1998/10/13 by Erik van Nimwegen, James P. Crutchfield, van Nimwegen, Erik +1
Biochemistry, Genetics and Molecular Biology · Computer Science · Physics and Astronomy · Social Sciences · #Adaptation and Self-Organizing Systems (nlin.AO) #Evolution and Genetic Dynamics #Evolutionary Game Theory and Cooperation #FOS: Biological sciences #FOS: Physical sciences #Metaheuristic Optimization Algorithms Research #Populations and Evolution (q-bio.PE) #adap-org #nlin.AO #q-bio.PE
paper · pdf · doi:10.48550/arxiv.adap-org/9810004
18 pages, 5 figures, 1 table; see archive at http://www.santafe.edu/~evca
arxiv created 1998/10/13 · openalex publication_date 1998/10/13 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Epochal dynamics, in which long periods of stasis in an evolving population are punctuated by a sudden burst of change, is a common behavior in both natural and artificial evolutionary processes. We analyze the population dynamics for a class of fitness functions that exhibit epochal behavior using a mathematical framework developed recently. In the latter the approximations employed led to a population-size independent theory that allowed us to determine optimal mutation rates. Here we extend this approach to include the destabilization of epochs due to finite-population fluctuations and show that this dynamical behavior often occurs around the optimal parameter settings for efficient search. The resulting, more accurate theory predicts the total number of fitness function evaluations to reach the global optimum as a function of mutation rate, population size, and the parameters specifying the fitness function. We further identify a generalized error threshold, smoothly bounding the two-dimensional regime of mutation rates and population sizes for which evolutionary search operates efficiently.