Abstract
Practically any engineering activity, be it design, construction, modeling, control, etc., sooner or later leads to the necessity of solving a set of optimization problems. In practice, these problems usually appear to be multi-modal, sometimes multi-criteria or non-stationary (changing during the searching process). Therefore, standard optimization methods applied to solve them is inefficient. These techniques are usually based on the so-called hard selection—new base points for further searching space exploration are selected from the best points previously obtained. Using such procedures, the solution sequence is usually trapped near to the first found local extremum, without any possibility to localize others. So, the possibility of finding a global optimum is strongly limited in this case. Methods, known from the literature, which try to overcome this limitation can be divided into two classes: enumerative and stochastic ones.
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References
Angeline, P., & Kinnear, K. E. (1996). Advances in genetic programming. Cambridge: MIT Press.
Arabas, J. (2001). Lectures on evolutionary algorithms. Warsaw (in Polish): WNT.
Bäck, T. (1995). Evolutionary algorithms in theory and practice. Oxford: Oxford University Press.
Bäck, T., & Schwefel, H.-P. (1993). An overview of evolutionary algorithms for parameter optimization. Evolutionary Computation, 1(1), 1–23.
Bäck, T., Fogel, D. B., & Michalewicz, Z. (Eds.). (1997). Handbook of evolutionary computation. New York: Institute of Physics Publishing and Oxford University Press.
Beyer, H. G., & Schwefel, H. P. (2002). Evolution strategies-a comprehensive introduction. Natural Computing, 1(1), 3–52.
Beyer, H. G., & Arnold, D. V. (2003). Qualms regarding the optimality of cumulative path length control in CSA/CMA-evolution strategies. Evolutionary Computation, 11(1), 19–28.
Birge, J., & Louveaux, F. (1997). Introduction to stochastic programming. New York: Springer.
Dasgupta, D., & Michalewicz, Z. (Eds.). (1997). Evolutionary algorithms for engineering applications. Berlin: Springer.
Davis, L. (Ed.). (1987). Genetic algorithms and simulated annealing. San Francisco: Morgan Kaufmann.
Fang, K.-T., Kotz, S., & Ng, K. W. (1990). Symmetric multivariate and related distributions. London: Chapman and Hall.
Fogel, D. B. (1995). Evolutionary computation: Toward a new philosophy of machine intelligence. New York: IEEE Press.
Fogel, D. B. (1998). Evolutionary computation: The fossil record. New York: IEEE Press.
Fogel, L. J., Owens, A. J., & Walsh, M. J. (1966). Artificial intelligence through simulated evolution. New York: Wiley.
Galar, R. (1985). Handicapped individual in evolutionary processes. Biological Cybernetics, 51, 1–9.
Galar, R. (1990). Soft selection in random global adaptation in \({R^n}\). A biocybernetic model of development. Wrocław (in Polish): Technical University of Wrocław Press.
Goldberg, D. E. (1989). Genetic algorithms in search, optimization and machine learning. Addison-Wesley, Reading.
Gutowski, M. (2001). Lévy flights as an underlying mechanism for global optimization algorithms. 5th Conference on Evolutionary Algorithms and Global Optimization (pp. 79–86). Warsaw: Warsaw University of Technology Press.
Hansen, N., & Ostermeyer, A. (2001). Completely derandomized self-adaptation in evolutionary strategies. Evolutionary Computation, 9(2), 159–195.
Hansen, N., Gemperle, F., Auger, A., & Koumoutsakos, P. (2006). When do heavy-tail distributions help? In T. Ph. Runarsson, H.-G Beyer, E. Burke, J. J. Merelo-Guervós, L.D. Whitley & X. Yao (Eds.), Problem solving from nature (PPSN) IX (Vol. 4193, pp. 62–71). Lecture Notes in Computer Science. Berlin: Springer.
Holland, J. H. (1992). Adaptation in natural and artificial systems. Cambridge: MIT Press.
Kappler, C. (1996). Are evolutionary algorithms improved by large mutation. In: H.-M. Voigt, W. Ebeling, I. Rechenberg & H.-P. Schwefel (Eds.), Problem solving from nature (PPSN) IV (Vol. 1141, pp. 388–397). Lecture Notes in Computer Science. Berlin: Springer.
Lee, C. Y., & Yao, X. (2004). Evolutionary programming using mutation based on the Lévy probability distribution. IEEE Transactions on Evolutionary Computation, 8(1), 1–13.
Michalewicz, Z. (1996). Genetic algorithms + data structures = evolution programs. Heidelberg: Springer.
Mitchel, M. (1996). An Introduction to genetic algorithms. Cambridge: MIT Press.
Nolan, J. P. (2007). Stable distributions-models for heavy tailed data. Boston: Birkhäuser.
