Abstract
Numerical optimization problems enjoy a significant popularity in evolutionary computation community; all major evolutionary techniques use such problems for various tests and experiments. However, many of these techniques (as well as other, classical optimization methods) encounter difficulties in solving some real-world problems which include non-trivial constraints. This paper discusses a new development which is based on the observation that very often the global solution lies on the boundary of the feasible region. Thus, for many constrained numerical optimization problems it might be beneficial to limit the search to that boundary, using problem-specific operators. Two test cases illustrate this approach: specific operators are designed from the simple analytical expression of the constraints. Some possible generalizations to larger classes of constraints are discussed as well.
Preview
Unable to display preview. Download preview PDF.
References
T. Bäck, F. Hoffmeister, and H.-P. Schwefel. A survey of evolution strategies. In R. K. Belew and L. B. Booker, editors, Proceedings of the 4 th International Conference on Genetic Algorithms, pages 2–9. Morgan Kaufmann, 1991.
J. C. Bean and A. B. Hadj-Alouane. A dual genetic algorithm for bounded integer programs. Technical Report TR 92-53, Department of Industrial and Operations Engineering, The University of Michigan, 1992.
F. Glover. Heuristics for integer programming using surrogate constraints. Decision Sciences, 8(1):156–166, 1977.
F. Glover and G. Kochenberger. Critical event tabu search for multidimensional knapsack problems. In Proceedings of the International Conference on Metaheuristics for Optimization, pages 113–133. Kluwer Publishing, 1995.
A. Homaifar, S. H.-Y. Lai, and X. Qi. Constrained optimization via genetic algorithms. Simulation, 62(4):242–254, 1994.
J.A. Joines and C.R. Houck. On the use of non-stationary penalty functions to solve nonlinear constrained optimization problems with GAs. In Z. Michalewicz, J. D. Schaffer, H.-P. Schwefel, D. B. Fogel, and H. Kitano, editors, Proceedings of the First IEEE International Conference on Evolutionary Computation, pages 579–584. IEEE Press, 1994.
A. Keane. Genetic Algorithms Digest, May 19 1994. V8n16.
R. G. Leriche, C. Knopf-Lenoir, and R. T. Haftka. A segragated genetic algorithm for constrained structural optimization. In L. J. Eshelman, editor, Proceedings of the 6 th International Conference on Genetic Algorithms, pages 558–565, 1995.
C. Margerin. Une introduction à la géométrie. Course at ENSTA — Palaiseau — France, 1990.
Z. Michalewicz. Genetic algorithms, numerical optimization and constraints. In L. J. Eshelman, editor, Proceedings of the 6th International Conference on Genetic Algorithms, pages 151–158. Morgan Kaufmann, 1995.
Z. Michalewicz. Genetic Algorithms+Data Structures=Evolution Programs. Springer Verlag, New-York, 1996. 3rd edition.
Z. Michalewicz and N. Attia. Evolutionary optimization of constrained problems. In Proceedings of the 3 rd Annual Conference on Evolutionary Programming, pages 98–108. World Scientific, 1994.
Z. Michalewicz and G. Nazhiyath. Genocop III: A co-evolutionary algorithm for numerical optimization problems with nonlinear constraints. In D. B. Fogel, editor, Proceedings of the Second IEEE International Conference on Evolutionary Computation, pages 647–651. IEEE Press, 1995.
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, 1996.
Z. Michalewicz and M. Schoenauer. Evolutionary Algorithms for Constrained Parameter Optimization Problems. Evolutionary Computation, 4(1), Spring 1996.
D. Powell and M. M. Skolnick. Using genetic algorithms in engineering design optimization with non-linear constraints. In S. Forrest, editor, Proceedings of the 5 th International Conference on Genetic Algorithms, pages 424–430. Morgan Kaufmann, 1993.
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. Fromman-Holzboog Verlag, 1973.
A. Smith and D. Tate. Genetic optimization using a penalty function. In S. Forrest, editor, Proceedings of the 5 th International Conference on Genetic Algorithms, pages 499–503. Morgan Kaufmann, 1993.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1996 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Schoenauer, M., Michalewicz, Z. (1996). Evolutionary computation at the edge of feasibility. In: Voigt, HM., Ebeling, W., Rechenberg, I., Schwefel, HP. (eds) Parallel Problem Solving from Nature — PPSN IV. PPSN 1996. Lecture Notes in Computer Science, vol 1141. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61723-X_989
Download citation
DOI: https://doi.org/10.1007/3-540-61723-X_989
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-61723-5
Online ISBN: 978-3-540-70668-7
eBook Packages: Springer Book Archive