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Part of the book series: Studies in Computational Intelligence ((SCI,volume 797))

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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.

    Google Scholar 

  • Arabas, J. (2001). Lectures on evolutionary algorithms. Warsaw (in Polish): WNT.

    Google Scholar 

  • Bäck, T. (1995). Evolutionary algorithms in theory and practice. Oxford: Oxford University Press.

    MATH  Google Scholar 

  • Bäck, T., & Schwefel, H.-P. (1993). An overview of evolutionary algorithms for parameter optimization. Evolutionary Computation, 1(1), 1–23.

    Article  Google Scholar 

  • Bäck, T., Fogel, D. B., & Michalewicz, Z. (Eds.). (1997). Handbook of evolutionary computation. New York: Institute of Physics Publishing and Oxford University Press.

    MATH  Google Scholar 

  • Beyer, H. G., & Schwefel, H. P. (2002). Evolution strategies-a comprehensive introduction. Natural Computing, 1(1), 3–52.

    Article  MathSciNet  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Birge, J., & Louveaux, F. (1997). Introduction to stochastic programming. New York: Springer.

    MATH  Google Scholar 

  • Dasgupta, D., & Michalewicz, Z. (Eds.). (1997). Evolutionary algorithms for engineering applications. Berlin: Springer.

    MATH  Google Scholar 

  • Davis, L. (Ed.). (1987). Genetic algorithms and simulated annealing. San Francisco: Morgan Kaufmann.

    MATH  Google Scholar 

  • Fang, K.-T., Kotz, S., & Ng, K. W. (1990). Symmetric multivariate and related distributions. London: Chapman and Hall.

    Book  Google Scholar 

  • Fogel, D. B. (1995). Evolutionary computation: Toward a new philosophy of machine intelligence. New York: IEEE Press.

    MATH  Google Scholar 

  • Fogel, D. B. (1998). Evolutionary computation: The fossil record. New York: IEEE Press.

    Book  Google Scholar 

  • Fogel, L. J., Owens, A. J., & Walsh, M. J. (1966). Artificial intelligence through simulated evolution. New York: Wiley.

    MATH  Google Scholar 

  • Galar, R. (1985). Handicapped individual in evolutionary processes. Biological Cybernetics, 51, 1–9.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • Goldberg, D. E. (1989). Genetic algorithms in search, optimization and machine learning. Addison-Wesley, Reading.

    Google Scholar 

  • 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.

    Google Scholar 

  • Hansen, N., & Ostermeyer, A. (2001). Completely derandomized self-adaptation in evolutionary strategies. Evolutionary Computation, 9(2), 159–195.

    Article  Google Scholar 

  • 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.

    Chapter  Google Scholar 

  • Holland, J. H. (1992). Adaptation in natural and artificial systems. Cambridge: MIT Press.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Michalewicz, Z. (1996). Genetic algorithms + data structures = evolution programs. Heidelberg: Springer.

    Book  Google Scholar 

  • Mitchel, M. (1996). An Introduction to genetic algorithms. Cambridge: MIT Press.

    Google Scholar 

  • Nolan, J. P. (2007). Stable distributions-models for heavy tailed data. Boston: Birkhäuser.

    Google Scholar 

  • 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.

    Article  MathSciNet  Google Scholar 

  • Obuchowicz, A. (2003a). Multidimensional mutations in evolutionary algorithms based on real-valued representation. International Journal of System Science, 34(7), 469–483.

    Article  MathSciNet  Google Scholar 

  • Obuchowicz, A. (2003b). Evolutionary algorithms in global optimization and dynamic system diagnosis. Zielona Góra: Lubuskie Scientific Society.

    MATH  Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • Obuchowicz, A., & Prętki, P. (2005). Isotropic symmetric \(\alpha \)-stable mutations for evolutionary algorithms. In IEEE congress on evolutionary computation (pp. 404–410). Edinburgh, UK.

    Google Scholar 

  • 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.

    Chapter  Google Scholar 

  • Obuchowicz, A. K., & Smołka, M. (2016). Application of \(\alpha \)-stable mutation in hierarchic evolutionary inverse solver. Journal on Computer Science, 17, 261–269.

    Article  MathSciNet  Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Chapter  Google Scholar 

  • Rechenberg, I. (1965). Cybernetic solution path of an experimental problem. In Royal aircraft establishment, Library Translation, 1122, Hants: Farnborough.

    Google Scholar 

  • Rudolph, G. (1997). Local convergence rates of simple evolutionary algorithms with Cauchy mutations. IEEE Transactions on Evolutionary Computation, 1(4), 249–258.

    Article  Google Scholar 

  • Samorodnitsky, G., & Taqqu, M. S. (1994). Stable non-Gaussian random processes. New York: Chapman and Hall.

    MATH  Google Scholar 

  • Schalkoff, R. J. (1990). Artificial intelligence: An engineering approach. New York: McGraw-Hill.

    Google Scholar 

  • Schwefel, H.-P. (1995). Evolution and optimum seeking. New York: Wiley.

    MATH  Google Scholar 

  • Trojanowski, K. (2008). Practical metaheuristics. Warsaw (in Polish): WIT Press.

    Google Scholar 

  • Trojanowski, K. (2009). Properties of quantum particles in multi-swarm for dynamic optimization. Fundamenta Informaticae, 95(2–3), 349–380.

    MathSciNet  MATH  Google Scholar 

  • Trojanowski, K., & Wierzchon, S. (2009). Immune-based algorithms for dynamic optimization. Information Sciences, 179, 1495–1515.

    Article  Google Scholar 

  • 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.

    Chapter  Google Scholar 

  • Yao, X., & Liu, Y. (1996). Fast evolutionary programming. 5th Annual Conference on Evolutionary Programming (pp. 419–429). Cambridge: MIT Press.

    Google Scholar 

  • Yao, X., & Liu, Y. (1997). Fast evolutionary strategies. Control. Cybernetics, 26(3), 467–496.

    MathSciNet  MATH  Google Scholar 

  • Yao, X., & Liu, Y. (1999). Evolutionary programming made faster. IEEE Transactions on Evolutionary Computation, 3(2), 82–102.

    Article  Google Scholar 

  • Zieliński, R. A., & Neumann, P. (1983). Stochastic methods of the function minimum searching. Berlin: Springer.

    Google Scholar 

Download references

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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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