Abstract
The representations currently used by local search and some evolutionary algorithms have the disadvantage that these algorithms are partially blind to “ridges” in the search space. Both heuristics search and gradient search algorithms can exhibit extremely slow convergence on functions that display ridge structures. A class of rotated representations are proposed and explored; these rotated representations can be based on Principal Components Analysis, or use the Gram-Schmidt orthogonalization method. Some algorithms, such as CMA-ES, already make use of similar rotated representations.
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References
Rosenbrock, H.: An automatic method for finding the greatest or least value of a function. Computer Journal 3, 175–184 (1960)
Brent, R.: Algorithms for Minization with Derivatives. Dover (1973)
Whitley, D., Barbulescu, L., Watson, J.: Local Search and High Precision Gray Codes. In: Foundations of Genetic Algorithms FOGA-6, Morgan Kaufmann, San Francisco (2001)
Rana, S., Whitley, D.: Representations, Search and Local Optima. In: 14th National Conf on Artificial Intelligence AAAI 1997, pp. 497–502(1997)
Syswerda, G.: Simulated Crossover in Genetic Algorithms. In: Whitley, D. (ed.) FOGA - 2, pp. 239–255. Morgan Kaufmann, San Francisco (1993)
Kazadi, S.T.: Conjugate schema and basis representation of crossover and mutation operators. Evolutionary Computation 6, 129–160 (1998)
Wyatt, D., Lipson, H.: Finding building blocks through eigenstructure adaptation. In: GECCO, pp. 1518–1529. Morgan Kaufmann, San Francisco (2003)
Salomon, R.: Reevaluating Genetic Algorithm Performance under Coordinate Rotation of Benchmark Functions. Biosystems 39(3), 263–278 (1960)
Mühlenbein, H., Schlierkamp-Voosen, D.: Predictive Models for the Breeder Genetic Algorithm. Journal of Evolutionary Computation 1, 25–49 (1993)
Oyman, A., Schwefel, H.B.H.: Where elitists start limping: Evolution strategies at ridge functions. In: Eiben, A.E., Bäck, T., Schoenauer, M., Schwefel, H.-P. (eds.) PPSN 1998. LNCS, vol. 1498, pp. 34–43. Springer, Heidelberg (1998)
DeJong, K.: An Analysis of the Behavior of a Class of Genetic Adaptive Systems. PhD thesis, University of Michigan, Dept. of Computer and Communication Sciences (1975)
Nelder, J., Mead, R.: A simplex method for function minimization. Computer Journal 7, 308–313 (1965)
Davis, L.: Bit-Climbing, Representational Bias, and Test Suite Design. In: Booker, L., Belew, R. (eds.) Proc. of the 4th Int’l. Conf. on GAs, pp. 18–23. Morgan Kaufmann, San Francisco (1991)
Bäck, T.: Evolutionary Algorithms in Theory and Practice. Oxford University Press, Oxford (1996)
Hansen, N., Ostermeier, A.: Completely derandomized self-adaptation in evolution strategies. Evolutionary Computation 9, 159–195 (2001)
Ostermeier, A., Gawelczyk, A., Hansen, N.: A derandomized approach to selfadaptation of evolution strategies. Evolutionary Computation 2, 369–380 (1994)
Hansen, N., Mãller, S., Koumoutsakos, P.: Reducing the time complexity of the derandomized evolution strategy with covariance matrix adaptation. Evolutionary Computation 11, 1–18 (2003)
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Whitley, D., Lunacek, M., Knight, J. (2004). Ruffled by Ridges: How Evolutionary Algorithms Can Fail. In: Deb, K. (eds) Genetic and Evolutionary Computation – GECCO 2004. GECCO 2004. Lecture Notes in Computer Science, vol 3103. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24855-2_26
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DOI: https://doi.org/10.1007/978-3-540-24855-2_26
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