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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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.

1 Introduction: the role of the user in heuristics Most state-of-the-art heuristics are characterized by a certain number of choices and free parameters, whose appropriate setting is a subject that raises issues of research methodology [5, 41, 51]. In some cases, these parameters are tuned through a feedback loop that includes the user as a crucial learning component: depending on preliminary algorithm tests some parameter values are changed by the

. Recent advances in optical fiber systems and transmission equipments play a primary role in today's telecommunications networks. The standardized SDH (Synchronous Digital Hierarchy) technology made the rings the most survivable architecture for designing high speed networks. Designing such networks involves not only the configuration of rings at the logical level but also the mapping of such configurations on the physical level, i.e. fiber paths. This paper deals with the problem of finding optimal clusters of nodes to be used as the basis for designing logical rings. In the simplest form, this problem is equivalent to k-equipartition, and can be modeled as a quadratic pseudo-boolean problem. We consider both linear and semidefinite relaxations and present numerical results on real data from France Telecom networks with up 900 nodes, and also on randomly generated problems. Key words. Graph Partitioning, Semidefinite Programming. 1. Introduction In the early eighties, a new broadb...

In this paper, new multilevel heuristics are proposed for finding a balanced bipartition of a graph. Multilevel schemes have been recently introduced for quickly solving the problem on graphs with thousands of nodes, graphs often present in domain-decomposition techniques for parallel computing. These heuristics firstly reduce the original graph by collapsing its nodes and arcs, thus generating a hierarchy of smaller and smaller graphs, then find a good partition of the smallest graph, and finally project and refine the so found partition backwards on the graph hierarchy. The multilevel algorithms proposed in this paper employ a novel greedy method and tabu search techniques during the partitioning and uncoarsening phases. Experimental results on a wide collection of benchmark graphs show that partitions of high quality are found in small computing times. Moreover, the effect of various parameter choices during the partitioning phase is experimentally studied.

Geometric crossover is a representation-independent generalization of the traditional crossover defined using the distance of the solution space. Using a distance tailored to the problem at hand, the formal definition of geometric crossover allows to design new problem-specific crossovers that embed problem-knowledge in the search. The standard encoding for multiway graph partitioning is highly redundant: each solution has a number of representations, one for each way of labeling the represented partition. Traditional crossover does not perform well on redundant encodings. We propose a new geometric crossover for graph partitioning based on a labeling-independent distance that filters the redundancy of the encoding. A correlation analysis of the fitness landscape based on this distance shows that it is well suited to graph partitioning. Our new genetic algorithm outperforms existing ones.

In this paper we provide a detailed and comprehensive survey of proposed approaches for network design, charting the evolution of models and techniques for the automatic planning of cellular wireless services. These problems present themselves as a trade-off between commitment to infrastructure and quality of service, and have become increasingly complex with the advent of more sophisticated protocols and wireless architectures. Consequently these problems are receiving increased attention from researchers in a variety of fields who adopt a wide range of models, assumptions and methodologies for problem solution. We seek to unify this dispersed and fragmented literature by charting the evolution of centralised planning for cellular systems. 1

Using space-filling curves to partition unstructured finite element meshes is a widely applied strategy when it comes to distributing load among several computation nodes. Compared to more elaborated graph partitioning packages, this geometric approach is relatively easy to implement and very fast. However, results are not expected to be as good as those of the latter, but no detailed comparison has ever been published. In this paper we will...

Abstract. This paper introduces tight upper bounds for the daily photograph scheduling problem of earth observation satellites. These bounds, which were unavailable until now, allow us to assess the quality of the heuristic solutions obtained previously. These bounds are obtained with a partition-based approach following the “divide and pas conquer ” principle. Dynamic programming and tabu search are conjointly used in this approach. We present also simplex-based linear programming relaxation and a relaxed knapsack approach for the problem.