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53
Landscapes and Their Correlation Functions
, 1996
"... Fitness landscapes are an important concept in molecular evolution. Many important examples of landscapes in physics and combinatorial optimation, which are widely used as model landscapes in simulations of molecular evolution and adaptation, are "elementary", i.e., they are (up to an additive const ..."
Abstract

Cited by 89 (15 self)
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Fitness landscapes are an important concept in molecular evolution. Many important examples of landscapes in physics and combinatorial optimation, which are widely used as model landscapes in simulations of molecular evolution and adaptation, are "elementary", i.e., they are (up to an additive constant) eigenfuctions of a graph Laplacian. It is shown that elementary landscapes are characterized by their correlation functions. The correlation functions are in turn uniquely determined by the geometry of the underlying configuration space and the nearest neighbor correlation of the elementary landscape. Two types of correlation functions are investigated here: the correlation of a time series sampled along a random walk on the landscape and the correlation function with respect to a partition of the set of all vertex pairs.
The Advantages of Landscape Neutrality in Digital Circuit Evolution
, 2000
"... . The paper studies the role of neutrality in the fitness landscapes associated with the evolutionary design of digital circuits and particularly the threebit binary multiplier. For the purpose of the study, digital circuits are evolved extrinsically on an array of logic cells. To evolve on an ..."
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Cited by 37 (15 self)
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. The paper studies the role of neutrality in the fitness landscapes associated with the evolutionary design of digital circuits and particularly the threebit binary multiplier. For the purpose of the study, digital circuits are evolved extrinsically on an array of logic cells. To evolve on an array of cells, a genotypephenotype mapping has been devised by which neutrality can be embedded in the resulting fitness landscape. It is argued that landscape neutrality is beneficial for digital circuit evolution. 1 Introduction Digital circuit evolution is a process of evolving configurations of logic gates for some prespecified computational program. Often the aim is for a highly efficient electronic circuit to emerge in a population of instances of the program. Digital electronic circuits have been evolved intrinsically [1] and extrinsically [26]. The former is associated with an evolutionary process in which each evolved electronic circuit is built and tested on hardware, whil...
Combinatorial Landscapes
 SIAM REVIEW
, 2002
"... Fitness landscapes have proven to be a valuable concept in evolutionary biology, combinatorial optimization, and the physics of disordered systems. A fitness landscape is a mapping from a configuration space into the real numbers. The configuration space is equipped with some notion of adjacency, ne ..."
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Cited by 33 (2 self)
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Fitness landscapes have proven to be a valuable concept in evolutionary biology, combinatorial optimization, and the physics of disordered systems. A fitness landscape is a mapping from a configuration space into the real numbers. The configuration space is equipped with some notion of adjacency, nearness, distance or accessibility. Landscape theory has emerged as an attempt to devise suitable mathematical structures for describing the "static" properties of landscapes as well as their influence on the dynamics of adaptation. In this review we focus on the connections of landscape theory with algebraic combinatorics and random graph theory, where exact results are available.
Landscapes  Complex Optimization Problems and Biopolymer Structures
 Computers Chem
, 1993
"... The evolution of RNA molecules in replication assays, viroids and RNA viruses can be viewed as an adaptation process on a 'fitness' landscape. The dynamics of evolution is hence tightly linked to the structure of the underlying landscape. Global features of landscapes can be described by statistical ..."
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Cited by 31 (16 self)
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The evolution of RNA molecules in replication assays, viroids and RNA viruses can be viewed as an adaptation process on a 'fitness' landscape. The dynamics of evolution is hence tightly linked to the structure of the underlying landscape. Global features of landscapes can be described by statistical measures like number of optima, lengths of walks, and correlation functions. The evolution of a quasispecies on such landscapes exhibits three dynamical regimes depending on the replication fidelity: Above the "localization threshold" the population is centered around a (local) optimum. Between localization and "dispersion threshold" the population is still centered around a consensus sequence, which, however, changes in time. For very large mutation rates the population spreads in sequence space like a gas. The critical mutation rates separating the three domains depend strongly on characteristics properties of the fitness landscapes. Statistical characteristics of RNA landscapes are acces...
Redundant representations in evolutionary computation
 EVOLUTIONARY COMPUTATION
, 2003
"... This paper investigates how the use of redundant representations influences the performance of genetic and evolutionary algorithms. Representations are redundant if the number of genotypes exceeds the number of phenotypes. A distinction is made between synonymously and nonsynonymously redundant ..."
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Cited by 25 (2 self)
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This paper investigates how the use of redundant representations influences the performance of genetic and evolutionary algorithms. Representations are redundant if the number of genotypes exceeds the number of phenotypes. A distinction is made between synonymously and nonsynonymously redundant representations. Representation are synonymously redundant if the genotypes that represent the same phenotype are very similar to each other. Nonsynonymously redundant representations do not allow genetic operators to work properly and result in a lower performance of evolutionary search. When using synonymously redundant representations, the performance of selectorecombinative genetic algorithms (GAs) depends on the modification of the initial supply. Theoretical models are developed that show the necessary population size to solve a problem and the number of generations goes with O(2 /r), where k r is the order of redundancy and r is the number of genotypic building blocks (BB) that represent the optimal phenotypic BB. Therefore, uniformly redundant representations do not change the behavior of GAs. Only by increasing r, which means overrepresenting the optimal solution, does GA performance increase. Therefore, nonuniformly redundant representations can only be used advantageously if apriori information exists regarding the optimal solution. The validity of the proposed theoretical concepts is illustrated for the binary trivial voting mapping and the realvalued linkbiased encoding. The empirical investigations show that the developed population sizing and time to convergence models allow an accurate prediction of the empirical results.
