Schwefel, H.-P., 1997. Evolutionary Computation --- A Study on Collective Learning. In: Callaos, N., Khoong, C.M., Cohen, E. (eds.): Proceedings of the World Multiconference on Systemics, Cybernetics and Informatics, vol. 2., Int'l Inst. of Informatics and Systemics, Orlando FL, pp. 198-205.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....various recombination operators (see [1] for further details) such as discrete and intermediate recombination. More elaborate evolution strategies feature individual step sizes i one for each parameter x i . Since the forms require relatively large population sizes of 200 to properly work [22] and since experimentation time is a severe constraint, these forms are not considered here. The breeder genetic algorithm [14] is the second algorithm considered in this paper, since this genetic algorithm variant 1 Constant factors, such as 1.5, 1.0, and 1 1.5, might work as well; see also ....

Schwefel, H.-P., 1997. Evolutionary Computation --- A Study on Collective Learning. In: Callaos, N., Khoong, C.M., Cohen, E. (eds.): Proceedings of the World Multiconference on Systemics, Cybernetics and Informatics, vol. 2., Int'l Inst. of Informatics and Systemics, Orlando FL, pp. 198-205.

....and recombination. It then assigns a fitness value (defined by a fitness or objective function) to each offspring. Depending on their fitness, each offspring is given a specific survival probability. For a good overview of these algorithms, the interested reader is referred to (Back, Hammel, and Schwefel, 1997). Since in the compound eye all angles i are real valued parameters, this paper employs evolution strategies (Rechenberg, 1973, 1994; Schwefel, 1995) and the breeder genetic algorithm (Muhlenbein and Schlierkamp Voosen, 1993) In their simplest form, evolution strategies maintain one global ....

....chooses the parents for the next generation only from the offspring, whereas the latter selection scheme selects from the union of the offspring and previous parents, i.e. fold elitism. In addition, some evolution strategies also feature various recombination operators (see (Back, Hammel, and Schwefel, 1997) for further details) such as discrete and intermediate recombination. More elaborate evolution strategies feature individual step sizes i , one for each parameter x i . Since these forms require relatively large population sizes of 200 to work properly (Schwefel, 1997) and since 1 ....

[Article contains additional citation context not shown here]

Schwefel, H.-P., 1997. Evolutionary Computation --- A Study on Collective Learning. In: Callaos, N., Khoong, C.M., Cohen, E. (eds.): Proceedings of the World Multiconference on Systemics, Cybernetics and Informatics, vol. 2., Int'l Inst. of Informatics and Systemics, Orlando FL, pp. 198-205.

....real life features. Biologists even hesitate to use the term progress in connection with evolutionary processes, though they admit that they themselves represent higher forms of life than archaebacteria, for example. This has led them to define fitness in a dangerous, i.e. tautological way [Sch97], misleading modellers to model selection as mating selection mainly. The fitter descendants produce more offspring than the less fit ones. Environmental selection is a pure random process within the famous Fisher Eigen model and completely missing within GA. EP, like GA working without birth ....

....algorithms can do so, as well, but biologists seldom listen long enough to EA experts in order to appreciate that. Another controversy is the observation of so called punctuated equilibria in nature, i.e. alternating modes of rapid changes and stagnation. But, this can happen within EA as well [Sch97]. Neither at the level of fitness values, nor and even less at the level of phenotypes, evolutionary processes are monotonic contrary to definitions of evolution in encyclopaedia, even rather modern ones. With respect to the question which evolutionary algorithm is the more appropriate one, ....

Schwefel H.-P. (1997) Evolutionary computation --- a study on collective learning. In Proc. World Multiconference on Systemics, Cybernetics, and Informatics (SCI '97), Caracas, July 7--11. In Print.

....used. The first form are ( evolution strategies with one global step size for each individual. The notation indicates that the procedure generates offspring from parents and that it selects the parents for the next generation only from the best offspring, i.e. selection without elitism [14]. Mutation is implemented by adding N(0; random numbers, with N(0; denoting normally distributed random numbers with expectation value zero and standard distribution . Each offspring inherits the step size from its parent, and prior to mutation, the inherited step size is modified by ....

Schwefel, H.-P., 1997. Evolutionary Computation --- A Study on Collective Learning. In: Callaos, N., Khoong, C.M., Cohen, E. (eds.): Proceedings of the World Multiconference on Systemics, Cybernetics and Informatics, vol. 2., Int'l Inst. of Informatics and Systemics, Orlando FL, pp. 198-205.

....multiplication operator a = b c that is defined as a i = b i c i , or correlated mutations x t x t C z. For further implementation details of the self adaptation of t and C, see Back and Schwefel (1993) Back and Kursawe (1995) Hansen and Ostermeier (1997) Schwefel (1995) and Schwefel (1997). It should be noted that correlated mutations C require O(n 2 ) additional operations. 5 Results Some main results are summarized in Figures 4 8. Figure 4 illustrates the scaling behavior of the EGS procedure when applied to the sphere model f sphere with different dimensions n. The figure ....

....EGS procedure with momentum as a function of the number (denoted as l) of test candidates when minimizing the ellipsoid f elli . The label ES refers to a (15,100) evolution strategy with individual step sizes t . ual step sizes yields only 80 orders of magnitude as has been presented in Schwefel (1997), In addition, it has been discussed in Schwefel (1997) that other evolution strategy variants with less offspring or less parents yield much worse performance. Figure 6 shows the normalized, logarithmic performance 0 10 20 30 40 50 60 70 0 500 1000 1500 2000 Log f Generations Schwefel s Ridge ....

[Article contains additional citation context not shown here]

Schwefel, H.-P. 1997. Evolutionary Computation --- A Study on Collective Learning. In Callaos, N., Khoong, C.M., and Cohen, E. (editors). Proceedings of the World Multiconference on Systemics, Cybernetics and Informatics (SCI '97) volume 2 Orlando, FL: International Institute of Informatics and Systemics. Pages 198-205.

....reproduction, and death, are capable of adapting faster. Of course, there are other natural tricks to deal with such situations additionally, e.g. polyploidy and epigenesis. Individual mortality seems to be a necessary ingredient of effective self adaptation of internal strategy parameters [15]. The principle of forgetting good intermediate solutions with positive probability is essential for simulated annealing, as well. Moreover, it helps in hunting dynamic minimizers in control problems, a situation in which an elitist EA, eagerly conserving already achieved improvements (e.g. ....

H.--P. Schwefel, Evolutionary computation --- A study on collective learning, In Proc. World Multiconference on Systemics, Cybernetics, and Informatics, N. Callaos, C. M. Khoong, E. Cohen, Eds., Int'l Inst. of Informatics and Systemics, Orlando, FL, vol. 2, pp. 198--205.

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