Nolan, J. P., Panorska, A. K., & McCulloch, J. H. (2001). Estimation of stable spectral measures-stable non-Gaussian models in finance and econometrics. Mathematical and Computer Modelling, 34(9), 1113–1122.
Obuchowicz, A. (2003a). Multidimensional mutations in evolutionary algorithms based on real-valued representation. International Journal of System Science, 34(7), 469–483.
Obuchowicz, A. (2003b). Evolutionary algorithms in global optimization and dynamic system diagnosis. Zielona Góra: Lubuskie Scientific Society.
Obuchowicz, A., & Prętki, P. (2004a). Evolutionary algorithms with \(\alpha \)-stable mutations. In IEEE 4th International Conference on Intelligent Systems Design and Application, Budapest, Hungary, CD-ROM.
Obuchowicz, A., & Prętki, P. (2004b). Phenotypic evolution with mutation based on symmetric \(\alpha \)-stable distributions. International Journal on Applied Mathematics and Computer Science, 14(3), 289–316.
Obuchowicz, A., & Prętki, P. (2005). Isotropic symmetric \(\alpha \)-stable mutations for evolutionary algorithms. In IEEE congress on evolutionary computation (pp. 404–410). Edinburgh, UK.
Obuchowicz, A., & Prętki, P. (2010). Evolutionary algorithms with stable mutational based on a discrete spectral measure. In L. Rutkowski, R. Scherer, R. Tadeusiewicz, L. A. Zadeh, & J. M. Zurada (Eds.), Artificial intelligence and soft computing: Part II (Vol. 6114, pp. 181–188). Lecture Notes on Artificial Intelligence. Berlin: Springer.
Obuchowicz, A. K., & Smołka, M. (2016). Application of \(\alpha \)-stable mutation in hierarchic evolutionary inverse solver. Journal on Computer Science, 17, 261–269.
Obuchowicz, A. K., Smołka, M., & Schaefer, R. (2015). Hierarchic genetic search with \(\alpha \)-stable mutation. In A. I. Esparcia-Alcázar, & A. M. Mora, (Eds), Applications of evolutionary computation (Vol. 9028, pp. 143–154). Lecture Notes in Computer Science. Berlin: Springer.
Prętki P., & Obuchowicz A. (2006). Directional distributions and their application to evolutionary algorithms. In L. Rutkowski, R. Scherer, R. Tadeusiewicz, L. A. Zadeh, & J. M. Zurada (Eds.), Artificial intelligence and soft computing (Vol. 4029, pp. 440–449). Lecture Notes on Artificial Intelligence. Berlin: Springer.
Rechenberg, I. (1965). Cybernetic solution path of an experimental problem. In Royal aircraft establishment, Library Translation, 1122, Hants: Farnborough.
Rudolph, G. (1997). Local convergence rates of simple evolutionary algorithms with Cauchy mutations. IEEE Transactions on Evolutionary Computation, 1(4), 249–258.
Samorodnitsky, G., & Taqqu, M. S. (1994). Stable non-Gaussian random processes. New York: Chapman and Hall.
Schalkoff, R. J. (1990). Artificial intelligence: An engineering approach. New York: McGraw-Hill.
Schwefel, H.-P. (1995). Evolution and optimum seeking. New York: Wiley.
Trojanowski, K. (2008). Practical metaheuristics. Warsaw (in Polish): WIT Press.
Trojanowski, K. (2009). Properties of quantum particles in multi-swarm for dynamic optimization. Fundamenta Informaticae, 95(2–3), 349–380.
Trojanowski, K., & Wierzchon, S. (2009). Immune-based algorithms for dynamic optimization. Information Sciences, 179, 1495–1515.
Trojanowski K., Raciborski, M., & Kaczynski, P. (2013). Adaptive differential evolution with hybrid rules of perturbation for dynamic optimization. In K. Madani, A. Dourado, A. Rosa, & J. Filipe (Eds.), Computational intelligence (Vol. 465, pp. 69–83). Studies in Computational Intelligence. Berlin: Springer.
Yao, X., & Liu, Y. (1996). Fast evolutionary programming. 5th Annual Conference on Evolutionary Programming (pp. 419–429). Cambridge: MIT Press.
Yao, X., & Liu, Y. (1997). Fast evolutionary strategies. Control. Cybernetics, 26(3), 467–496.
Yao, X., & Liu, Y. (1999). Evolutionary programming made faster. IEEE Transactions on Evolutionary Computation, 3(2), 82–102.
Zieliński, R. A., & Neumann, P. (1983). Stochastic methods of the function minimum searching. Berlin: Springer.
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Obuchowicz, A. (2019). Introduction. In: Stable Mutations for Evolutionary Algorithms. Studies in Computational Intelligence, vol 797. Springer, Cham. https://doi.org/10.1007/978-3-030-01548-0_1
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