Abstract
This chapter presents a framework that unifies various search mechanisms for solving constrained nonlinear programming (NLP) problems. These problems are characterized by functions that are not necessarily differentiable and continuous. Our proposed framework is based on the first-order necessary and sufficient condition developed for constrained local minimization in discrete space that shows the equivalence between discrete-neighborhood saddle points and constrained local minima. To look for discrete-neighborhood saddle points, we formulate a discrete constrained NLP in an augmented Lagrangian function and study various mechanisms for performing ascents of the augmented function in the original-variable subspace and descents in the Lagrange-multiplier subspace. Our results show that CSAGA, a combined constrained simulated annealing and genetic algorithm, performs well when using crossovers, mutations, and annealing to generate trial points. Finally, we apply iterative deepening to determine the optimal n umber of generations in CSAGA and show that its performance is robust with respect to changes in population size.
Research supported by National Aeronautics and Space Administration Contract NAS2-37143.
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.
References
Aarts, E. and Korst, J. (1989) Simulated Annealing and Boltzmann Machines. J. Wiley and Sons.
Bertsekas, D. P. (1982) Constrained Optimization and Lagrange Multiplier Methods. Academic Press.
Corana, A., Marchesi, M., Martini, C. and Ridella, S. (1987) Minimizing multimodal functions of continuous variables with the simulated annealing algorithm. ACM Trans. on Mathematical Software, 13(3):262–280.
Eiben, A. E. and Ruttkay, Zs. (1996) Self-adaptivity for constraint satisfaction: Learning penalty functions. Proceedings of the 3rd IEEE Conference on Evolutionary Computation, 258–261.
Floudas, C. A. and Pardalos, P. M. (1990) A Collection of Test Problems for Constrained Global Optimization Algorithms, volume 455 of Lecture Notes in Computer Science. Springer-Verlag.
Joines, J. and Houck, C. (1994) On the use of non-stationary penalty functions to solve nonlinear constrained optimization problems with gas. Proceedings of the First IEEE International Conference on Evolutionary Computation, 579–584.
Korf, R. E. (1985) Depth-first iterative deepening: An optimal admissible tree search. Artificial Intelligence, 27:97–109.
Koziel, S. and Michalewicz, Z. (1999) Evolutionary algorithms, homomorphous mappings, and constrained parameter optimization. Evolutionary Computation, 7(l):19–44.
Luenberger, D. G. (1984) Linear and Nonlinear Programming. Addison-Wesley Publishing Company, Reading, MA.
Michalewicz, Z. and Nazhiyath, G. (1995) Genocop III: A co-evolutionary algorithm for numerical optimization problems with nonlinear constraints. Proceedings of IEEE International Conference on Evolutionary Computation, 2:647–651.
Michalewicz, Z. and Schoenauer, M. (1996) Evolutionary algorithms for constrained parameter optimization problems. Evolutionary Computation, 4(l):1–32.
Wah, B. W. and Chen, Y. X. (2000) Optimal anytime constrained simulated annealing for constrained global optimization. Sixth Int’l Conf. on Principles and Practice of Constraint Programming.
Wah, B. W. and Wang, T. (1999) Simulated annealing with asymptotic convergence for nonlinear constrained global optimization. Principles and Practice of Constraint Programming, 461–475.
Wah, B. W. and Wu, Z. (1999) The theory of discrete Lagrange multipliers for nonlinear discrete optimization. Principles and Practice of Constraint Programming, 28–42.
Wu, Z. (1998) Discrete Lagrangian Methods for Solving Nonlinear Discrete Constrained Optimization Problems. M.Sc. Thesis, Dept. of Computer Science, Univ. of Illinois, Urbana, IL.
Wu, Z. (2000) The Theory and Applications of Nonlinear Constrained Optimization using Lagrange Multipliers. Ph.D. Thesis, Dept. of Computer Science, Univ. of Illinois, Urbana, IL.
Rights and permissions
Copyright information
© 2003 Kluwer Academic Publishers
About this chapter
Cite this chapter
Wah, B.W., Chen, YX. (2003). Constrained Genetic Algorithms and Their Applications in Nonlinear Constrained Optimization. In: Evolutionary Optimization. International Series in Operations Research & Management Science, vol 48. Springer, Boston, MA. https://doi.org/10.1007/0-306-48041-7_10
Download citation
DOI: https://doi.org/10.1007/0-306-48041-7_10
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-7923-7654-5
Online ISBN: 978-0-306-48041-6
eBook Packages: Springer Book Archive