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Metaheuristics in combinatorial optimization: Overview and conceptual comparison
 ACM COMPUTING SURVEYS
, 2003
"... The field of metaheuristics for the application to combinatorial optimization problems is a rapidly growing field of research. This is due to the importance of combinatorial optimization problems for the scientific as well as the industrial world. We give a survey of the nowadays most important meta ..."
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Cited by 169 (14 self)
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The field of metaheuristics for the application to combinatorial optimization problems is a rapidly growing field of research. This is due to the importance of combinatorial optimization problems for the scientific as well as the industrial world. We give a survey of the nowadays most important metaheuristics from a conceptual point of view. We outline the different components and concepts that are used in the different metaheuristics in order to analyze their similarities and differences. Two very important concepts in metaheuristics are intensification and diversification. These are the two forces that largely determine the behaviour of a metaheuristic. They are in some way contrary but also complementary to each other. We introduce a framework, that we call the I&D frame, in order to put different intensification and diversification components into relation with each other. Outlining the advantages and disadvantages of different metaheuristic approaches we conclude by pointing out the importance of hybridization of metaheuristics as well as the integration of metaheuristics and other methods for optimization.
MAXMIN Ant System
 FUTURE GENERATION COMPUTER SYSTEMS
, 2000
"... Ant System, the first Ant Colony Optimization algorithm, showed to be a viable method for attacking hard combinatorial optimization problems. Yet, its performance, when compared to more finetuned algorithms, was rather poor for large instances of traditional benchmark problems like the Traveling Sa ..."
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Cited by 79 (4 self)
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Ant System, the first Ant Colony Optimization algorithm, showed to be a viable method for attacking hard combinatorial optimization problems. Yet, its performance, when compared to more finetuned algorithms, was rather poor for large instances of traditional benchmark problems like the Traveling Salesman Problem. To show that Ant Colony Optimization algorithms could be good alternatives to existing algorithms for hard combinatorial optimization problems, recent research in this ares has mainly focused on the development of algorithmic variants which achieve better performance than AS. In this article, we present ¨�©� � –¨��� � Ant System, an Ant Colony Optimization algorithm derived from Ant System. ¨�©� � –¨��� � Ant System differs from Ant System in several important aspects, whose usefulness we demonstrate by means of an experimental study. Additionally, we relate one of the characteristics specific to ¨� ¨ AS — that of using a greedier search than Ant System — to results from the search space analysis of the combinatorial optimization problems attacked in this paper. Our computational results on the Traveling Salesman Problem and the Quadratic Assignment Problem show that ¨�©� � – ¨��� � Ant System is currently among the best performing algorithms for these problems.
A Measure of Landscapes
 Evolutionary Computation
, 1995
"... The structure of a fitness landscape is still an illdefined concept. This paper introduces a statistical fitness landscape analysis, that can be used on a multitude of fitness landscapes. The result of this analysis is a statistical model that, together with some statistics denoting the explanatory ..."
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Cited by 55 (3 self)
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The structure of a fitness landscape is still an illdefined concept. This paper introduces a statistical fitness landscape analysis, that can be used on a multitude of fitness landscapes. The result of this analysis is a statistical model that, together with some statistics denoting the explanatory and predictive value of this model, can serve as a measure for the structure of the landscape. The analysis is based on a statistical time series analysis known as the BoxJenkins approach, that, among others, estimates the autocorrelations of a time series of fitness values generated by a random walk on the landscape. From these estimates, a correlation length for the landscape can be derived. Keywords: Fitness landscapes, Correlation structure, Correlation length 1 Introduction "We need a real theory relating the structure of rugged multipeaked fitness landscapes to the flow of a population upon those landscapes. We do not yet have such a theory." This quote, from Stuart A. Kauffman [...
Fitness Landscapes, Memetic Algorithms, and Greedy Operators for Graph Bipartitioning
 Evolutionary Computation
, 2000
"... The fitness landscape of the graph bipartitioning problem is investigated by performing a search space analysis for several types of graphs. The analysis shows that the structure of the search space is significantly different for the types of instances studied. Moreover, with increasing epistasis ..."
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Cited by 48 (13 self)
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The fitness landscape of the graph bipartitioning problem is investigated by performing a search space analysis for several types of graphs. The analysis shows that the structure of the search space is significantly different for the types of instances studied. Moreover, with increasing epistasis, the amount of gene interactions in the representation of a solution in an evolutionary algorithm, the number of local minima for one type of instance decreases and, thus, the search becomes easier. We suggest that other characteristics besides high epistasis might have greater influence on the hardness of a problem. To understand these characteristics, the notion of a dependency graph describing gene interactions is introduced.
Replication and Mutation on Neutral Networks
, 2000
"... Folding of RNA sequences into secondary structures is viewed as a map that assigns a uniquely de ned base pairing pattern to every sequence. The mapping is noninvertible since many sequences fold into the same minimum free energy (secondary) structure or shape. The preimages of this map, called ne ..."
