Comments on "Theoretical analysis of evolutionary algorithms with an infinite population size in continuous space. I. Basic properties of selection and mutation" [with reply]

1998 ◽  
Vol 9 (2) ◽  
pp. 341-343 ◽  
Author(s):  
Yong Gao ◽  
Xiaofeng Qi ◽  
F. Palmieri
Keyword(s):  
Theoretical Analysis ◽  
Evolutionary Algorithms ◽  
Population Size ◽  
Continuous Space ◽  
Basic Properties ◽  
Infinite Population

scholarly journals A Revisit of Infinite Population Models for Evolutionary Algorithms on Continuous Optimization Problems

2020 ◽  
Vol 28 (1) ◽  
pp. 55-85
Author(s):  
Bo Song ◽  
Victor O.K. Li
Keyword(s):  
Population Dynamics ◽  
Evolutionary Algorithms ◽  
Population Size ◽  
Optimization Problems ◽  
Continuous Optimization ◽  
Analytical Framework ◽  
Population Models ◽  
Initial Population ◽  
Infinite Population ◽  
Continuous Optimization Problems

Infinite population models are important tools for studying population dynamics of evolutionary algorithms. They describe how the distributions of populations change between consecutive generations. In general, infinite population models are derived from Markov chains by exploiting symmetries between individuals in the population and analyzing the limit as the population size goes to infinity. In this article, we study the theoretical foundations of infinite population models of evolutionary algorithms on continuous optimization problems. First, we show that the convergence proofs in a widely cited study were in fact problematic and incomplete. We further show that the modeling assumption of exchangeability of individuals cannot yield the transition equation. Then, in order to analyze infinite population models, we build an analytical framework based on convergence in distribution of random elements which take values in the metric space of infinite sequences. The framework is concise and mathematically rigorous. It also provides an infrastructure for studying the convergence of the stacking of operators and of iterating the algorithm which previous studies failed to address. Finally, we use the framework to prove the convergence of infinite population models for the mutation operator and the [Formula: see text]-ary recombination operator. We show that these operators can provide accurate predictions for real population dynamics as the population size goes to infinity, provided that the initial population is identically and independently distributed.

scholarly journals Mediative Fuzzy Logic for Controlling Population Size in Evolutionary Algorithms

2009 ◽  
Vol 01 (02) ◽  
pp. 108-119
Author(s):  
Oscar MONTIEL ◽  
Oscar CASTILLO ◽  
Patricia MELIN ◽  
Roberto SEPULVEDA
Keyword(s):  
Fuzzy Logic ◽  
Evolutionary Algorithms ◽  
Population Size

scholarly journals SINGULAR ORBITS AND DYNAMICS AT INFINITY OF A CONJUGATE LORENZ-LIKE SYSTEM

2015 ◽  
Vol 20 (2) ◽  
pp. 148-167 ◽  
Author(s):  
Fengjie Geng ◽  
Xianyi Li
Keyword(s):  
Theoretical Analysis ◽  
Lyapunov Exponents ◽  
Heteroclinic Orbits ◽  
Chaotic Attractors ◽  
Heteroclinic Cycles ◽  
Basic Properties ◽  
Homoclinic And Heteroclinic Orbits ◽  
Quadratic Nonlinearities ◽  
Singular Orbits

A conjugate Lorenz-like system which includes only two quadratic nonlinearities is proposed in this paper. Some basic properties of this system, such as the distribution of its equilibria and their stabilities, the Lyapunov exponents, the bifurcations are investigated by some numerical and theoretical analysis. The forming mechanisms of compound structures of its new chaotic attractors obtained by merging together two simple attractors after performing one mirror operation are also presented. Furthermore, some of its other complex dynamical behaviours, which include the existence of singularly degenerate heteroclinic cycles, the existence of homoclinic and heteroclinic orbits and the dynamics at infinity, etc, are formulated in detail. In the meantime, some problems deserving further investigations are presented.

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