Abstract
This paper investigates on some properties of encodings of evolutionary algorithms for spanning tree based problems. Although debate continues on how and why evolutionary algorithms work, many researchers have observed that an EA is likely to perform well when its encoding and operators exhibit locality, heritability and diversity. To analyze these properties of various encodings, we use two kinds of analytical methods; static analysis and dynamic analysis and use the Optimum Communication Spanning Tree (OCST) problem as a test problem. We show it through these analysis that the encoding with extremely high locality and heritability may lose the diversity in population. And we show that EA using Edge Window Decoder (EWD) has high locality and high heritability but nevertheless it preserves high diversity for generations.
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References
Eckert, C., Gottlieb, J.: Direct Representation and Variation Operators for the Fixed Charge Transportation Problem. In: Guervós, J.J.M., Adamidis, P.A., Beyer, H.-G., Fernández-Villacañas, J.-L., Schwefel, H.-P. (eds.) PPSN 2002. LNCS, vol. 2439, pp. 77–87. Springer, Heidelberg (2002)
Gaube, T., Rothlauf, F.: The Link and Node Biased Encoding Revisited: Bias and Adjustment of Parameters. In: Boers, E.J.W., Gottlieb, J., Lanzi, P.L., Smith, R.E., Cagnoni, S., Hart, E., Raidl, G.R., Tijink, H. (eds.) EvoIASP 2001, EvoWorkshops 2001, EvoFlight 2001, EvoSTIM 2001, EvoCOP 2001, and EvoLearn 2001. LNCS, vol. 2037, pp. 1–10. Springer, Heidelberg (2001)
Gen, M., Chen, R.: Genetic Algorithms and Engineering Design. Wiley, Chichester (1997); also see (for Prüfer encoding) http://www.ads.tuwien.ac.at/publications/bib/pdf/gottlieb-01.pdf
Gottlieb, J., Eckert, C.: A Comparision of Two Representations for the Fixed Charge Transportation Problem. In: Deb, K., Rudolph, G., Lutton, E., Merelo, J.J., Schoenauer, M., Schwefel, H.-P., Yao, X. (eds.) PPSN 2000. LNCS, vol. 1917, pp. 345–354. Springer, Heidelberg (2000)
Julstrom, B.A.: The Blob Code: A Better String Coding of Spanning Trees for Evolutionary Search. In: Genetic and Evolutionary Computation Conference Workshop Program, pp. 256–261. Morgan Kaufmann, San Francisco (2001)
Manderick, B., de Weger, M., Spiessens, P.: The genetic algorithm and the structure of the fitness landscape. In: Proceedings of the 4th International Conference on Genetic Algorithms, pp. 143–150 (1991)
Merz, P., Freisleben, B.: Fitness Landscapes, Memetic Algorithms, and Greedy Operators for Graph Bipartitioning. Evolutionary Computation 8(1), 61–91 (2000)
Palmer, C.C., Kershenbaum, A.: An Approach to a Problem in Network Design Using Genetic Algorithms. Networks 26, 151–163 (1995)
Raidl, G.R.: Empirical Analysis of Locality, Heritability and Heuristic Bias in Evolutionary Algorithms: A Case Study for the Multidimensional Knapsack Problem, Evolutionary Computation Journal, MIT Press 13(4), (to appear, 2005)
Raidl, G.R., Julstrom, B.A.: Edge-Sets: An Effective Evolutionary Coding of Spanning Trees. IEEE Transactions on Evolutionary Computation 7(3), 225–239 (2003)
Reeves, C.R., Yamada, T.: Genetic algorithms, path relinking, and the flowshop sequencing problem. Evolutionary Computation 6, 45–60
Rothlauf, F.: Locality, Distance Distortion, and Binary Representations of Integers, Working Papers (July 2003)
Rothlauf, F., Goldberg, D.E., Heinzl, A.: Network Random Keys - A Tree Network Representation Scheme for Genetic and Evolutionary Algorithms. Evolutionary Computation 10(1), 75–97 (2002)
Rothlauf, F., Gerstacker, J., Heinzl, A.: On the Optimal Communication Spanning Tree Problem, Working Papers in Information Systems, University of Mannheim (2003)
Rothlauf, F.: On the Locality of Representations, Working Paper in Information Systems, University of Mannheim (2003)
Schuter, P.: Artificial Life and Molecular Evolutionary Biology. In: Moran, F., et al. (eds.) Advances in Artificial Life, pp. 3–19. Springer, Heidelberg (1995)
Sendhoff, B., Kreutz, M., Seelen, W.V.: A condition for the genotype-phenotype mapping: Causalty. In: Proceedings of the Seventh International Conference on Genetic Algorithms, Morgan Kaufmann, San Francisco (1997)
Soak, S.M., Corne, D., Ahn, B.H.: The Edge-Window-Decoder Representation for Tree-Based Problems, IEEE Transaction on Evolutionary Computation (submitted,2004)
Watson, J.P., Barbulescu, L., Whitley, L.D., Howe, A.E.: Constrasting Structured and Random Permutation Flow-Shop Scheduling Problems: Search-Space Topology and Algorithm Performance, http://www.cs.colostate.edu/~genitor/Pubs.html
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Soak, SM., Corne, D., Ahn, BH. (2006). On a Property Analysis of Representations for Spanning Tree Problems. In: Talbi, EG., Liardet, P., Collet, P., Lutton, E., Schoenauer, M. (eds) Artificial Evolution. EA 2005. Lecture Notes in Computer Science, vol 3871. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11740698_10
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DOI: https://doi.org/10.1007/11740698_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-33589-4
Online ISBN: 978-3-540-33590-0
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