Download PDF by M. Iglesias, B. Naudts, A. Verschoren, C. Vidal (auth.), R.: Foundations of Generic Optimization: Volume 1: A

By M. Iglesias, B. Naudts, A. Verschoren, C. Vidal (auth.), R. Lowen, A. Verschoren (eds.)

ISBN-10: 1402036655

ISBN-13: 9781402036651

ISBN-10: 1402036663

ISBN-13: 9781402036668

From the reviews:

"This e-book bargains with combinatorial points of epistasis, in particular normalized epistasis, an idea that exists in genetics and evolutionary algorithms. It begins with the idea of evolutionary algorithms. This illustrative advent makes the e-book readable self sufficient on different textbooks. … The booklet is especially good written and provides many vital and invaluable effects. … It exhibits additionally that tricky useful difficulties can merely be successfully solved through a mix of Modelling, arithmetic and Computing." (Christian Posthoff, Zentralblatt MATH, Vol. 1108 (10), 2007)

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Extra resources for Foundations of Generic Optimization: Volume 1: A Combinatorial Approach to Epistasis

Example text

After only a few generations, however, stochastic errors break this balance, and the problem becomes similar to a onemax problem [100]. One optimum is reached quickly, the other optimum is ignored. Breaking the symmetry of the twomax problem may result in a deceptive problem. The particular form shown is called a trap function [1]. Depending on the relative heights of the optimal and sub-optimal peaks and the location of the fitness 0 strings (closer to all 1s, or closer to all 0s), one can control the fraction of times the GA is deceived and led in the direction of the sub-optimal peak.

33 Elaborating on items 3 and 6, these authors apply the Gambler’s ruin model to estimate the probability of mistakingly choosing an inferior building block over a better one for a given population size. Their result is a population sizing equation n = −2 k−1 √ σBB πm ln(α) . d The equation indicates that the population size n gets larger as the average variance σBB of the building blocks increases, and smaller as the signal difference d (the difference between the average fitnesses in the competition) increases.

Know the building block takeover and convergence times 6. decide well among competing building blocks 7. mix the building blocks properly. notation is more natural when we consider the correspondence between natural numbers and their binary expansion. 5 On the role of toy problems. . 33 Elaborating on items 3 and 6, these authors apply the Gambler’s ruin model to estimate the probability of mistakingly choosing an inferior building block over a better one for a given population size. Their result is a population sizing equation n = −2 k−1 √ σBB πm ln(α) .

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Foundations of Generic Optimization: Volume 1: A Combinatorial Approach to Epistasis by M. Iglesias, B. Naudts, A. Verschoren, C. Vidal (auth.), R. Lowen, A. Verschoren (eds.)


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