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73
Drift analysis and average time complexity of evolutionary algorithms
 Artificial Intelligence
, 2001
"... The computational time complexity is an important topic in the theory of evolutionary algorithms (EAs). This paper reports some new results on the average time complexity of EAs. Based on drift analysis, some useful drift conditions for deriving the time complexity of EAs are studied, including cond ..."
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Cited by 107 (33 self)
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The computational time complexity is an important topic in the theory of evolutionary algorithms (EAs). This paper reports some new results on the average time complexity of EAs. Based on drift analysis, some useful drift conditions for deriving the time complexity of EAs are studied, including conditions under which an EA will take no more than polynomial time (in problem size) to solve a problem and conditions under which an EA will take at least exponential time (in problem size) to solve a problem. The paper first presents the general results, and then uses several problems as examples to illustrate how these general results can be applied to concrete problems in analyzing the average time complexity of EAs. While previous work only considered (1 + 1) EAs without any crossover, the EAs considered in this paper are fairly general, which use a finite population, crossover, mutation, and selection.
Plasticity, evolvability, and modularity in RNA
 J EXP ZOOL
, 2000
"... RNA folding from sequences into secondary structures is a simple yet powerful, biophysically grounded model of a genotype–phenotype map in which concepts like plasticity, evolvability, epistasis, and modularity can not only be precisely defined and statistically measured but also reveal simultaneou ..."
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Cited by 102 (3 self)
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RNA folding from sequences into secondary structures is a simple yet powerful, biophysically grounded model of a genotype–phenotype map in which concepts like plasticity, evolvability, epistasis, and modularity can not only be precisely defined and statistically measured but also reveal simultaneous and profoundly nonindependent effects of natural selection. Molecular plasticity is viewed here as the capacity of an RNA sequence to assume a variety of energetically favorable shapes by equilibrating among them at constant temperature. Through simulations based on experimental designs, we study the dynamics of a population of RNA molecules that evolve toward a predefined target shape in a constant environment. Each shape in the plastic repertoire of a sequence contributes to the overall fitness of the sequence in proportion to the time the sequence spends in that shape. Plasticity is costly, since the more shapes a sequence can assume, the less time it spends in any one of them. Unsurprisingly, selection leads to a reduction of plasticity (environmental canalization). The most striking observation, however, is the simultaneous slowdown and eventual halting of the evolutionary process. The reduction of plasticity entails genetic canalization, that is, a dramatic loss of variability (and hence a loss of evolvability) to the point of lockin. The causal bridge between environmental canalization and genetic canalization
Finite Markov Chain Results in Evolutionary Computation: A Tour d'Horizon
, 1998
"... . The theory of evolutionary computation has been enhanced rapidly during the last decade. This survey is the attempt to summarize the results regarding the limit and finite time behavior of evolutionary algorithms with finite search spaces and discrete time scale. Results on evolutionary algorithms ..."
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Cited by 68 (2 self)
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. The theory of evolutionary computation has been enhanced rapidly during the last decade. This survey is the attempt to summarize the results regarding the limit and finite time behavior of evolutionary algorithms with finite search spaces and discrete time scale. Results on evolutionary algorithms beyond finite space and discrete time are also presented but with reduced elaboration. Keywords: evolutionary algorithms, limit behavior, finite time behavior 1. Introduction The field of evolutionary computation is mainly engaged in the development of optimization algorithms which design is inspired by principles of natural evolution. In most cases, the optimization task is of the following type: Find an element x 2 X such that f(x ) f(x) for all x 2 X , where f : X ! IR is the objective function to be maximized and X the search set. In the terminology of evolutionary computation, an individual is represented by an element of the Cartesian product X \Theta A, where A is a possibly...
Ruggedness and Neutrality  The NKp family of Fitness Landscapes
 Alive VI: Sixth International Conference on Articial Life
, 1998
"... It has come to be almost an article of faith amongst population biologists and GA researchers alike that the principal feature of a fitness landscape as regards evolutionary dynamics is "ruggedness", particularly as measured by the autocorrelation function. In this paper we demonstrate th ..."
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Cited by 60 (3 self)
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It has come to be almost an article of faith amongst population biologists and GA researchers alike that the principal feature of a fitness landscape as regards evolutionary dynamics is "ruggedness", particularly as measured by the autocorrelation function. In this paper we demonstrate that autocorrelation alone may be inadequate as a mediator of evolutionary dynamics, specifically in the presence of large scale neutrality. We introduce the NKp family of landscapes (a variant on NK landscapes) which possess the remarkable property that varying the degree of neutrality has minimal effect on the correlation structure. It is demonstrated that NKp landscapes feature neutral networks which have a "constant innovation" property comparable with the neutral networks observed in models of RNA secondary structure folding landscapes. We show that evolutionary dynamics on NKp landscapes vary dramatically with the degree of neutrality  at high neutrality the dynamics are characterised by populat...
Evolving Mechanisms of Morphogenesis: on the Interplay between Differential Adhesion and Cell Differentiation
, 2000
"... Differential cell adhesion, mediated by e.g. integrin and cadherins/catenines, plays an important role in morphogenesis and it has been shown that there is intimate crosstalk between their expression and modification, and intercellular signalling, cell differentiation, cell growth and apoptosis. I ..."
