Abstract
The class of symmetric functions is based on the OneMax function by a subsequent assigning application of a real valued function. In this work we derive a sharp boundary between those problem instances that are solvable in polynomial time by the Metropolis algorithm and those that need at least exponential time. This result is both proven theoretically and illustrated by experimental data. The classification of functions into easy and hard problem instances allows a deep insight into the problem solving power of the Metropolis algorithm and can be used in the process of selecting an optimization algorithm for a concrete problem instance.
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References
Ackley, D.H.: A Connectionist Machine for Genetic Hillclimbing. Kluwer, Boston (1987)
Droste, S., Jansen, T., Wegener, I.: Dynamic parameter control in simple evolutionary algorithms. In: Martin, W.N., Spears, W.M. (eds.) Foundations of Genetic Algorithms, vol. 6, pp. 275–294. Morgan Kaufmann, San Francisco (2001)
Kaden, L.: Laufzeitkriterien für genetische Algorithmen mit und ohne dynamische Anpassung der Selektionsstrategie. Studienarbeit, University of Stuttgart, Germany (2002)
Kirkpatrick, S., Gelatt Jr., C.D., Vecchi, M.P.: Optimization by simulated annealing. Science 220(4598), 671–680 (1983)
Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H., Teller, E.: Equation of state calculations by fast computing machines. Journal of Chemical Physics 21(6), 1087–1092 (1953)
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Kaden, L., Weicker, N., Weicker, K. (2009). Metropolis and Symmetric Functions: A Swan Song. In: Cotta, C., Cowling, P. (eds) Evolutionary Computation in Combinatorial Optimization. EvoCOP 2009. Lecture Notes in Computer Science, vol 5482. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01009-5_18
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DOI: https://doi.org/10.1007/978-3-642-01009-5_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-01008-8
Online ISBN: 978-3-642-01009-5
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