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17
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 76 (30 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...
Where are bottleneck in NK fitness landscapes
 Gedeon (Eds.), Proceedings of the 2003 Congress on Evolutionary Computation CEC2003, IEEE
, 2003
"... Abstract Usually the offspringparent fitness correlation is used to visualize and analyze some caracteristics of fitness landscapes such as evolvability. In this paper, we introduce a more general representation of this correlation, the Fitness Cloud (FC). We use the bottleneck metaphor to emphasi ..."
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Cited by 7 (4 self)
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Abstract Usually the offspringparent fitness correlation is used to visualize and analyze some caracteristics of fitness landscapes such as evolvability. In this paper, we introduce a more general representation of this correlation, the Fitness Cloud (FC). We use the bottleneck metaphor to emphasise fitness levels in landscape that cause local search process to slow down. For a local search heuristic such as hillclimbing or simulated annealing, FC allows to visualize bottleneck and neutrality of landscapes. To confirm the relevance of the FC representation we show where the bottlenecks are in the wellknow NK fitness landscape and also how to use neutrality information from the FC to combine some neutral operator with local search heuristic.
Phase transition in a random NK landscape model
, 2008
"... An analysis for the phase transition in a random NK landscape model, NK(n,k,z), is given. This model is motivated from population genetics and the solubility problem for the model is equivalent to a random (k + 1)SAT problem. Gao and Culberson [Y. Gao, J. Culberson, An analysis of phase transition ..."
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Cited by 6 (0 self)
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An analysis for the phase transition in a random NK landscape model, NK(n,k,z), is given. This model is motivated from population genetics and the solubility problem for the model is equivalent to a random (k + 1)SAT problem. Gao and Culberson [Y. Gao, J. Culberson, An analysis of phase transition in NK landscapes, Journal of Artificial Intelligence Research 17 (2002) 309–332] showed that a random instance generated by NK(n, 2,z) with z>z0 = 27−7√5 4 is asymptotically insoluble. Based on empirical results, they conjectured that the phase transition occurs around the value z = z0. We prove that an instance generated by NK(n, 2,z)with z<z0 is soluble with positive probability by providing a polynomial time algorithm. Using branching process arguments, we prove again that an instance generated by NK(n, 2,z)with z>z0 is asymptotically insoluble. The results show the phase transition around z = z0 for NK(n, 2,z). In the course of the analysis, we introduce a generalized random 2SAT formula, which is of self interest, and show its phase transition phenomenon.
Models and Search Strategies for Applied Molecular Evolution
 Annual Reports in Combinatorial Chemistry and Molecular Diversity
, 1997
"... Introduction In just a few years, molecular diversity techniques have revolutionized pharmaceutical design and experimental methods for studying receptor binding, consensus sequences, genetic regu latory mechanisms, and many other issues in biochemistry and chemistry [30, 69 71, 78, 79]. Because o ..."
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Cited by 3 (1 self)
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Introduction In just a few years, molecular diversity techniques have revolutionized pharmaceutical design and experimental methods for studying receptor binding, consensus sequences, genetic regu latory mechanisms, and many other issues in biochemistry and chemistry [30, 69 71, 78, 79]. Because of the enormous libraries of ligands that can be used and the rapidity of the techniques, methods of applied molecular evolution such as SELEX and phage display have become particularly popular [30, 78, 86,126,127, 142,151]. These methods have been enormously successful, yet the theoretical work developed for them so far is quite limited. The success of these methods is not trivial: the huge number of sequences being searched through, the low concentrations of individual species, and the noise and biases inherent in the techniques would seem to make these experiments very difficult. Understanding why they work so well, and showing how they can perform better and for more complex molecular se
B2.7.2 NK Fitness Landscapes
 IN
, 1997
"... NK fitness landscapes are stochastically generated fitness functions on bit strings, parameterized (with N genes and K interactions between genes) so as to make them tunably `rugged'. Under the `natural' genetic operators of bitflipping mutation or recombination, NK landscapes produce ..."
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Cited by 3 (0 self)
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NK fitness landscapes are stochastically generated fitness functions on bit strings, parameterized (with N genes and K interactions between genes) so as to make them tunably `rugged'. Under the `natural' genetic operators of bitflipping mutation or recombination, NK landscapes produce multiple domains of attraction for the evolutionary dynamics. NK landscapes have been used in models of epistatic gene interactions, coevolution, genome growth, and Wright's shifting balance model of adaptation. Theory for adaptive walks on NK landscapes has been derived, and generalizations that extend beyond Kauffman's original framework have been utilized in these applications.
Fitness landscapes and the precautionary principle: The geometry of environmental risk
 Environmental Management
, 1999
"... ABSTRACT / A generalized mathematical model for exploring the implications of the Precautionary Principle is developed. This model draws on recent developments in the field of complex adaptive systems theory. The existence and importance of the Precautionary Principle in the field of environmental ..."
