Clustering is the unsupervised classification of patterns (observations, data items, or feature vectors) into groups (clusters). The clustering problem has been addressed in many contexts and by researchers in many disciplines; this reflects its broad appeal and usefulness as one of the steps in exploratory data analysis. However, clustering is a difficult problem combinatorially, and differences in assumptions and contexts in different communities has made the transfer of useful generic concepts and methodologies slow to occur. This paper presents an overview of pattern clustering methods from a statistical pattern recognition perspective, with a goal of providing useful advice and references to fundamental concepts accessible to the broad community of clustering practitioners. We present a taxonomy of clustering techniques, and identify cross-cutting themes and recent advances. We also describe some important applications of clustering algorithms such as image segmentation, object recognition, and information retrieval.

Abstract—Open Shortest Path First (OSPF) is the most commonly used intra-domain internet routing protocol. Traffic flow is routed along shortest paths, splitting flow at nodes where several outgoing links are on shortest paths to the destination. The weights of the links, and thereby the shortest path routes, can be changed by the network operator. The weights could be set proportional to their physical distances, but often the main goal is to avoid congestion, i.e. overloading of links, and the standard heuristic recommended by Cisco is to make the weight of a link inversely proportional to its capacity. Our starting point was a proposed AT&T WorldNet backbone with demands projected from previous measurements. The desire was to optimize the weight setting based on the projected demands. We showed that optimizing the weight settings for a given set of demands is NP-hard, so we resorted to a local search heuristic. Surprisingly it turned out that for the proposed AT&T WorldNet backbone, we found weight settings that performed

Abstract It is well known that the performance of a stochastic local search proceduredepends upon the setting of its noise parameter, and that the optimal setting varies with the problem distribution. It is therefore desirable to develop general prinici-ples for tuning the procedures. We present two statistical measures of the local search process that allow one to quickly find the optimal noise settings. Theseproperties are independent of the fine details of the local search strategies, and appear to be relatively independent of the structure of the problem domains. Weapplied these principles to the problem of evaluating new search heuristics, and discovered two promising new strategies.

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

. A new hybrid procedure that combines genetic operators to existing heuristics is proposed to solve the Quadratic Assignment Problem (QAP). Genetic operators are found to improve the performance of both local search and tabu search. Some guidelines are also given to design good hybrid schemes. These hybrid algorithms are then used to improve on the best known solutions of many test problems in the literature. 1. Introduction The quadratic assignment problem (QAP) can be stated as: min OE2P (n) n X i=1 n X j=1 a ij b OE(i)OE(j) ; where A = (a ij ) and B = (b kl ) are two n \Theta n matrices and P (n) is the set of all permutations of f1; :::; ng. Matrix A is often referred to as a distance matrix between sites, and B as a flow matrix between objects. In most cases, the matrices A and B are symmetrical with a null diagonal. A permutation may then be interpreted as an assignment of objects to sites with a quadratic cost associated to it. There are many applications that can be fo...

:- Due to the stubborn nature of the deterministic job-shop scheduling problem many solutions proposed are of hybrid construction cutting across the traditional disciplines. The problem has been investigated from a variety of perspectives resulting in several analytical techniques combining generic as well as problem specific strategies. We seek to assess a subclass of this problem in which the objective is minimising makespan, by providing an overview of the history, the techniques used and the researchers involved. The sense and direction of their work is evaluated by assessing the reported results of their techniques on the available benchmark problems. From these results the current situation and pointers for future work are provided. KEYWORDS:- Scheduling Theory; Job-Shop; Review; Computational Study; 1. INTRODUCTION Current market trends such as consumer demand for variety, shorter product life cycles and competitive pressure to reduce costs have resulted in the need for zero i...

but often the main goal is to avoid congestion, i.e. overloading of links, and the standard heuristic recommended by Cisco (a major router vendor) is to make the weight of a link inversely proportional to its capacity. We study the problem of optimizing OSPF weights for a given a set of projected demands so as to avoid congestion. We show this problem is NP-hard and propose a local search heuristic to solve it. We also provide worst-case results about the performance of OSPF routing vs. an optimal multi-commodity flow routing. Our numerical experiments compare the results obtained with our local search heuristic to the optimal multi-commodity flow routing, as well as simple and commonly used heuristics for setting the weights. Experiments were done with a proposed nextgeneration AT&T WorldNet backbone as well as synthetic internetworks.

The past twenty years has seen a rapid growth of interest in stochastic search algorithms, particularly those inspired by natural processes in physics and biology. Impressive results have been demonstrated on complex practical optimisation problems and related search applications taken from a variety of fields, but the theoretical understanding of these algorithms remains weak. This results partly from the insufficient attention that has been paid to results showing certain fundamental limitations on universal search algorithms, including the so-called "No Free Lunch" Theorem. This paper extends these results and draws out some of their implications for the design of search algorithms, and for the construction of useful representations. The resulting insights focus attention on tailoring algorithms and representations to particular problem classes by exploiting domain knowledge. This highlights the fundamental importance of gaining a better theoretical grasp of the ways i...

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