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Article overview
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A Revisit of Infinite Population Models for Evolutionary Algorithms on Continuous Optimization Problems | Bo Song
; Victor O.K. Li
; | Date: |
26 Sep 2015 | Abstract: | 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 paper, 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 $k$-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. | Source: | arXiv, 1509.7946 | Services: | Forum | Review | PDF | Favorites |
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