This paper deals with the problem of scheduling n tasks on m identical processors in the presence of communication delays. A new approach of modelisation by a decision graph and a resolution by a tabu search method is proposed. Initial solutions are constructed by list algorithms, and then improved by a tabu algorithm operating in two phases. The experiments carried on arbitrary graphs show the efficiency of our method and that it outperformed the principle existent heuristics.

In this work we propose a ranking procedure. This procedure uses an ordinal information about the criterion weights and a non-cardinal or mixed information for the potential actions evaluation. The advantage of this procedure is that it uses the linear programming software packages to compute the intervals of relative proximities from where the rankings are obtained.

We consider the simulation of transient performance measures of high reliable fault-tolerant computer systems. The most widely used mathematical tools to model the behavior of these systems are Markov processes. Here, we deal basically with the simulation of the mean time to failure (MTTF) and the reliability, R(t), of the system at time t. Some variance reduction techniques are used to reduce the simulation time. We will combine two of these techniques: Importance Sampling and Conditioning Technique. The resulting hybrid algorithm performs significant reduction of simulation time and gives stables estimations.

A second order optimality condition for multiobjective optimization with a set constraint is developed; this condition is expressed as the impossibility of nonhomogeneous linear systems. When the constraint is given in terms of inequalities and equalities, it can be turned into a John type multipliers rule, using a nonhomogeneous Motzkin Theorem of the Alternative. Adding weak second order regularity assumptions, Karush, Kuhn-Tucker type conditions are therefore deduced.

We study networks with positive and negative customers (or Generalized networks of queues and signals) in a random environment. This environment may change the arrival rates, the routing probabilities, the service rates and also the effect of signals. We prove that the steady-state distribution has a product form. This property is obtained as a corollary of a much more general result on multidimensional Markov chains.

Comparing q-ary relations on a set $\cal O$ of elementary objects is one of the most fundamental problems ofclassification and combinatorial data analysis. In this paper the specific comparison task that involves classificationtree structures (binary or not) is considered in this context. Two mathematical representations are proposed. One isdefined in terms of a weighted binary relation; the second uses a 4-ary relation. The most classical approaches totree comparison are discussed in the context of a set theoretic representation of these relations. Formal andcombinatorial computing aspects of a construction method for a very general family of association coeficients betweenrelations are presented. The main purpose of this article is to specify the components of this construction, based on apermutational procedure, when the structures to be compared are classification trees.

In this paper we study the well definedness of the central path associated to agiven nonlinear (convex) semidefinite programming problem. Under standard assumptions,we establish that the existence of the central path is equivalent to the nonemptiness andboundedness of the optimal set. Other equivalent conditions are given, such as the existenceof a strictly dual feasible point or the existence of a single central point.The monotonicbehavior of the logarithmic barrier and the objective function along the trajectory is alsodiscussed. Finally, the existence and optimality of cluster points are established.

Sequential scoring rules are multi-stage social choice tules that work as follows: at each stage of the process, a scoreis computed for each alternative by taking into account its position in the individual preference rankings, and thealternative with the lowest score is eliminated. The current paper studies the ability of these rules for choosing theCondorcet winner (or the strong Condorcet winner) when individual preferences are single-peaked.

In this paper we study bi-directional nearness in a network based on AHP (Analytic Hierarchy Process) and ANP(Analytic Network Process). Usually we use forward (one-dimensional) direction nearness based on Euclidean distance.Even if the nearest point to i is point j, the nearest point to j is not necessarily point i. Sowe propose theconcept of bi-directional nearness defined by AHP'ssynthesizing of weights “for” direction and “from” direction.This concept of distance is a relative distance based on the configuration ofthe set of points located on a plane ornetwork. In order to confirm the usefulness of our study we apply the proposed nearness to solving methods of TSP(Traveling Salesman Problem), where to find an approximate solution of TSP we improved Nearest-Neighbor Method.Some numerical experiments of TSP were carried out. To decide a nearest point we used two kind of nearness, forwarddirection nearness and bi-directional nearness. As a result, by using bi-directional nearness,we obtained goodapproximate solution of TSP. Moreover, the relation between AHP and ANP, through an example, is considered.

We show in this paper that timed Petri nets, with one resource shared by all the transitions, are directly connected tothe modelling of integer linear programs (ILP). To an ILP can be automatically associated an equivalent Petri net. Theoptimal reachability delay is an optimal solution of the ILP. We show next that a net can model any ILP. I order to dothis, we give a new sufficient reachability condition for the marking equation, which also holds for general Petri netswithout timed transitions.