SelfAdaptive Exploration in Evolutionary Search
, 2001
"... We address a primary question of computational as well as biological research on evolution: How can an exploration strategy adapt in such a way as to exploit the information gained about the problem at hand? We first introduce an integrated formalism of evolutionary search which provides a unified v ..."
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Cited by 16 (6 self)
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We address a primary question of computational as well as biological research on evolution: How can an exploration strategy adapt in such a way as to exploit the information gained about the problem at hand? We first introduce an integrated formalism of evolutionary search which provides a unified view on different specific approaches. On this basis we discuss the implications of indirect modeling (via a ``genotypephenotype mapping'') on the exploration strategy. Notions such as modularity, pleiotropy and functional phenotypic complex are discussed as implications. Then, rigorously reflecting the notion of selfadaptability, we introduce a new definition that captures selfadaptability of exploration: different genotypes that map to the same phenotype may represent (also topologically) different exploration strategies; selfadaptability requires a variation of exploration strategies along such a ``neutral space''. By this definition, the concept of neutrality becomes a central concern of this paper. Finally, we present examples of these concepts: For a specific grammartype encoding, we observe a large variability of exploration strategies for a fixed phenotype, and a selfadaptive drift towards short representations with highly structured exploration strategy that matches the ``problem's structure''.
Optimal Search on a Technology Landscape
, 1998
"... Technological change at the #rmlevel has commonly been modeled as random sampling from a #xed distribution of possibilities. Such models, however, typically ignore empirically important aspects of the #rm's search process,notably the observation that the present state of the #rm guides future innov ..."
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Cited by 16 (0 self)
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Technological change at the #rmlevel has commonly been modeled as random sampling from a #xed distribution of possibilities. Such models, however, typically ignore empirically important aspects of the #rm's search process,notably the observation that the present state of the #rm guides future innovation. In this paper we explicitly treat this aspect of the #rm's search for technological improvements by introducing a #technology landscape" into an otherwise standard dynamic programming setting where the optimal strategy is to assign a reservation price to each possible technology. Search is modeled as movement,constrained by the cost of innovation, over the technology landscape. Simulations are presented on a stylized technology landscape while analytic results are derived using landscapes that are similar to Markov random #elds. We #nd that early in the search for technological improvements,if the initial position is poor or average,it is optimal to search far away on the technology l...
Random Field Models For Fitness Landscapes
, 1996
"... In many cases fitness landscapes are obtained as particular instances of random fields by assigning a large number of random parameters. Models of this type are often characterized reasonably well by their covariance matrices. We characterize isotropic random fields on finite graphs in terms of thei ..."
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Cited by 14 (6 self)
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In many cases fitness landscapes are obtained as particular instances of random fields by assigning a large number of random parameters. Models of this type are often characterized reasonably well by their covariance matrices. We characterize isotropic random fields on finite graphs in terms of their Fourier series expansions and investigate the relation between the covariance matrix of the random field model and the correlation structure of the individual landscapes constructed from this random field. Our formalism suggests to approximate landscape with known autocorrelation function by a random field model that has the same correlation structure.
Discrete Models of Biopolymers
, 2000
"... Discretized models of biopolymer structures can be used not only as approximations of the actual spatial structures but also as a computationally feasible approach to the generic features of the sequencestructure relationships. We review the combinatorics of nucleic acid secondary structures as wel ..."
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Cited by 14 (5 self)
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Discretized models of biopolymer structures can be used not only as approximations of the actual spatial structures but also as a computationally feasible approach to the generic features of the sequencestructure relationships. We review the combinatorics of nucleic acid secondary structures as well as lattice models of proteins, and show how properties such as the existence of extended neutral networks or shape space covering can be explained on this basis.
Landscape Statistics of the Low Autocorrelated Binary String Problem
, 2000
"... . The statistical properties of the energy landscape of the low autocorrelated binary string problem (LABSP) are studied numerically and compared with those of several classic disordered models. Using two global measures of landscape structure which have been introduced in the Simulated Annealing l ..."
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Cited by 12 (5 self)
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. The statistical properties of the energy landscape of the low autocorrelated binary string problem (LABSP) are studied numerically and compared with those of several classic disordered models. Using two global measures of landscape structure which have been introduced in the Simulated Annealing literature, namely, depth and di#culty, we find that the landscape of LABSP, except perhaps for a very large degeneracy of the local minima energies, is qualitatively similar to some wellknown landscapes such as that of the meanfield 2spin glass model. Furthermore, we consider a meanfield approximation to the pure model proposed by Bouchaud and Mezard (1994, J. Physique I France 4 1109) and show both analytically and numerically that it describes extremely well the statistical properties of LABSP. PACS numbers: 75.10.Nr, 05.50.+q, 64.60.Cn To whom correspondence should be addressed. Email: studla@tbi.univie.ac.at, Phone: **43 1 4277 52737, Fax: **43 1 4277 52793 The low autocorrelated ...