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150
On Evolution, Search, Optimization, Genetic Algorithms and Martial Arts  Towards Memetic Algorithms
, 1989
"... Short abstract, isn't it? P.A.C.S. numbers 05.20, 02.50, 87.10 1 Introduction Large Numbers "...the optimal tour displayed (see Figure 6) is the possible unique tour having one arc fixed from among 10 655 tours that are possible among 318 points and have one arc fixed. Assuming that one could ..."
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Cited by 186 (10 self)
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Short abstract, isn't it? P.A.C.S. numbers 05.20, 02.50, 87.10 1 Introduction Large Numbers "...the optimal tour displayed (see Figure 6) is the possible unique tour having one arc fixed from among 10 655 tours that are possible among 318 points and have one arc fixed. Assuming that one could possibly enumerate 10 9 tours per second on a computer it would thus take roughly 10 639 years of computing to establish the optimality of this tour by exhaustive enumeration." This quote shows the real difficulty of a combinatorial optimization problem. The huge number of configurations is the primary difficulty when dealing with one of these problems. The quote belongs to M.W Padberg and M. Grotschel, Chap. 9., "Polyhedral computations", from the book The Traveling Salesman Problem: A Guided tour of Combinatorial Optimization [124]. It is interesting to compare the number of configurations of realworld problems in combinatorial optimization with those large numbers arising in Cosmol...
Species Adaption Genetic Algorithms: A Basis for a Continuing SAGA
, 1992
"... For Artificial Life applications it is useful to extend Genetic Algorithms from a finite search space with fixedlength genotypes to openended evolution with variablelength genotypes. A new theoretical analysis is required, as Holland's Schema Theorem only applies to fixed lengths. It will be argu ..."
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Cited by 106 (27 self)
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For Artificial Life applications it is useful to extend Genetic Algorithms from a finite search space with fixedlength genotypes to openended evolution with variablelength genotypes. A new theoretical analysis is required, as Holland's Schema Theorem only applies to fixed lengths. It will be argued, using concepts of epistasis and fitness landscapes drawn from theoretical biology, that in the long run a population must havegenotypes of nearly equal length, and this length can only increase slowly. As the length increases, the population will be nearly converged, and hence evolving as a species.
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 ..."
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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.
From Boolean to Probabilistic Boolean Networks as Models of Genetic Regulatory Networks
 Proc. IEEE
, 2002
"... Mathematical and computational modeling of genetic regulatory networks promises to uncover the fundamental principles governing biological systems in an integrarive and holistic manner. It also paves the way toward the development of systematic approaches for effective therapeutic intervention in di ..."
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Cited by 84 (17 self)
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Mathematical and computational modeling of genetic regulatory networks promises to uncover the fundamental principles governing biological systems in an integrarive and holistic manner. It also paves the way toward the development of systematic approaches for effective therapeutic intervention in disease. The central theme in this paper is the Boolean formalism as a building block for modeling complex, largescale, and dynamical networks of genetic interactions. We discuss the goals of modeling genetic networks as well as the data requirements. The Boolean formalism is justified from several points of view. We then introduce Boolean networks and discuss their relationships to nonlinear digital filters. The role of Boolean networks in understanding cell differentiation and cellular functional states is discussed. The inference of Boolean networks from real gene expression data is considered from the viewpoints of computational learning theory and nonlinear signal processing, touching on computational complexity of learning and robustness. Then, a discussion of the need to handle uncertainty in a probabilistic framework is presented, leading to an introduction of probabilistic Boolean networks and their relationships to Markov chains. Methods for quantifying the influence of genes on other genes are presented. The general question of the potential effect of individual genes on the global dynamical network behavior is considered using stochastic perturbation analysis. This discussion then leads into the problem of target identification for therapeutic intervention via the development of several computational tools based on firstpassage times in Markov chains. Examples from biology are presented throughout the paper. 1
Toward an evolvable model of development for autonomous agent synthesis
, 1994
"... We are interested in the synthesis of autonomous agents using evolutionary techniques. Most work in this area utilizes a direct mapping from genotypic space to phenotypic space. In order to address some of the limitations of this approach, we present a simplified yet biologically defensible model of ..."
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Cited by 81 (3 self)
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We are interested in the synthesis of autonomous agents using evolutionary techniques. Most work in this area utilizes a direct mapping from genotypic space to phenotypic space. In order to address some of the limitations of this approach, we present a simplified yet biologically defensible model of the developmental process. The design issues that arise when formulating this model at the molecular, cellular and organismal level are discussed, and for each of these issues we describe how they were resolved in our implementation. We present and analyze some of the morphologies that can be explored using this model, specifically one that has agentlike properties. In addition, we demonstrate that this developmental model can be evolved. 1.
RNA Folding and Combinatory Landscapes
, 1993
"... In this paper we view the folding of polynucleotide (RNA) sequences as a map that assigns to each sequence a minimum free energy pattern of base pairings, known as secondary structure. Considering only the free energy leads to an energy landscape over the sequence space. Taking into account structur ..."
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Cited by 70 (29 self)
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In this paper we view the folding of polynucleotide (RNA) sequences as a map that assigns to each sequence a minimum free energy pattern of base pairings, known as secondary structure. Considering only the free energy leads to an energy landscape over the sequence space. Taking into account structure generates a less visualizable nonscalar "landscape", where a sequence space is mapped into a space of discrete "shapes". We investigate the statistical features of both types of landscapes by computing autocorrelation functions, as well as distributions of energy and structure distances, as a function of distance in sequence space. RNA folding is characterized by very short structure correlation lengths compared to the diameter of the sequence space. The correlation lengths depend strongly on the size and the pairing rules of the underlying nucleotide alphabet. Our data suggest that almost every minimum free energy structure is found within a small neighborhood of any random sequence. The...
Fitness Landscapes and Memetic Algorithm Design
 New Ideas in Optimization
, 1999
"... Introduction The notion of fitness landscapes has been introduced to describe the dynamics of evolutionary adaptation in nature [40] and has become a powerful concept in evolutionary theory. Fitness landscapes are equally well suited to describe the behavior of heuristic search methods in optimizat ..."
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Cited by 58 (7 self)
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Introduction The notion of fitness landscapes has been introduced to describe the dynamics of evolutionary adaptation in nature [40] and has become a powerful concept in evolutionary theory. Fitness landscapes are equally well suited to describe the behavior of heuristic search methods in optimization, since the process of evolution can be thought of as searching a collection of genotypes in order to find the genotype of an organism with highest fitness and thus highest chance of survival. Thinking of a heuristic search method as a strategy to "navigate" in the fitness landscape of a given optimization problem may help in predicting the performance of a heuristic search algorithm if the structure of the landscape is known in advance. Furthermore, the analysis of fitness landscapes may help in designing highly effective search algorithms. In the following we show how the analysis of fitness landscapes of combinatorial optimization problems can aid in designing the components of
Gene Perturbation and Intervention in Probabilistic Boolean Networks
 Bioinformatics
"... Motivation: A major objective of gene regulatory network modeling, in addition to gaining a deeper understanding of genetic regulation and control, is the development of computational tools for the identification and discovery of potential targets for therapeutic intervention in diseases such as can ..."
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Cited by 57 (19 self)
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Motivation: A major objective of gene regulatory network modeling, in addition to gaining a deeper understanding of genetic regulation and control, is the development of computational tools for the identification and discovery of potential targets for therapeutic intervention in diseases such as cancer. We consider the general question of the potential effect of individual genes on the global dynamical network behavior, both from the view of random gene perturbation as well as intervention in order to elicit desired network behavior.