Individual items of flow in a telecommunications or a transportation network may need to beseparated by a minimum distance or time, called a “headway”. If link dependent, such restrictions in general have the effect that the minimum time path for a “convoy” of items to travel from a given origin to a given destinationwill depend on the size of the convoy. The Quickest Path problemseeks a path to minimise this convoy travel time.A closely related bicriterion problem is the Maximum Capacity Shortest Path problem. For this latter problem,an effective implementation is devised for an algorithm to determine desired sets of efficient solutions which in turn facilitates the searchfor a “best” compromise solution. Numerical experience with the algorithm is reported.

We consider the unit execution time unit communication time (UET-UCT) scheduling model with hierarchical communica tions [CITE], and we study the impact of the hierarchical communications hypothesis on the hardness of approximation. We prove that there is no polynomial time approximation algorithm with performance guarantee smaller than 5/4 (unless P = NP). This result is an extension of the result of Hoogeveen et al. [CITE] who proved that there is no polynomial time ρ-approximation algorithm with p < 7/6 for the classical UET-UCT scheduling problem with homogeneous communication delays and an unrestricted number of identical machines.

We consider a special packing-covering pair of problems. Thepacking problem is a natural generalization of finding a(weighted) maximum independent set in an interval graph, thecovering problem generalizes the problem of finding a (weighted)minimum clique cover in an interval graph. The problem pairinvolves weights and capacities; we consider the case of unitweights and the case of unit capacities. In each case we describea simple algorithm that outputs a solution to the packing problemand to the covering problem that are within a factor of 2 of eachother. Each of these results implies an approximative min-maxresult. For the general case of arbitrary weights and capacitieswe describe an LP-based (2 + ε)-approximation algorithm forthe covering problem. Finally, we show that, unlessP = NP, the covering problem cannot be approximated inpolynomial time within arbitrarily good precision.

In this paper we study the main properties of the strongBerge equilibrium, then we prove a theorem of its existence based on the KyFan inequality and finally, we provide an algorithm for its determination.

A branch-and-bound method for solving the min cut with size constraint problemis presented. At each node of the branch-and-bound tree the feasible set isapproximated by an ellipsoid and a lower bound is computed by minimizing thequadratic objective function over this ellipsoid. An upper bound is alsoobtained by a Tabu search method. Numerical results will be presented.

We present, in this article, a hybrid approach forsolvingthe 0–1 multidimensional knapsack problem (MKP). This approach combineslinearprogramming and Tabu search.The resulting algorithm improves on the best result on many well-knownhard benchmarks.

In this note, we present a slight modification of an algorithm for thestrict feasibility problem. This modification reducesthe number of iterations.

In this paper, we present anew mathematical programming formulation for the Euclidean SteinerTree Problem (ESTP) in ℜ. We relax the integralityconstrains on this formulation and transform the resultingrelaxation, which is convex, but not everywhere differentiable,into a standard convex programming problem in conic form. Weconsider then an efficient computation of an ϵ-optimalsolution for this latter problem using interior-point algorithm.

We propose here a pricing Model which is an extension of the Cooperative Game concept and which includes a notion of Elastic Demand. We present some existence results as well as some algorithms. We conclude by discussing this model in the context of some Production and Transportation problems.

We present a review of the main “global optimization" methods. The paper comprises one introduction and two parts. In the introduction, we recall some generalities about non linear constraint-less optimization and we list some classifications which have been proposed for the global optimization methods. We then describe, in the first part, various “classical" global optimization methods, most of which available long before the appearance of Simulated Annealing (a key event in this field). There exists plenty of papers and books dealing with these methods, and studying in particular their convergence properties. The second part of the paper is devoted to more recent or atypical methods, mostly issued from combinatorial optimization. The three main methods are “metaheuristics": Simulated Annealing (and derived techniques), Tabu Search and Genetic Algorithms; we also describe three other less known methods. For these methods, theoretical studies of convergence are less abundant in the literature, and the use of convergence results is by far more limited in practice. However, the fitting of some of these techniques to continuous variables problems gave very promising results; that question is not discussed in detail in the paper, but useful references allowing to deepen the subject are given.

In this paper, we analyse the multiobjective problem generated byapplying a goal programming approach to deal with linearassignment type problem. We specify sufficient conditions for asolution to be efficient for this problem. The notion ofefficiency with respect to a neighborhood is also introduced andcharacterized through sufficient conditions. Unfortunately, theseconditions are not necessary in general.

