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63
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 295 (16 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
, 1999
"... 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 124 (3 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 63 (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 [...
Iterated Local Search for the Quadratic Assignment Problem
 FG INTELLEKTIK, FB INFORMATIK
, 1999
"... Iterated local search (ILS) is a surprisingly simple but at the same time powerful metaheuristic for finding high quality approximate solutions for combinatorial optimization problems. ILS is based on the repeated application of a local search algorithm to initial solution which are obtained by m ..."
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Cited by 60 (10 self)
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Iterated local search (ILS) is a surprisingly simple but at the same time powerful metaheuristic for finding high quality approximate solutions for combinatorial optimization problems. ILS is based on the repeated application of a local search algorithm to initial solution which are obtained by mutations of previously found local optima  in most ILS algorithms these mutations are applied to the best found solution since the start of the search. In this article we present and analyze the application of ILS to the quadratic assignment problem (QAP). We first justify the potential usefulness of an ILS approach to this problem by an analysis of the QAP search space. An investigation of the runtime behavior of the ILS algorithm reveals a stagnation behavior of the algorithm  it may get stuck for many iterations in local optima. To avoid such stagnation situations we propose enhancements of the ILS algorithm based on extended acceptance criteria as well as populationbased...
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 55 (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.
Information characteristics and the structure of landscapes
 Evolutionary Computation
, 2000
"... Various techniques for statistical analysis of the structure of tness landscapes have been proposed. An important feature of these techniques is that they study the ruggedness of landscapes by measuring their correlation characteristics. This paper proposes a new information analysis of tness lands ..."
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Cited by 34 (3 self)
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Various techniques for statistical analysis of the structure of tness landscapes have been proposed. An important feature of these techniques is that they study the ruggedness of landscapes by measuring their correlation characteristics. This paper proposes a new information analysis of tness landscapes. The underlying idea is to consider a tness landscape as an ensemble of objects that are related to the tness of neighboring points. Three information characteristics of the ensemble are dened and studied. They are termed: information content, partial information content, and information stability. The information characteristics of a range of landscapes with known correlation features are analyzed in an attempt to reveal the advantages of the information analysis. We show that the proposed analysis is an appropriate tool for investigating the structure of tness landscapes.
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 31 (9 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 17 (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
The linear ordering problem: instances, search space analysis and algorithms
 Journal of Mathematical Modelling and Algorithms
"... The linear ordering problem is anhard problem that arises in a variety of applications. Due to its interest in practice, it has received considerable attention and a variety of algorithmic approaches to its solution have been proposed. In this paper we give a detailed search space analysis of avail ..."
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Cited by 15 (2 self)
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The linear ordering problem is anhard problem that arises in a variety of applications. Due to its interest in practice, it has received considerable attention and a variety of algorithmic approaches to its solution have been proposed. In this paper we give a detailed search space analysis of available LOP benchmark instance classes that have been used in various researches. The large fitnessdistance correlations observed for many of these instances suggest that adaptive restart algorithms like iterated local search or memetic algorithms, which iteratively generate new starting solutions for a local search based on previous search experience, are promising candidates for obtaining high performing algorithms. We therefore experimentally compared two such algorithms and the final experimental results suggest that, in particular, the memetic algorithm is the new stateoftheart approach to the LOP. 1
On the classification of NPcomplete problems in terms of their correlation coefficient
 Discrete Applied Mathematics
"... Local search and its variants simulated annealing and tabu search are very popular metaheuristics to approximatively solve NPhard optimization problems. Several experimental studies in the literature have shown that in practice some problems (e.g. the Traveling Salesman Problem, Quadratic Assignmen ..."
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Cited by 15 (2 self)
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Local search and its variants simulated annealing and tabu search are very popular metaheuristics to approximatively solve NPhard optimization problems. Several experimental studies in the literature have shown that in practice some problems (e.g. the Traveling Salesman Problem, Quadratic Assignment Problem) behave very well with these heuristics, whereas others do not (e.g. the Low Autocorrelation Binary String Problem). The autocorrelation function, introduced by Weinberger, measure the ruggedness of a landscape which is formed by a cost function and a neighborhood. We use a derived parameter, named the autocorrelation coefficient, as a tool to better understand these phenomena. In this paper we mainly study cost functions including penalty terms. Our results can be viewed as a first attempt to theoretically justify why it is often better in practice to enlarge the solution space and add penalty terms than to work solely on feasible solutions. Moreover, some new results as well as p...