Genetic Algorithms as Global Random Search Methods: An Alternative Perspective

Abstract

Genetic algorithm behavior is described in terms of the construction and evolution of the sampling distributions over the space of candidate solutions. This novel perspective is motivated by analysis indicating that the schema theory is inadequate for completely and properly explaining genetic algorithm behavior. Based on the proposed theory, it is argued that the similarities of candidate solutions should be exploited directly, rather than encoding candidate solutions and then exploiting their similarities. Proportional selection is characterized as a global search operator, and recombination is characterized as the search process that exploits similarities. Sequential algorithms and many deletion methods are also analyzed. It is shown that by properly constraining the search breadth of recombination operators, convergence of genetic algorithms to a global optimum can be ensured.

Authors' Reply

“…Our work, which has been heavily influenced by the contributions of mathematicians such as Ermakov and Zhygljawsky ( [4], [6], [45], [46], [48] in the paper), has been tailored to give our readers an easierto-read account of these results in a form which, without sacrificing too much of the mathematical rigor, would view random genetic searches in a unified framework with similar ideas coming from statistical physics, population genetics, and engineering.…”

“…To the best of my knowledge, it was the first effort to model GA's as a special class of global random search methods in the literature and provided a promising alternative to the Markov chain models of GA's of Fogel [2], Rudolph [3], Eiben et al [4], and Vose [5]. See Peck and Dhawan [6] for the further development. The potential of this new viewpoint deserves further explorations, but caution must be paid.…”

PCA image coding with iterative clustering

“…GA usually has good searching capability when the fitness landscape of the problem is unclear or riddled with several local optima. GA has been successfully applied to numerous fields of science and engineering (Fogel 1999;Peck and Dhawan 1995). In the proposed algorithm, we partition the dataset into several clusters, and the number of principal components using PCA can vary for each cluster.…”

A repartition method improving visual quality for PCA image coding

“…In the selective breeding of plants or animals, for example, offspring is produced as a combination of the parent chromosomes according to certain characteristics that are determined at the genetic level. When the fitness landscape (or cost surface) of the problem is unclear or riddled with a large number of local optima, the GA usually has good searching capability because the candidate solutions will not become stuck at the local optima [23]. The GA has been successfully applied to many fields of science and engineering [12].…”