Convergence Analysis of Canonical Genetic Algorithms (1994)
| Venue: | IEEE Transactions on Neural Networks |
| Citations: | 150 - 0 self |
BibTeX
@ARTICLE{Rudolph94convergenceanalysis,
author = {Günter Rudolph},
title = {Convergence Analysis of Canonical Genetic Algorithms},
journal = {IEEE Transactions on Neural Networks},
year = {1994},
volume = {5},
pages = {96--101}
}
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Abstract
This paper analyzes the convergence properties of the canonical genetic algorithm (CGA) with mutation, crossover and proportional reproduction applied to static optimization problems. It is proved by means of homogeneous finite Markov chain analysis that a CGA will never converge to the global optimum regardless of the initialization, crossover operator and objective function. But variants of CGAs that always maintain the best solution in the population, either before or after selection, are shown to converge to the global optimum due to the irreducibility property of the underlying original nonconvergent CGA. These results are discussed with respect to the schema theorem. Keywords: canonical genetic algorithm, global convergence, Markov chains, schema theorem 1 Introduction Canonical genetic algorithms (CGA) as introduced in [1] are often used to tackle static optimization problems of the type maxff(b) j b 2 IB l g (1) assuming that 0 ! f(b) ! 1 for all b 2 IB l = f0; 1g l and ...
