Abstract
We propose a simple method of directly measuring a mutation operator’s short-term exploration-exploitation behaviour, based on its transition matrix. Higher values for this measure indicate a more exploitative operator. Since operators also differ in their degree of long-term bias towards particular areas of the search space, we propose a simple method of directly measuring this bias, based on the Markov chain stationary state. We use these measures to compare numerically the behaviours of two well-known mutation operators, the genetic algorithm per-gene bitflip mutation and the genetic programming subtree mutation.
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References
Bertsimas, D., Tsitsiklis, J.: Simulated annealing. Statistical Science, 10–15 (1993)
Dignum, S., Poli, R.: Crossover, sampling, bloat and the harmful effects of size limits. In: O’Neill, M., Vanneschi, L., Gustafson, S., Esparcia Alcázar, A.I., De Falco, I., Della Cioppa, A., Tarantino, E. (eds.) EuroGP 2008. LNCS, vol. 4971, pp. 158–169. Springer, Heidelberg (2008)
Droste, S., Jansen, T., Wegener, I.: On the analysis of the (1+1) evolutionary algorithm. Theoretical Computer Science 276(1), 51–81 (2002)
Eiben, A.E., Aarts, E.H.L., Hee, K.M.V.: Global convergence of genetic algorithms: A Markov chain analysis. In: Schwefel, H.-P., Männer, R. (eds.) PPSN 1990. LNCS, vol. 496, pp. 3–12. Springer, Heidelberg (1991)
Garnier, J., Kallel, L., Schoenauer, M.: Rigorous hitting times for binary mutations. Evolutionary Computation 7(2), 173–203 (1999)
Hu, T., Payne, J.L., Banzhaf, W., Moore, J.H.: Evolutionary dynamics on multiple scales: a quantitative analysis of the interplay between genotype, phenotype, and fitness in linear genetic programming. Genetic Programming and Evolvable Machines 13(3), 305–337 (2012)
Kemeny, J.G., Snell, J.L.: Finite Markov chains, vol. 210. Springer, New York (1976)
Koza, J.R.: Genetic Programming: On the Programming of Computers by Means of Natural Selection. The MIT Press, Cambridge (1992)
Levin, D.A., Peres, Y., Wilmer, E.L.: Markov chains and mixing times. AMS Bookstore (2009), http://pages.uoregon.edu/dlevin/MARKOV/
Moraglio, A., Krawiec, K., Johnson, C.G.: Geometric semantic genetic programming. In: Coello, C.A.C., Cutello, V., Deb, K., Forrest, S., Nicosia, G., Pavone, M. (eds.) PPSN 2012, Part I. LNCS, vol. 7491, pp. 21–31. Springer, Heidelberg (2012)
Moritz, R., Ulrich, T., Thiele, L., Buerklen, S.: Mutation operator characterization: Exhaustiveness, locality, and bias. In: Congress on Evolutionary Computation. IEEE, New Orleans (2011)
Ni, J., Drieberg, R.H., Rockett, P.I.: The use of an analytic quotient operator in genetic programming. Transactions on Evolutionary Computation 17(1) (2013)
O’Reilly, U.M., Oppacher, F.: Program search with a hierarchical variable length representation: Genetic programming, simulated annealing and hill climbing. In: Davidor, Y., Schwefel, H.-P., Männer, R. (eds.) PPSN 1994. LNCS, vol. 866, pp. 397–406. Springer, Heidelberg (1994), http://www.springer.de/cgi-bin/search_book.pl?isbn=3-540-58484-6
Pagie, L., Hogeweg, P.: Evolutionary Consequences of Coevolving Targets. Evolutionary Computation 5, 401–418 (1997)
Poli, R., McPhee, N.F., Rowe, J.E.: Exact schema theory and Markov chain models for genetic programming and variable-length genetic algorithms with homologous crossover. Genetic Programming and Evolvable Machines 5(1), 31–70 (2004)
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McDermott, J. (2014). Measuring Mutation Operators’ Exploration-Exploitation Behaviour and Long-Term Biases. In: Nicolau, M., et al. Genetic Programming. EuroGP 2014. Lecture Notes in Computer Science, vol 8599. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44303-3_9
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DOI: https://doi.org/10.1007/978-3-662-44303-3_9
Publisher Name: Springer, Berlin, Heidelberg
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