Download citation
DOI: https://doi.org/10.1007/BFb0040777
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-64891-8
Online ISBN: 978-3-540-68515-9
eBook Packages: Springer Book Archive