A cooperative game is defined as a set of players and a cost function. The distribution of the whole cost between theplayers can be done using the core concept, that is the set of all undominated cost allocations which prevent playersfrom grouping. In this paper we study a game whose cost function comes from the optimal solution of a linear integercovering problem. We give necessary and sufficient conditions for the core to be nonempty and characterize itsallocations using linear programming duality. We also discuss a special allocation, called the nucleolus. Wecharacterize that allocation and show that it can be computed in polynomial time using a column generation method.

Proximal Point Methods (PPM) can be traced to the pioneer works of Moreau [16], Martinet [14,15] and Rockafellar [19, 20] who used as regularization function the square of the Euclideannorm. In this work, we study PPM in the context of optimization and we derive a class of suchmethods which contains Rockafellar's result. We also present a less stringent criterion to theacceptance of an approximate solution to the subproblems that arise in the inner loops of PPM.Moreover, we introduce a new family of augmented Lagrangian methods for convex constrainedoptimization, that generalizes the PE+ class presented in [2].

The present study proposes an extended opportunity-basedage replacement policy where opportunities occur according to a Poissonprocess. When the age, x of the system satisfies x < S for aprespecified value S, a corrective replacement is conducted if theobjective system fails. In case x satisfies S ≤ x < T foranother prespecified value T, we take an opportunity to preventivelyreplace the system by a new one with probability p, and do not takethe opportunity with probability 1 - p. At the moment x reaches T,a preventive replacement is executed independently of opportunities. Thelong-term average cost of the proposed policy is formulated. Theconditions under which optimal values for S and T exist for aprespecified value of T and S, respectively, are then clarified. Numerical examples are also presented to illustrate the theoreticalunderpinnings of the proposed replacement policy formulation.

The main purpose of this paper is to give a method forconstruction of the reduced reachability graph for Stochastic Petri Nets(SPN), the symbolic graph. This construction is achieved by exploitingthe structural symetries in the net using the theory of bisimulation ofplaces for detecting isomorphic parts in the net. The symbolic graph,being isomorphic to an agregated Markov chain, may be used to provequalitative properties as liveness, boundness, ... Moreover, thisreduced graph make more easy the computation of the performance measuresof interest as the mean number of tokens in a place, the mean number offiring transition ... We have so developped a tool, SSPN (StochasticSymetric Petri nets), for generating the symbolic graph and deducingqualitatives and quantitatives properties.

We focus on performance study of routers in high-speednetwork through a queuing network analytical model. Such a model givesaccurate results about classical performance criteria. For example,analytical study of packet loss probabilities in a router uses aproduct-form queuing network. The analytical results are compared tosimulation results, and they provide routers managers with invaluableinformation for internal memories tuning.

In this paper, we present a new linear time algorithm forscheduling UECT (Unit Execution and Communication Time) trees on twoidentical processors. The chosen criterion is the makespan. The used strategy is based on clustering of tasks. We show that this algorithm builds optimal schedules. Some extensions are discussed for non UECT tasks.

In this paper we give the expression of the multiplecorrelation coefficient in a linear model according to the coefficientsof correlation. This expression makes it possible to analyze from anumerical point of view the instability of estimates in the case ofcollinear explanatory variables in the linear model or in theautoregressive model. This numerical approach, that we show on twoexamples, thus supplements the usual approach of the quasi colinearity,founded on the statistical properties of the estimators.

Most location problems on networks consider discretenodal demand. However, for many problems, demands are betterrepresentedby continuous functions along the edges, in addition to nodaldemands. Several papers consider the optimal location problemof one or more facilities when demands are continuously distributedalong the network, and the objective function dealt with is themedian one. Nevertheless, in location of public services itis desirable to use an equity criterion. One of the latter is varianceofdistance distribution which has been studied only for discrete nodaldemands. In this paper the variance problem has been generalizedto the case where one allows the demand to arisediscretely on the nodes as well as continuously along the edges. Properties and behaviour of the objective function arestudied. Likewise we present an exact algorithm forsolving this problem in a network, which reduces the complexityof the exhaustive procedure.

The solution of a variety of classes of globaloptimisation problemsis required in theimplementation of a framework for sensitivity analysis in multicriteria decision analysis. These problems have linear constraints, some of which have a particularstructure, anda variety of objective functions, which may be smooth or non-smooth. Thecontext in which theyarise implies a need for a single, robust solution method.The literature contains few experimental results relevant to such aneed.We report on our experience with the implementation of threestochastic algorithms for global optimisation: the multi-level singlelinkage algorithm,the topographical algorithm and the simulated annealing algorithm.Issues relating to their implementation and use to solve practicalproblems are discussed. Computational results suggest that, for the class of problems considered, simulated annealing performs well.