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ABSTRACT / A generalized mathematical model for exploring the implications of the Precautionary Principle is developed. This model draws on recent developments in the field of complex adaptive systems theory. The existence and importance of the Precautionary Principle in the field of environmental law is taken as given and used as justification for the development of models for exploring the principle's implications.
2003a) Satisficing, Deliberate Experimentation and Designing without Final Goals: Modeling InnovationRelated Business Strategy Choice through Simulation Analysis. Paper presented at the DRUID Conference
"... In the recent years, a number of economists and organizational scientist have started to work on a new approach to analyze the dynamics of innovation driven technological and institutional change. The standard search models heavily relying on the neoclassical assumptions and apparatus are seen now a ..."
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Cited by 1 (1 self)
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In the recent years, a number of economists and organizational scientist have started to work on a new approach to analyze the dynamics of innovation driven technological and institutional change. The standard search models heavily relying on the neoclassical assumptions and apparatus are seen now as incomplete, in what they neglect
A STEP TOWARD CONSTANT TIME LOCAL SEARCH FOR OPTIMIZING PSEUDO BOOLEAN FUNCTIONS
, 2013
"... Pseudo Boolean Functions (PBFs) are the objective functions for a wide class of hard optimization problems, such as MAXSAT and MAXCUT. Since these problems are NPHard, researchers and practitioners rely on incomplete solvers, such as Stochastic Local Search (SLS), for large problems. BestImprove ..."
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Pseudo Boolean Functions (PBFs) are the objective functions for a wide class of hard optimization problems, such as MAXSAT and MAXCUT. Since these problems are NPHard, researchers and practitioners rely on incomplete solvers, such as Stochastic Local Search (SLS), for large problems. BestImprovement Local Search (BILS) is a common form of SLS, which always takes the move yielding the highest improvement in the objective function. Generally, the more runtime SLS is given, the better solution can be obtained. This thesis aims at algorithmically accelerating SLS for PBFs using Walsh Analysis. The contributions of this thesis are threefold. First, a general approach for executing an approximate bestimprovement move in constant time on average using Walsh analysis, “WalshLS”, is described. Conventional BILS typically requires examining all n neighbors to decide which move to take, given the number of variables is n. With Walsh analysis, however, we can determine which neighbors need to be checked. As long as the objective function is epistatically bounded by a constant k (k is the number of variables per subfunctions), the number of neighbors that need to be checked is constant regardless of problem size. An impressive speedup of runtime (up to 449×) is observed in our empirical studies.
Integratedadaptive genetic algorithms
 In ECAL
, 2003
"... The aim of this paper is to show that exploiting knowledge extracted from the optimization process is important for the success of an evolutionary solver. In the context of NK fitness landscapes, we identify two causes for the difficulty of an optimization problem: the intrinsic combinatorial diffic ..."
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The aim of this paper is to show that exploiting knowledge extracted from the optimization process is important for the success of an evolutionary solver. In the context of NK fitness landscapes, we identify two causes for the difficulty of an optimization problem: the intrinsic combinatorial difficulty and the randomsearch hybridization. We apply these concepts for the royal road fitness landscape. Experimental results indicate that IntegratedAdaptive Genetic Algorithms (IAGA) are particularly suited for tackling randomsearch hybridization. A learnasyougo system aimed at a finegrained adaptation of operators behavior increases the solving power and convergence speed of IAGA. We conclude that the royal road problem is actually being “royal ” not for the traditional GA, but for a class of adaptive genetic algorithms. 1.
SelfOrganized Combinatorial Optimization
, 2008
"... In this paper, we present a selforganized computing approach to solving hard combinatorial optimization problems, e.g., the traveling salesman problem (TSP). First of all, we provide an analytical characterization of such an approach, by means of formulating combinatorial optimization problems into ..."
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In this paper, we present a selforganized computing approach to solving hard combinatorial optimization problems, e.g., the traveling salesman problem (TSP). First of all, we provide an analytical characterization of such an approach, by means of formulating combinatorial optimization problems into autonomous multientity systems and thereafter examining the microscopic characteristics of optimal solutions with respect to discrete state variables and local fitness functions. Next, we analyze the complexity of searching in the solution space based on the representation of fitness network and the observation of phase transition. In the second part of the paper, following the analytical characterization, we describe a decentralized, selforganized algorithm for solving combinatorial optimization problems. The validation results obtained by testing on a set of benchmark TSP instances have demonstrated the effectiveness and efficiency of the proposed algorithm. The link established between the microscopic characterization of hard computational systems and the design of selforganized computing methods provides a new way of studying and tackling hard combinatorial optimization problems.