Our concern here, is the characterization of dissimilarity indexes defined over finite sets, whose spatial representation is spherical. Consequently, we propose a methodology (NormedMultiDimensional Scaling) to determine the spherical euclidean representation of a set ofitems best accounting for the initial dissimilarity between items. Thismethodology has the advantage of being graphically readable on individual qualitiesof projection like the normed PCA, of which it constitutes a generalization. Moreover, it avoids the arbitrary character of spherical encoding which the use of similitude functions currently used in MDS, implies.

We address the 3-Machine Assembly-Type Flowshop Scheduling Problem (3MAF). This problem is known to be NP-complete in the strongsense. We propose an exact branch and bound method based on a recursiveenumeration of potential inputs and outputs of the machines. Using this algorithm,several large size instances have been solved to optimality.

The relations between automatic clustering methods and inferentiel statistical models have mostely been studied when the data involves only one set. We propose to study these relations in the caseof data involving two sets. We shall look at cross clustering methods assuggested by Govaert [6]; we show that these methods, like the simple clusteringmethods, can be considered as a clustering approach of a mixture model. Weintroduce the notion of crossed mixture from a concret example and define thenotions of likelihood and associated clustered likelihood. Then, we study therelations which exist between the crossed mixture models and simple models and weshow that these relations are completely similar to those which exist betweenthe crossed clustering methods and simple clustering methods.

Fractional programming consists in optimizing a ratio oftwo functions subject to some constraints. Different versions of thismodel, linear or nonlinear, have applications in various fields likecombinatorial optimization, stochastic programming, data bases, andeconomy. Three resolution methods are presented: direct solution,parametric approach and solution of an equivalent problem.

This paper presents an application of Multiple Attribute Utility Theory onstrategic choices concerning energy transportation. The environmental assessmentof a network reinforcement strategy is emphasized. Our assessment bringsabout to consider multidimensional variables in MCDM. However, Multi-AttributedUtility Theory (MAUT) cannot, as a practical matter, manage such variables. We therefore work out a methodology to transform multidimensional variablesinto unidimensional ones. We apply it then to a pratical case. From the application, we draw some conclusions on Multi-Attributed Utility Theoryand on its interest for strategic choices dealing with environmental consequences.

We consider a generalized proximal point method (GPPA) forsolving the nonlinear complementarity problem with monotone operators inRn . It differs from the classical proximal point method discussedby Rockafellar for the problem of finding zeroes of monotone operatorsin the use of generalized distances, called φ-divergences,instead of the Euclidean one. These distances play not only aregularization role but also a penalization one, forcing the sequencegenerated by the method to remain in the interior of the feasible set,so that the method behaves like an interior point one. Under appropriateassumptions on the φ-divergence and the monotone operator weprove that the sequence converges if and only if the problem hassolutions, in which case the limit is a solution. If the problem doesnot have solutions, then the sequence is unbounded. We extend previousresults for the proximal point method concerning convex optimizationproblems.

Comparing q-ary relations on a set ${\cal O}$ ofelementary objects is one of the most fundamental problems ofclassification and combinatorial data analysis. In this paper thespecific comparison task that involvesclassification tree structures (binary or not) is considered in thiscontext. Two mathematical representationsare proposed. One is defined in terms of a weighted binary relation; the second uses a 4-ary relation.The most classical approaches to tree comparison are discussed in thecontext of a set theoretic representation of these relations. Formalandcombinatorial computing aspects of a construction method for a verygeneralfamily of association coefficients between relations are presented. The main purpose of this article is to specify the componentsof this construction, based on a permutational procedure, when thestructuresto be compared are classification trees.

An algebraic and combinatorial approach to the study ofthe Quadratic Assignment Problem produced theoretical results that canbe applied to (meta) heuristics to give them information about theproblem structure, allowing the construction of algorithms. In thispaper those results were applied to inform a Simulated Annealing-typeheuristic (which we called RedInv-SA). Some results from tests withknown literature instances are presented.

We show that the problem of deciding if there is a scheduleof length three for the multiprocessor scheduling problem on identicalmachines and unit execution time tasks in -complete even for bipartitegraphs, i.e. for precedence graphs of depth one. This complexity resultextends a classical result of Lenstra and Rinnoy Kan [5].

Single server queues with repeated attempts are useful inthe modeling of computer and telecommunication systems. In addition, weconsider in this paper the possibility of disasters. When a disasteroccurs, all the customers present in the system are destroyedimmediately. Using a regenerative approach, we derive a numericallystable recursion scheme for the state probabilities. This model can beemployed to analyze the behaviour of a buffer in computers with virusinfections.

In this paper, a discrete-event simulation model iscoupled with a genetic algorithm to treat highly combinatorialscheduling problems encountered in a production campaign of a finechemistry plant. The main constraints and features of fine chemistryhave been taken into account in the development of the model, thusallowing a realistic evaluation of the objective function used in thestochastic optimization procedure. After a presentation of problemcombinatorics, the coupling strategy is then proposed and illustrated byan example of industrial size (24 equipment items, 140 products, 12different production recipes and 40 products to be recycled during thecampaign). This example serves as an incentive to show how the approachcan improve production performance. Three technical criteria have beenstudied: campaign completion time, average product cycle time, respectof due-dates. Two kinds of optimization variables have been considered:product input order and/or allocation of heuristics for conflittreatment. The results obtained are then analysed and some perspectivesof this work are presented.

The standard multiple criteria optimization starts with anassumption that the criteria are incomparable. However, there are manyapplications in which the criteria express ideas of allocation ofresources meant to achieve some equitable distribution. This paperfocuses on solving linear multiple criteria optimization problems withuniform criteria treated in an equitable way. An axiomatic definition ofequitable efficiency is introduced as an refinement ofPareto-optimality. Various generation techniques are examined and thestructure of the equitably efficient set is analyzed.