Abstract
The paper analyzes the performance improvement imposed by the application of \(\alpha \)-stable probability distributions to the mutation operator of the Hierarchic Genetic Strategy (HGS), in solving ill-conditioned, multimodal global optimization problems in continuous domains. The performed experiments range from standard benchmarks (Rastrigin and multi-peak Gaussian) to an advanced inverse parametric problem of the logging measurement inversion, associated with the oil and gas resource investigation. The obtained results show that the application of \(\alpha \)-stable mutation can first of all decrease the total computational cost. The second advantage over the HGS with the standard, normal mutation consists in finding much more well-fitted individuals at the highest-accuracy HGS level located in attraction basins of local and global fitness minimizers. It might allow us to find more minimizers by performing local convex searches started from that points. It also delivers more information about the attraction basins of the minimizers, which can be helpful in their stability analysis.
The work presented in this paper has been partially supported by Polish National Science Center grants no. DEC-2011/03/B/ST6/01393.
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References
Tarantola, A.: Inverse Problem Theory. Society for Industrial and Applied Mathematics, Mathematics and its Applications. SIAM, Philadelphia (2005)
Garibaldi, L., Surace, C., Holford, K., Ostachowicz, W.M.: Damage Assessment of Structures. Trans Tech Publications, Zürich (1999)
Burczyński, T., Kuś, W., Długosz, A., Orantek, P.: Optimization and defect identification using distributed evolutionary algorithms. Eng. Appl. Artif. Intell. 17(4), 337–344 (2004)
Barabasz, B., Gajda, E., Pardo, D., Paszyński, M., Schaefer, R., Szeliga, D.: \(hp\)-HGS twin adaptive strategy for inverse resistivity logging measurements. In: Borkowski, A., Lewiński, T., Dzierżanowski, G. (eds.) Proceedings of the 19th International Conference on Computational Methods in Mechanics CMM 2011, pp. 121–122. Warsaw University of Technology, Warsaw (2011)
Paruch, M., Majchrzak, E.: Identification of tumor region parameters using evolutionary algorithms and multiple reciprocity boundary element method. Eng. Appl. Artif. Intell. 20(5), 647–655 (2007)
Engl, H., Hanke, M., Neubauer, A.: Regularization of Inverse Problems, Mathematics and its Applications. Springer, Heidelberg (1996)
Barabasz, B., Migórski, S., Schaefer, R., Paszyński, M.: Multi-deme, twin adaptive strategy hp-HGS. Inverse Prob. Sci. Eng. 19(1), 3–16 (2011)
Pardalos, P., Romeijn, H.: Handbook of Global Optimization (Nonconvex Optimization and its Applications). Kluwer, Dordrecht (1995)
Marti, R.: Multi-start methods. In: Glover, F., Kochenberger, G. (eds.) Handbook of MetaHeuristics, pp. 355–368. Kluwer, Dordrecht (2003)
Schaefer, R.: Genetic search reinforced by the population hierarchy in Foundations of Genetic Algorithms 7, pp. 383–399. Morgan Kaufman, San Francisco (2003)
Wierzba, B., Semczuk, A., Kołodziej, J., Schaefer, R.: Hierarchical Genetic Strategy with real number encoding. In: Proceedings of the 6th Conference on Evolutionary Algorithms and Global Optimization, pp. 231–237 (2003)
Paszyński, M., Barabasz, B., Schaefer, R.: Efficient adaptive strategy for solving inverse problems. In: Shi, Y., van Albada, G.D., Dongarra, J., Sloot, P.M.A. (eds.) ICCS 2007, Part I. LNCS, vol. 4487, pp. 342–349. Springer, Heidelberg (2007)
Paszyński, M., Gajda-Zagórska, E., Schaefer, R., Pardo, D.: \(hp\)-hgs strategy for inverse ac/dc resistivity logging measurement simulations. Comput. Sci. 14(4), 629–644 (2013)
Gajda-Zagórska, E., Schaefer, R., Smołka, M., Paszyński, M., Pardo, D.: A hybrid method for inversion of 3D DC logging measurements. Natural Computing. (2014). doi:10.1007/s11047-014-9440-y
Barabasz, B., Gajda-Zagórska, E., Migórski, S., Paszyński, M., Schaefer, R., Smołka, M.: A hybrid algorithm for solving inverse problems in elasticity. Int. J. Appl. Math. Comput. Sci. 24(4), 865–886 (2014)
Demkowicz, L., Kurtz, J., Pardo, D., Paszyński, M., Rachowicz, W., Zdunek, A.: Computing with hp Finite Elements II. Frontiers: Three-Dimensional Elliptic and Maxwell Problems with Applications. Chapman & Hall/CRC, Boca Raton (2007)
Obuchowicz, A.: Multidimensional mutations in evolutionary algorithms based on real-valued representation. Int. J. Syst. Sci. 34(7), 469–483 (2003)
Fang, K., Kotz, S., Ng, K.: Symmetric Multivariate and Related Distributions. Chapman and Hall, London (1990)
Rudolph, G.: Local convergence rates of simple evolutionary algorithms with cauchy mutations. IEEE Trans. Evol. Comput. 1(4), 249–258 (1997)
Obuchowicz, A., Prȩtki, P.: Phenotypic evolution with mutation based on symmetric \(\alpha \)-stable distributions. Int. J. Appl. Math. Comput. Sci. 14(3), 289–316 (2004)
Schaefer, R., Barabasz, B.: Asymptotic behavior of hp–adaptive finite element method coupled with the hierarchic genetic strategy) by solving inverse problems. In: Bubak, M., van Albada, G.D., Dongarra, J., Sloot, P.M.A. (eds.) ICCS 2008. LNCS, vol. 5103, pp. 682–691. Springer, Heidelberg (2008)
Samorodnitsky, G., Taqqu, M.: Stable Non-Gaussian Random Processes. Chapman and Hall, New York (1994)
Obuchowicz, A., Prȩtki, P.: Isotropic symmetric \(\alpha \)-stable mutations. In: IEEE Congress of Evolutionary Computation, pp. 404–410. IEEE Press (2005)
Obuchowicz, A.: Multidimensional mutations in evolutionary algorithms based on real-valued representation. Int. J. Syst. Serv. 34, 469–483 (2003)
Smołka, M., Schaefer, R.: A memetic framework for solving difficult inverse problems. In: Esparcia-Alcázar, A.I., Mora, A.M. (eds.) Applications of Evolutionary Computation. LNCS, vol. 8602, pp. 137–148. Springer, Heidelberg (2014)
Smołka, M., Schaefer, R., Paszyński, M., Pardo, D., Álvarez-Aramberri, J.: Agent-oriented hierarchic strategy for solving inverse problems. Int. J. Appl. Math. Comput. Sci. (2015, accepted)
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Obuchowicz, A.K., Smołka, M., Schaefer, R. (2015). Hierarchic Genetic Search with \(\alpha \)-Stable Mutation. In: Mora, A., Squillero, G. (eds) Applications of Evolutionary Computation. EvoApplications 2015. Lecture Notes in Computer Science(), vol 9028. Springer, Cham. https://doi.org/10.1007/978-3-319-16549-3_12
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