By Enrique Ramirez de Arellano
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And AI 5 घ1992ङ 79í88 16. : Convergence Analysis of Canonical Genetic Algorithms. IEEE Tr. on NN. 1, Vol. 5 घ1994ङ 98í101 17. : Convergence Properties of Evolutionary Algorithms. Verlag Kovac, Hamburg घ1997ङ 18. : Theoretical Analysis of Evolutionary Algorithms, I-II. IEEE Tr. on NN. 1, Vol. 5 घ1994ङ 102í129 19. : Non-negative Matrices and Markov Chains. 2nd ed. Springer, New York घ1981ङ 20. : Raising Theoretical Questions about the Utility of Genetic Algorithms. Proc. EP '97, LNCS Series, Springer घ1997ङ 275í284 21.
The results can be found in Fig. 1. 20 le+08 "path" . ~ ...... 3~3/~,~-- _...... le+07 le+06 100000 / // 10000 ,/ /4 / 1000 / / / 100 / 10 0 20 I t I n I ~ I 40 60 80 100 120 140 160 Fig. 1. (1 + 1) EA 4 A Variant of the on PATHs/n_ 1 and bound 3n3/~2 "/-ff (1 + 1) E A We already mentioned in Sect. 1, that different definitions of local maxima can be found in the literature, resulting in different definitions of unimodality. For instance, Horn, Goldberg, and Deb 6 define a local optimum as a point or region of the search space with strictly higher fitness than all neighbors.
4 Exponential Niche Maintenance Times Fitness sharing tends to maintain multiple high-quality niches for long periods of time. Expected times to loss of one or more niches have been shown to grow exponentially with increasing population size N 8, 12. Mahfoud 12, and Horn, Goldberg, and Deb 10 developed a closed-form expression for the case of nonoverlapping niches (perfect sharing): Etobs - (r: + 1) r}V+l (6) The expected absorption time above grows exponentially in N for any r/ > 0. 26 2 Fast Convergence to Niching Equilibrium Now that we have an upper bound on the (very long) expected lifetimes of niches, we turn to the question of how such steady-states are reached, and in particular, how quickly they are reached.
Algebraic Geometry and Complex Analysis. Proc. workshop Patzcuaro, Michoacan, Mexico, 1987 by Enrique Ramirez de Arellano