Abstract
Recently, a local-search heuristic algorithm called Extremal Optimization (EO) has been successfully applied in some combinatorial optimization problems. However, there are only limited papers studying on the mechanism of EO applied to the numerical optimization problems so far. This paper presents the studies on the applications of EO to numerical constrained optimization problems with a set of popular benchmark problems. To enhance and improve the search performance and efficiency of EO, we developed a novel EO strategy with population based search. The newly developed EO algorithm is named population-based EO (PEO). Additionally, we adopted the adaptive Lévy mutation, which is more likely to generate an offspring that is farther away from its parent than the commonly employed Gaussian mutation. Compared with three state-of-the-art stochastic search methods with six popular benchmark problems, it has been shown that our approach is a good choice to deal with the numerical constrained optimization problems.
Keywords
- Search Point
- Gaussian Mutation
- Punctuate Equilibrium
- Extremal Optimization
- Numerical Optimization Problem
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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
Runarsson, T.P., Yao, X.: Stochastic Ranking for Constrained Evolutionary Optimization. IEEE Transactions on Evolutionary Computation 4, 284–294 (2000)
Hamida, S.B., Schoenauer, M., ASCHEA,: New Results Using Adaptive Segregational Constraint Handling. In: Proceedings of the Congress on Evolutionary Computation 2002 (CEC 2002), pp. 884–889 (2002)
Mezura-Montes, E., Coello, C.A.C.: A Simple Multimembered Evolution Strategy to Solve Constrained Optimization Problems. IEEE Transactions on Evolutionary Computation 9, 1–17 (2005)
Boettcher, S., Percus, A.G.: Nature’s Way of Optimizing. Artificial Intelligence 119, 275–286 (2000)
Bak, P., Sneppen, K.: Punctuated Equilibrium and Criticality in a Simple Model of Evolution. Physical Review Letters 71, 4083–4086 (1993)
Bak, P., Tang, C., Wiesenfeld, K.: Self-Organized Criticality. Physical Review Letters 59, 381–384 (1987)
De Sousa, F.L., Ramos, F.M.: Function Optimization Using Extremal Dynamics. In: 4th International Conference on Inverse Problems in Engineering Rio de Janeiro, Brazil (2002)
De Sousa, F.L., Vlassov, V., Ramos, F.M.: Generalized Extremal Optimization: an Application in Heat Pipe Design. Applied Mathematical Modeling 28, 911–931 (2004)
Boettcher, S.: Extremal Optimization: Heuristics via Coevolutionary Avalanches. Computing in Science and Engineering 2, 275–282 (2000)
Yao, X., Liu, Y., Lin, G.: Evolutionary Programming Made Faster. IEEE Transactions on Evolutionary Computation 3, 82–102 (1999)
Lee, C.Y., Yao, X.: Evolutionary Algorithms with Adaptive Lévy Mutations. In: Proceedings of the 2001 Congress on Evolutionary Computation, pp. 568–575 (2001)
Mantegna, R.: Fast, Accurate Algorithm for Numerical Simulation of Lévy Stable Stochastic Process. Physical Review E 49, 4677–4683 (1994)
Boettcher, S., Percus, A.G.: Extremal Optimization at the Phase Transition of the 3-Coloring Problem. Physical Review E 69, 66–703 (2004)
Boettcher, S.: Extremal Optimization for the Sherrington-Kirkpatrick Spin Glass. European Physics Journal B 46, 501–505 (2005)
Menai, M.E., Batouche, M.: Efficient Initial Solution to Extremal Optimization Algorithm for Weighted MAXSAT Problem. In: Chung, P.W.H., Hinde, C.J., Ali, M. (eds.) IEA/AIE 2003. LNCS, vol. 2718, pp. 592–603. Springer, Heidelberg (2003)
Moser, I., Hendtlass, T.: Solving Problems with Hidden Dynamics-Comparison of Extremal Optimization and Ant Colony System. In: Proceedings of 2006 IEEE Congress on Evolutionary Computation (CEC’2006), pp. 1248–1255. IEEE Computer Society Press, Los Alamitos (2006)
Chen, Y.W., Lu, Y.Z., Yang, G.: Hybrid Evolutionary Algorithm with Marriage of Genetic Algorithm and Extremal Optimization for Production Scheduling. International Journal of Advanced Manufacturing Technology (accepted)
Lu, Y.Z., Chen, M.R., Chen, Y.W.: Studies on Extremal Optimization and its Applications in Solving Real World Optimization Problems. In: Proceedings of 2007 IEEE Series Symposium on Computation Intelligence, Hawaii, USA, April 1-5, 2007, IEEE Computer Society Press, Los Alamitos (2007)
Chen, M.R., Lu, Y.Z., Yang, G.: Multiobjective Optimization Using Population-Based Extremal Optimization. In: Proceedings of the First International Conference on Bio-Inspired Computing: Theory and Applications(BIC-TA, 2006), (2006) (to be published)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Chen, MR., Lu, YZ., Yang, G. (2007). Population-Based Extremal Optimization with Adaptive Lévy Mutation for Constrained Optimization. In: Wang, Y., Cheung, Ym., Liu, H. (eds) Computational Intelligence and Security. CIS 2006. Lecture Notes in Computer Science(), vol 4456. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74377-4_16
Download citation
DOI: https://doi.org/10.1007/978-3-540-74377-4_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74376-7
Online ISBN: 978-3-540-74377-4
eBook Packages: Computer ScienceComputer Science (R0)