Abstract
Evolution strategies (ES)are efficient optimization methods for continuous problems. However, many combinatorial optimization methods can not be represented by using continuous representations. The development of the network random key representation which represents trees by using real numbers allows one to use ES for combinatorial tree problems.
In this paper we apply ES to tree problems using the network random key representation. We examine whether existing recommendations regarding optimal parameter settings for ES, which were developed for the easy sphere and corridor model, are also valid for the easy one-max tree problem.
The results show that the \( \frac{1} {5} \)-success rule for the (1+1)-ES results in low performance because the standard deviation is continuously reduced and we get early convergence. However, for the (μ+λ)-ES and the (μ, λ)-ES the recommendations from the literature are confirmed for the parameters of mutation \( \tau _1 \) and \( \tau _2 \) and the ratio μ/λ. This paper illustrates how existing theory about ES is helpful in finding good parameter settings for new problems like the one-max tree problem.
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References
H.-P. Schwefel. Kybernetische Evolution als Strategie der experimentellen Forschung in der Strömungstechnik. Master’s thesis, Technische Universität Berlin, 1965.
I. Rechenberg. Cybernetic solution path of an experimental problem. Technical Report 1122, Royal Aircraft Establishment, Library Translation, Farnborough, Hants., UK, 1965.
H.-P. Schwefel. Experimentelle Optimierung einer Zweiphasendüse. Bericht 35, AEG Forschungsinstitut Berlin, Projekt MHD-Staustahlrohr, 1968.
J. H. Holland. Adaptation in natural and artificial systems. University of Michigan Press, Ann Arbor, MI, 1975.
F. Rothlauf, D. E. Goldberg, and A. Heinzl. Network random keys-a tree network representation scheme for genetic and evolutionary algorithms. Technical Report No. 8/2000, University of Bayreuth, Germany, 2000. to be published in Evolutionary Computation.
J. C. Bean. Genetics and random keys for sequencing and optimization. Technical Report 92–43, Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, MI, June 1992.
Franz Rothlauf. Towards a Theory of Representations for Genetic and Evolutionary Algorithms: Development of Basic Concepts and their Application to Binary and Tree Representations. PhD thesis, University of Bayreuth/Germany, 2001.
C. C. Palmer. An approach to a problem in networkdesign using genetic algorithms. unpublished PhD thesis, Polytechnic University, Troy, NY, 1994.
H. Prüfer. Neuer Beweis eines Satzesüber Permutationen. Archiv für Mathematikund Physik, 27:742–744, 1918.
Günther R. Raidl. An efficient evolutionary algorithm for the degree-constrained minimum spanning tree problem. In Proceedings of 2000 IEEE International Conference on Evolutionary Computation, pages 43–48, Piscataway, NJ, 2000. IEEE.
F. Abuali, R. Wainwright, and D. Schoenefeld. Determinant factorization and cycle basis: Encoding schemes for the representation of spanning trees on incomplete graphs. In Proceedings of the 1995 ACM/SIGAPP Symposium on Applied Comuting, pages 305–312, Nashville, TN, February 1995. ACM Press.
R. Hamming. Coding and Information Theory. Prentice-Hall, 1980.
D. E. Goldberg, K. Deb, and D. Thierens. Toward a better understanding of mixing in genetic algorithms. Journal of the Society of Instrument and Control Engineers, 32(1):10–16, 1993.
I. Rechenberg. Bionik, Evolution und Optimierung. Naturwissenschaftliche Rundschau, 26(11):465–472, 1973.
H.-P. Schwefel. Evolutionsstrategie und numerische Optimierung. PhD thesis, Technical University of Berlin, 1975.
T. Bäck. Evolutionary Algorithms in Theory and Practice. Oxford University Press, New York, 1996.
H.-P. Schwefel. Evolution and Optimum Seeking. Wisley & Sons, New York, 1995.
H.-P. Schwefel. Numerische Optimierung von Computer-Modellen mittels der Evolutionsstrategie. Birkhäuser, Basel, 1977. from Interdisciplinary Systems Research, volume 26.
F. Kursawe. Grundlegende empirische Untersuchungen der Parameter von Evolutionsstrategien-Metastrategien. PhD thesis, University of Dortmund, 1999.
V. Nissen. Einführung in evolutionäre Algorithmen: Optimierung nach dem Vorbild der Evolution. Vieweg, Wiesbaden, 1997.
H.-P. Schwefel. Collective phenomena in evolutionary systems. In P. Checkland and I. Kiss, editors, Problems of Constancy and Change-The Complementarity of Systems Approaches to Complexity, volume 2, pages 1025–1033, Budapest, 1987. Papers presented at the 31st Annual Meeting of the International Society for General System Research.
Barbara Schindler. Einsatz von Evolutionären Stratgien zur Optimierung baumförmiger Kommunikationsnetzwerke. Master’s thesis, Universität Bayreuth, Lehrstuhl für Wirtschaftsinformatik, Mai 2001.
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Schindler, B., Rothlauf, F., Pesch, HJ. (2002). Evolution Strategies, Network Random Keys, and the One-Max Tree Problem. In: Cagnoni, S., Gottlieb, J., Hart, E., Middendorf, M., Raidl, G.R. (eds) Applications of Evolutionary Computing. EvoWorkshops 2002. Lecture Notes in Computer Science, vol 2279. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46004-7_15
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DOI: https://doi.org/10.1007/3-540-46004-7_15
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