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177
Variable Neighborhood Search
, 1997
"... Variable neighborhood search (VNS) is a recent metaheuristic for solving combinatorial and global optimization problems whose basic idea is systematic change of neighborhood within a local search. In this survey paper we present basic rules of VNS and some of its extensions. Moreover, applications a ..."
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Cited by 342 (26 self)
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Variable neighborhood search (VNS) is a recent metaheuristic for solving combinatorial and global optimization problems whose basic idea is systematic change of neighborhood within a local search. In this survey paper we present basic rules of VNS and some of its extensions. Moreover, applications are briefly summarized. They comprise heuristic solution of a variety of optimization problems, ways to accelerate exact algorithms and to analyze heuristic solution processes, as well as computerassisted discovery of conjectures in graph theory.
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 294 (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.
Variable Neighborhood Search for Extremal Graphs 6. Analyzing Bounds for the Connectivity Index
, 2001
"... Recently, Araujo and De la Pena [1] gave bounds for the connectivity index of chemical trees as a function of this index for general trees and the ramification index of trees. They also gave bounds for the connectivity index of chemical graphs as a function of this index for maximal subgraphs which ..."
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Cited by 49 (9 self)
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Recently, Araujo and De la Pena [1] gave bounds for the connectivity index of chemical trees as a function of this index for general trees and the ramification index of trees. They also gave bounds for the connectivity index of chemical graphs as a function of this index for maximal subgraphs which are trees and the cyclomatic number of the graphs. The ramification index of a tree is first shown to be equal to the number of pending vertices minus 2. Then, in view of extremal graphs obtained with the system AutoGraphiX, all bounds of Araujo and De la Pena [1] are improved, yielding tight bounds, and in one case corrected. Moreover, chemical trees of given order and number of pending vertices with minimum and with maximum connectivity index are characterized.
The pmedian problem: A survey of metaheuristic approaches
 European J Operational Research 179 927
, 2007
"... The pmedian problem, like most location problems, is classified as NPhard, and so, heuristic methods are usually used for solving it. The pmedian problem is a basic discrete location problem with real application that have been widely used to test heuristics. Metaheuristics are frameworks for bui ..."
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Cited by 25 (2 self)
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The pmedian problem, like most location problems, is classified as NPhard, and so, heuristic methods are usually used for solving it. The pmedian problem is a basic discrete location problem with real application that have been widely used to test heuristics. Metaheuristics are frameworks for building heuristics. In this survey, we examine the pmedian, with the aim of providing an overview on advances in solving it using recent procedures based on metaheuristic rules.
A variable neighborhood search heuristic for periodic routing problems
 European Journal of Operational Research
"... The aim of this paper is to propose a new heuristic for the Periodic Vehicle Routing Problem (PVRP) without time windows. The PVRP extends the classical Vehicle Routing Problem to a planning horizon of several days. Each customer requires a certain number of visits within this time horizon while the ..."
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Cited by 22 (1 self)
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The aim of this paper is to propose a new heuristic for the Periodic Vehicle Routing Problem (PVRP) without time windows. The PVRP extends the classical Vehicle Routing Problem to a planning horizon of several days. Each customer requires a certain number of visits within this time horizon while there is some flexibility on the exact days of the visits. Hence, one has to choose the visit days for each customer and to solve a VRP for each day. Our method is based on Variable Neighborhood Search (VNS). Computational results are presented, that show that our approach is competitive and even outperforms existing solution procedures proposed in the literature. Also considered is the special case of a single vehicle, i.e. the Periodic Traveling Salesman Problem (PTSP). It is shown that slight changes of the proposed VNS procedure is also competitive for the PTSP.
Self Generating Metaheuristics in Bioinformatics: The Proteins Structure Comparison Case
 Genetic Programming and Evolvable Machines
, 2004
"... In this paper we describe the application of a so called "SelfGenerating" Memetic Algorithm to the Maximum Contact Map Overlap problem (MAXCMO). The maximum overlap of contact maps is emerging as a leading modeling technique to obtain structural alignment among pairs of protein structure ..."
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Cited by 19 (6 self)
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In this paper we describe the application of a so called "SelfGenerating" Memetic Algorithm to the Maximum Contact Map Overlap problem (MAXCMO). The maximum overlap of contact maps is emerging as a leading modeling technique to obtain structural alignment among pairs of protein structures. Identifying structural alignments (and hence similarity among proteins) is essential to the correct assessment of the relation between proteins structure and function. A robust methodology for structural comparison could have impact on the process of rational drug design.
Fuzzy JMeans: a new heuristic for fuzzy clustering
, 2002
"... A fuzzy clustering problem consists of assigning a set of patterns to a given number of clusters with respect to some criteria such that each of them may belong to more than one cluster with different degrees of membership. In order to solve it, we first propose a new local search heuristic, called ..."
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Cited by 16 (5 self)
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A fuzzy clustering problem consists of assigning a set of patterns to a given number of clusters with respect to some criteria such that each of them may belong to more than one cluster with different degrees of membership. In order to solve it, we first propose a new local search heuristic, called FuzzyJMeans, where the neighbourhood is defined by all possible centroidtopattern relocations. The “integer” solution is then moved to a continuous one by an alternate step, i.e., by finding centroids and membership degrees for all patterns and clusters. To alleviate the difficulty of being stuck in local minima of poor value, this local search is then embedded into the Variable Neighbourhood Search metaheuristic. Results on five standard test problems from the literature are reported and compared with those obtained with the wellknown FuzzyCMeans heuristic. It appears that solutions of substantially better quality are obtained with the proposed methods than with this former one.
Iterated Local Search: Framework and Applications
"... The importance of high performance algorithms for tackling difficult optimization problems cannot be understated, and in many cases the most effective methods are metaheuristics. When designing a metaheuristic, simplicity should be favored, both conceptually and in practice. Naturally, it must also ..."
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Cited by 16 (1 self)
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The importance of high performance algorithms for tackling difficult optimization problems cannot be understated, and in many cases the most effective methods are metaheuristics. When designing a metaheuristic, simplicity should be favored, both conceptually and in practice. Naturally, it must also
Fuzzy JMeans and VNS Methods for Clustering Genes from Microarray Data
 Bioinformatics
, 2004
"... Motivation: In the interpretation of gene expression data from a group of microarray experiments that include samples from either different patients or conditions, special consideration must be given to the pleiotropic and epistatic roles of genes, as observed in the variation of gene coexpression ..."
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Cited by 13 (1 self)
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Motivation: In the interpretation of gene expression data from a group of microarray experiments that include samples from either different patients or conditions, special consideration must be given to the pleiotropic and epistatic roles of genes, as observed in the variation of gene coexpression patterns. Crisp clustering methods assign each gene to one cluster, thereby omitting information about the multiple roles of genes. Results: Here we present the application of a local search heuristic, Fuzzy JMeans, embedded into the Variable Neighborhood Search metaheuristic for the clustering of microarray gene expression data. We show that for all data sets studied this algorithm outperforms the standard Fuzzy CMeans heuristic. Different methods for the utilization of cluster membership information in determining gene coregulation are presented. The clustering and data analyses were performed on simulated data sets as well as experimental cDNA microarray data for breast cancer and human blood from the Stanford Microarray Database. Availability: The source code of the clustering software (C programming language) is freely available