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Cited by 56 (3 self)
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Differential cell adhesion, mediated by e.g. integrin and cadherins/catenines, plays an important role in morphogenesis and it has been shown that there is intimate crosstalk between their expression and modification, and intercellular signalling, cell differentiation, cell growth and apoptosis. In this paper, we introduce and use a formal model to explore the morphogenetic potential of the interplay between these processes. We demonstrate the formation of interesting morphologies. Initiated by cell di!erentiation, differential cell adhesion leads to a long transient of cell migrations, e.g. engulfing and intercalation of cells and cell layers. This transient can be sustained dynamically by further cell differentiation, and by cell growth/division and cell death which are triggered by the (also long range) forces (stretching and squeezing) generated by the cell adhesion. We study the interrelation between modes of cell differentiation and modes of morphogenesis. We use an evolutionary process to zoom in on generegulation networks which lead to cell differentiation. Morphogenesis is not selected for but appears as a sideeffect. The evolutionary dynamics shows the hallmarks of evolution on a rugged landscape, including long neutral paths. We show that a combinatorially large set of morphologies occurs in the vicinity of a neutral path which sustains cell differentiation. Thus, an almost linear molecular phylogeny gives rise to mosaic evolution on the morphological level.
Effect of neutral selection on the evolution of molecular species
 In Proc. R. Soc. London B
, 1998
"... We introduce a new model of evolution on a fitness landscape possessing a tunable degree of neutrality. The model allows us to study the general properties of molecular species undergoing neutral evolution. We find that a number of phenomena seen in RNA sequencestructure maps are present also in ou ..."
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Cited by 49 (1 self)
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We introduce a new model of evolution on a fitness landscape possessing a tunable degree of neutrality. The model allows us to study the general properties of molecular species undergoing neutral evolution. We find that a number of phenomena seen in RNA sequencestructure maps are present also in our general model. Examples are the occurrence of “common ” structures which occupy a fraction of the genotype space which tends to unity as the length of the genotype increases, and the formation of percolating neutral networks which cover the genotype space in such a way that a member of such a network can be found within a small radius of any point in the space. We also describe a number of new phenomena which appear to be general properties of neutrally evolving systems. In particular, we show that the maximum fitness attained during the adaptive walk of a population evolving on such a fitness landscape increases with increasing degree of neutrality, and is directly related to the fitness of the most fit percolating network. 1
TANGLED WEBS  Evolutionary Dynamics on Fitness Landscapes with Neutrality
, 1997
"... The bulk of research on the dynamics of populations of genotypes evolving on fitness landscapes has concentrated on the rôle of correlation and landscape ruggedness as a putative indicator of the qual... ..."
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Cited by 43 (4 self)
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The bulk of research on the dynamics of populations of genotypes evolving on fitness landscapes has concentrated on the rôle of correlation and landscape ruggedness as a putative indicator of the qual...
Resource sharing and coevolution in evolving cellular automata
 IEEE Transactions on Evolutionary Computation
, 2000
"... Abstract—Coevolution, between a population of candidate solutions and a population of test cases, has received increasing attention as a promising biologically inspired method for improving the performance of evolutionary computation techniques. However, the results of studies of coevolution have be ..."
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Cited by 34 (2 self)
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Abstract—Coevolution, between a population of candidate solutions and a population of test cases, has received increasing attention as a promising biologically inspired method for improving the performance of evolutionary computation techniques. However, the results of studies of coevolution have been mixed. One of the seemingly more impressive results to date was the improvement via coevolution demonstrated by Juillé and Pollack on evolving cellular automata to perform a classification task. Their study, however, like most other studies on coevolution, did not investigate the mechanisms giving rise to the observed improvements. In this paper, we probe more deeply into the reasons for these observed improvements and present empirical evidence that, in contrast to what was claimed by Juillé and Pollack, much of the improvement seen was due to their “resource sharing ” technique rather than to coevolution. We also present empirical evidence that resource sharing works, at least in part, by preserving diversity in the population. Index Terms—Cellular automata, cooperative systems, distributed decision making, genetic algorithms, pattern classification. I.
2001a Adaptive evolution on neutral networks
 Bull. Math. Biol
"... We study the evolution of large but finite asexual populations evolving in fitness landscapes in which all mutations are either neutral or strongly deleterious. We demonstrate that despite the absence of higher fitness genotypes, adaptation takes place as regions with more advantageous distributions ..."
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Cited by 33 (1 self)
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We study the evolution of large but finite asexual populations evolving in fitness landscapes in which all mutations are either neutral or strongly deleterious. We demonstrate that despite the absence of higher fitness genotypes, adaptation takes place as regions with more advantageous distributions of neutral genotypes are discovered. Since these discoveries are typically rare events, the population dynamics can be subdivided into separate epochs, with rapid transitions between them. Within one epoch, the average fitness in the population is approximately constant. The transitions between epochs, however, are generally accompanied by a significant increase in the average fitness. We verify our theoretical considerations with two analytically tractable bitstring models. 1.
Optimizing Epochal Evolutionary Search: PopulationSize Dependent Theory
, 2001
"... 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 ..."
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Cited by 31 (4 self)
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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, which incorporates techniques from the fields of mathematical population genetics, molecular evolution theory, and statistical mechanics. Our analysis 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. This allows us to determine the optimal evolutionary parameter settings for this class of fitness functions. We identify a generalized error threshold that smoothly bounds the twodimensional regime of mutation rates and population sizes for which epochal evolutionary search operates most efficiently. Specifically, we analyze the dynamics of epoch destabilization under finitepopulation sampling fluctuations and show how the evolutionary parameters effectively introduce a coarse graining of the fitness function. More generally, we find that the optimal parameter settings for epochal evolutionary search correspond to behavioral regimes in which the consecutive epochs are marginally stable against the sampling fluctuations. Our results suggest that in order to achieve optimal search, one should set evolutionary parameters such that the coarse graining of the fitness function induced by the sampling fluctuations is just large enough to hide local optima.