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Deception, dominance and implicit parallelism in genetic search

Deception, dominance and implicit parallelism in genetic search This paper presents several theorems concerning the nature of deception, its relationship to hyperplane dominance, and the central role that deception plays in function optimization using genetic algorithms. The theoretical results relate to four general themes. First, the concept of a “deceptive attractor” is introduced; it is shown that a deceptive attractor must be the complement of the global solution for a problem to be fully deceptive. It is also shown that the deceptive attractor must either be a local optimum in Hamming space, or adjacent to a local optimum in Hamming space if the problem is fully deceptive. Second, it can be shown that the global solution to nondeceptive problems can be inferred (theoretically and often in practice) by determining the “winners” of the order-1 hyperplanes. The third theme relates the concept of deception and dominance. If a dominance relationship exists between two hyperplanes then deception is impossible between those two partitions of hyperspace; analogously, deception between two hyperplanes precludes a dominance relationship. The fourth theme relates to deception and implicit parallelism. It can be shown that if a genetic algorithm reliably allocates exponentially more trials to the observed best, then implicit parallelism (and the 2-arm bandit analogy) breaks down when deception is present. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annals of Mathematics and Artificial Intelligence Springer Journals

Deception, dominance and implicit parallelism in genetic search

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References (18)

Publisher
Springer Journals
Copyright
Copyright
Subject
Computer Science; Artificial Intelligence; Mathematics, general; Computer Science, general; Complex Systems
ISSN
1012-2443
eISSN
1573-7470
DOI
10.1007/BF01530780
Publisher site
See Article on Publisher Site

Abstract

This paper presents several theorems concerning the nature of deception, its relationship to hyperplane dominance, and the central role that deception plays in function optimization using genetic algorithms. The theoretical results relate to four general themes. First, the concept of a “deceptive attractor” is introduced; it is shown that a deceptive attractor must be the complement of the global solution for a problem to be fully deceptive. It is also shown that the deceptive attractor must either be a local optimum in Hamming space, or adjacent to a local optimum in Hamming space if the problem is fully deceptive. Second, it can be shown that the global solution to nondeceptive problems can be inferred (theoretically and often in practice) by determining the “winners” of the order-1 hyperplanes. The third theme relates the concept of deception and dominance. If a dominance relationship exists between two hyperplanes then deception is impossible between those two partitions of hyperspace; analogously, deception between two hyperplanes precludes a dominance relationship. The fourth theme relates to deception and implicit parallelism. It can be shown that if a genetic algorithm reliably allocates exponentially more trials to the observed best, then implicit parallelism (and the 2-arm bandit analogy) breaks down when deception is present.

Journal

Annals of Mathematics and Artificial IntelligenceSpringer Journals

Published: Apr 5, 2005

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