The p-principal points of a random variable X with finitesecond momentare those ppoints in ${\mathbb R}$ minimizing the expected squared distance from X tothe closest point.Although the determination of principal points involves in general theresolution of a multiextremal optimization problem, existing procedures inthe literature provide just a local optimum. In this paper we show thatstandard Global Optimization techniques can be applied.

We study a continuous version of the capacity and flow assignment problem(CFA) where the design cost is combined with an average delay measureto yield a non convex objective function coupled with multicommodity flowconstraints. A separable convexification of each arc cost function is proposedto obtain approximate feasible solutions within easily computable gaps fromoptimality. On the other hand, DC (difference of convex functions) programming can be usedto compute accurate upper bounds and reduce the gap.The technique is shown to be effective when topology is assumedfixed and capacity expansion on some arcs is considered.

In this paper we present a method to perform fast simulation oflarge Markovian systems. This method is based on the use of threeconcepts: Markov chain uniformization, event-driven dynamics,and modularity. An application of urban trafficsimulation is presented to illustrate the performance of our approach.

To cope with its development, a French operator of mobile telephone networkmust periodically plan the purchase and the installation of new hardware,in such a way that a hierarchy of constraints (required and preferred)is satisfied.This paper presents the “constructive repair” method we used to solvethis problem within the allowed computing time (1 min). This method repairsthe planning during its construction. A sequence of repair procedures is defined: if a given repair cannot be achieved on a partial solution,a stronger repair (possibly relaxing more important constraints) is called upon.We tested our method on ten (both hand-made and real) problems. All our solutions were at least as good as thoses computed by hand by the engineer in charge with the planning.

Assume that n tasks must be processed by one machine in a fixed sequence. The processing time, the preferred starting time and the earliness and tardiness costs per time unit are known for each task. The problem is to allocate each task a starting time such that the total cost incurred by the early and tardy tasks is minimum. Garey et al. have proposed a nice O(nlogn) algorithm for the special case of symmetric and task-independent costs. In this paper we first extend that algorithm to the case of asymmetric and task-independent cost without increasing its worst-case complexity. For the general case of asymmetric and task-dependent costs, we propose an O(n3 logn) algorithm based on a strong dominance property that yields to model the scheduling problem as a minimum cost path in a valued directed acyclic graph.

The Reverse Elimination Method (REM) is a dynamic strategy for managing the tabu list. It is based on logical interdependencies between the solutions encountered during recent iterations of the search. REM provides both a necessary and sufficient condition to prevent cycling. The purpose of this paper is first to incorporate in REM a chronological order rule when cycling is unavoidable, thereby assuring the finite convergence of Tabu Search. Secondly, we correct a generalization of REM, the so-called REM-t method proposed by Glover (1990) where t is an integer parameter which controls the number of tabu attributes. A suitable adjustment of this parameter t can be designed in order to create a balance between diversification and intensification. In this paper, new dynamic rules for controlling the adjustment of the parameter t, are proposed. Finally, to illustrate the differences between the variants proposed for managing the tabu list, we test some of them on the 0–1 multidimensional knapsack problem.

This paper presents a state-of-the-art survey on multicriteria scheduling and introduces a definition of a multicriteria scheduling problem. It provides a framework that allows to tackle multicriteria scheduling problems, according to Decision Aid concepts. This problem is decomposed into three different problems. The first problem is about obtaining a model. The second one is how to take criteria into account and the third one is about solving a scheduling problem. An extension to an existing notation for scheduling problems is proposed for multicriteria scheduling problems. Then, basic results from the literature on multicriteria optimization are presented. These results are used to build the final scheduling problem to solve. Finally a survey is presented for one-machine, parallel machines and flowshop multicriteria scheduling problems.

A method to infer X-trees (valued trees having X as set of leaves) from incomplete distance arrays (where some entries are uncertain or unknown) is described. It allows us to build an unrooted tree using only 2n-3 distance values between the n elements of X, if they fulfill some explicit conditions. This construction is based on the mapping between X-tree and a weighted generalized 2-tree spanning X.

In this paper we will describe a new class of coloring problems, arising from military frequency assignment, where we want tominimize the number of distinct n-uples of colors used to color a givenset of n-complete-subgraphs of a graph. We will propose two relaxations based onSemi-Definite Programming models for graph and hypergraphcoloring, to approximate those (generally) NP-hard problems, as well asa generalization of the works of Karger et al. for hypergraph coloring,to find good feasible solutions with a probabilisticapproach.