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Cited by 26 (8 self)
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Folding of RNA sequences into secondary structures is viewed as a map that assigns a uniquely de ned base pairing pattern to every sequence. The mapping is noninvertible since many sequences fold into the same minimum free energy (secondary) structure or shape. The preimages of this map, called neutral networks, are uniquely associated with the shapes and vice versa. Random graph theory is used to construct networks in sequence space which are suitable models for neutral networks. The theory of molecular quasispecies has been applied to replication and mutation on singlepeak tness landscapes. This concept is extended by considering evolution on degenerate multipeak landscapes which originate from neutral networks by assuming that one particular shape is tter than all others. On such a singleshape landscape the superior tness value is assigned to all sequences belonging
MAGMA: A Multiagent Architecture for Metaheuristics
 IEEE TRANS. ON SYSTEMS, MAN AND CYBERNETICS  PART B
, 2002
"... In this work we introduce a multiagent architecture conceived as a conceptual and practical framework for metaheuristic algorithms (MAGMA, MultiAGent Metaheuristics Architecture). Metaheuristics can be seen as the result of the interaction among di erent kinds of agents: level 0 agents constructing ..."
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Cited by 11 (1 self)
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In this work we introduce a multiagent architecture conceived as a conceptual and practical framework for metaheuristic algorithms (MAGMA, MultiAGent Metaheuristics Architecture). Metaheuristics can be seen as the result of the interaction among di erent kinds of agents: level 0 agents constructing initial solutions, level1 agents improving solutions and level2 agents providing the high level strategy. In this framework, classical metaheuristic algorithms can be smoothly accommodated and extended, and new algorithms can be easily designed by defining which agents are involved and their interactions. Furthermore, with the introduction of a fourth level of agents, coordinating lower level agents, MAGMA can also describe, in a uniform way, cooperative search and, in general, any combination of metaheuristics. We propose
Fitness Landscapes And Performance Of MetaHeuristics
 MetaHeuristics: Advances and Trends in Local Search Paradigms for Optimization
, 1999
"... We perform a statistical analysis of the structure of the search space of some planar, euclidian instances of the traveling salesman problem. We want to depict this structure from the point of view of iterated local search algorithms. ..."
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Cited by 10 (0 self)
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We perform a statistical analysis of the structure of the search space of some planar, euclidian instances of the traveling salesman problem. We want to depict this structure from the point of view of iterated local search algorithms.
Correlation Length, Isotropy, and Metastable States
, 1997
"... A landscape is rugged if it has many local optima, if it gives rise to short adaptive walks, and if it exhibits a rapidly decreasing paircorrelation function (and hence if it has a short correlation length). The "correlation length conjecture" allows to estimate the number of metastable states fro ..."
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Cited by 10 (6 self)
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A landscape is rugged if it has many local optima, if it gives rise to short adaptive walks, and if it exhibits a rapidly decreasing paircorrelation function (and hence if it has a short correlation length). The "correlation length conjecture" allows to estimate the number of metastable states from the correlation length, provided the landscape is "typical". Isotropy, originally introduced as a geometrical condition on the covariance matrix of a random field, can be reinterpreted as maximum entropy condition that lends a precise meaning to the notion of a "typical" landscape. The XYHamiltonian, which violates isotropy only to a relatively small extent, is an ideal model for investigating the influence of anisotropies. Numerical estimates for the number of local optima and predictions obtained from the correlation length conjecture indeed show deviations that increase with the extent of anisotropies in the model.
Local Minima in the Graph Bipartitioning Problem
, 1996
"... We report numerical simulations on the number of local minima in the landscape of the Graph Bipartitioning Problem and provide an explanation in terms of the correlation length of its landscape. ..."
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Cited by 9 (5 self)
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We report numerical simulations on the number of local minima in the landscape of the Graph Bipartitioning Problem and provide an explanation in terms of the correlation length of its landscape.
Canonical Approximation of Fitness Landscapes
, 1996
"... We present a method for approximating a fitness landscape as a superposition of "elementary" landscapes. Given a correlation function of the landscape in question we show that the relative amplitudes of contributions with pary interactions can be computed. We show an application to RNA free energy ..."
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Cited by 8 (5 self)
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We present a method for approximating a fitness landscape as a superposition of "elementary" landscapes. Given a correlation function of the landscape in question we show that the relative amplitudes of contributions with pary interactions can be computed. We show an application to RNA free energy landscapes. 1. Fitness Landscapes Since Sewall Wright's seminal paper [1] the notion of a fitness landscape underlying the dynamics of evolutionary optimization has proved to be one of the most powerful concepts in evolutionary theory. Implicit in this idea is a collection of genotypes arranged in an abstract metric space, with each genotype next to those other genotypes which can be reached by a single mutation, as well as a value assigned to each genotype. Such a construction is by no means restricted to the theory of biological evolution. Hamiltonians of disordered systems, such as spin glasses [2, 3], and the cost functions of combinatorial optimization problems [4] have the same mathema...