Theoretical Analysis of Phenotypic Diversity in Real-Valued Evolutionary Algorithms With More-Than-One-Element Replacement

This paper investigates the evolutionary dynamics of steady-state real-valued evolutionary algorithms (RVEAs) with more-than-one-element replacement theoretically, whereas most theoretical studies of RVEAs have considered single-or all-element replacement. The subject RVEAs are of interest because t...

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Bibliographic Details
Published in:IEEE transactions on evolutionary computation Vol. 15; no. 2; pp. 248 - 266
Main Author: Someya, Hiroshi
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.04.2011
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Adaptation model
Algorithmics. Computability. Computer arithmetics
Applied sciences
Computational efficiency
Computer science; control theory; systems
Controllability
Convergence
Diversity control
Dynamic tests
Equations
Evolution
Evolutionary
Evolutionary algorithms
Evolutionary computation
Exact sciences and technology
Heuristic algorithms
Islands
Mathematical model
Mathematical models
parameter setting
real-coded genetic algorithms
selection pressure
self-adaptive features
Steady-state
Studies
Theoretical computing
Real number
Stability
real-coded genetic algorithms
selection pressure
Evolutionary algorithm
Adaptability
Quantization
Evolution equation
Replacement
Modeling
Steady state
Diversity control
Control constraint
self-adaptive features
parameter setting
Genetic algorithm
Size effect
Controllability
Population size
Population dynamics
ISSN:1089-778X, 1941-0026
Online Access:Get full text
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Summary:This paper investigates the evolutionary dynamics of steady-state real-valued evolutionary algorithms (RVEAs) with more-than-one-element replacement theoretically, whereas most theoretical studies of RVEAs have considered single-or all-element replacement. The subject RVEAs are of interest because they appear in various fashions, such as real-coded genetic algorithms (RCGAs) and island RVEAs. The analysis is conducted to deepen the understanding of how RVEA components and their parameters influence the phenotypic diversity in the parental pool. First, the diversity evolution is modeled mathematically and then a constraint of diversity control is derived from this model. The control method is demonstrated and the accuracy of the theoretical predictions is evaluated through experiments. The shortest convergence time is estimated. The analysis requires few assumptions about either the variation operators or selection schemes, and therefore is applicable to various RVEAs. As such an application in RCGAs, the influence on the diversity evolution of offspring-population size, parental-pool size, crossover-operator parameter, and selection-pressure parameters of two selection mechanisms is quantified. The computational efficiency, search stability, and selection-pressure controllability are then evaluated. The analysis results are discussed from a practical point of view in parameter settings for preventing premature convergence.
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ISSN:1089-778X
1941-0026
DOI:10.1109/TEVC.2010.2083668