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 computer-assisted discovery of conjectures in graph theory.

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.

Iterated Local Search has many of the desirable features of a metaheuristic: it is simple, easy to implement, robust, and highly effective. The essential idea of Iterated Local Search lies in focusing the search not on the full space of solutions but on a smaller subspace defined by the solutions that are locally optimal for a given optimization engine. The success of Iterated Local Search lies in the biased sampling of this set of local optima. How effective this approach turns out to be depends mainly on the choice of the local search, the perturbations, and the acceptance criterion. So far, in spite of its conceptual simplicity, it has lead to a number of state-of-the-art results without the use of too much problem-specific knowledge. But with further work so that the different modules are well adapted to the problem at hand, Iterated Local Search can often become a competitive or even state of the art algorithm. The purpose of this review is both to give a detailed description of this metaheuristic and to show where it stands in terms of performance. O.M. acknowledges support from the Institut Universitaire de France. This work was partially supported by the “Metaheuristics Network”, a Research Training Network funded by the Improving Human Potential programme of the CEC, grant HPRN-CT-1999-00106. The information provided is the sole responsibility of the authors and does not reflect the Community’s opinion. The Community is not responsible for any use that might be made of data appearing in this publication. 1 1

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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 run-time 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 population-based...

The recent Variable Neighborhood Search (VNS) metaheuristic combines local search with systematic changes of neighborhood in the descent and escape from local optimum phases. When solving large instances of various problems, its efficiency may be enhanced through decomposition. The resulting two level VNS, called Variable Neighborhood Decomposition Search (VNDS), is presented and illustrated on the p-median problem. Results on 1400, 3038 and 5934 node instances from the TSP library show VNDS improves notably upon VNS in less computing time, and gives much better results than Fast Interchange (FI), in the same time that FI takes for a single descent. Moreover, Reduced VNS (RVNS), which does not use a descent phase, gives results similar to those of FI in much less computing time.

A new local search heuristic, called J-Means, is proposed for solving the minimum sum-of-squares clustering problem. The neighborhood of the current solution is defined by all possible centroid-to-entity relocations followed by corresponding changes of assignments. Moves are made in such neighborhoods until a local optimum is reached. The new heuristic is compared with two other well-known local search heuristics, KMeans and H-Means as well as with H-Means+, an improved version of the latter in which degeneracy is removed. Moreover, another heuristic, which fits into the Variable Neighborhood Search metaheuristic framework and uses J-Means in its local search step, is proposed too. Results on standard test problems from the literature are reported. It appears that J-Means outperforms the other local search methods, quite substantially when many entities and clusters are considered. 1 Introduction Consider a set X = fx 1 ; : : : ; xN g, x j = (x 1j ; : : : ; x qj ) 2 R q of N entiti...

This paper is concerned with the development of intelligent decision support methodologies for nurse rostering problems in large modern hospital environments. We present an approach which hybridises heuristic ordering with variable neighbourhood search. We show that the search can be extended and the solution quality can be significantly improved by the careful combination and repeated use of heuristic ordering, variable neighbourhood search and backtracking. The amount of computational time that is allowed plays a significant role and we analyse and discuss this. The algorithms are evaluated against a commercial Genetic Algorithm on commercial data. We demonstrate that this methodology can significantly outperform the commercial algorithm. This paper is one of the few in the scientific nurse rostering literature which deal with commercial data and which compare against a commercially implemented algorithm.

The paper analyses recent developments of a number of memory-based metaheuristics such as taboo search, scatter search, genetic algorithms and ant colonies. It shows that the implementations of these general solving methods are more and more similar. So, a unified presentation is proposed under the name of Adaptive Memory Programming (AMP). A number of methods recently developed for the quadratic assignment, vehicle routing and graph colouring problems are reviewed and presented under the adaptive memory programming point of view. AMP presents a number of interesting aspects such as a high parallelization potential and the ability of dealing with real and dynamic applications.