In this paper, we study the differentiability of the trajectories of the logarithmic barrier algorithm for a nonlinearprogram when the set Λ* of the Karush-Kuhn-Tucker multiplier vectors is emptyowing to the fact that the constraint qualifications are not satisfied.



We deal here with a scheduling problem GPPCSP (Generalized Parallelism and Preemption Constrained Scheduling Problem) which is an extension of both the well-known Resource Constrained Scheduling Problem and the Scheduling Problem with Disjunctive Constraints. We first propose a reformulation of GPPCSP: according to it, solving GPPCSP means finding a vertex of the Feasible Vertex Subset of an Antichain Polyhedron. Next, we state several theoretical results related to this reformulation process and to structural properties of this specific Feasible Vertex Subset (connectivity, ...). We end by focusing on the preemptive case of GPPCSP and by identifying specific instances of GPPCSP which are such that any vertex of the related Antichain Polyhedron may be projected on its related Feasible Vertex Subset without any deterioration of the makespan. For such an instance, the GPPCSP problem may be solved in a simple way through linear programming.

In this paper we establish necessary as well assufficient conditions for a given feasible point to be a globalminimizer of smooth minimization problems with mixed variables.These problems, for instance, cover box constrained smooth minimizationproblems and bivalent optimization problems. In particular, ourresults provide necessary global optimality conditions for differenceconvex minimization problems, whereas our sufficient conditionsgive easily verifiable conditions for global optimality of variousclasses of nonconvex minimization problems, including the class ofdifference of convex and quadratic minimization problems. Wediscuss numerical examples to illustrate the optimalityconditions

In this paper we present a generic primal-dualinterior point methods (IPMs) for linear optimization in which the search direction depends on a univariate kernel function which is also used as proximity measure in the analysis of the algorithm. The proposed kernel function does not satisfy all the conditions proposed in [2].We show that the corresponding large-update algorithm improves the iteration complexity with a factor $n^{\frac16}$ when compared with the method based on the use of the classical logarithmic barrier function. For small-update interior point methods the iteration bound is $O(\sqrt{n}\log\frac{n}{\epsilon}),$ which is currently the best-known bound for primal-dual IPMs.

This paper describes a new representation for the solutions of the resource-constrained project scheduling problem (RCPSP) denoted Activity Set List. The most efficient heuristics for the problem use the activity list representation and the serial SGS method to construct the corresponding solution (schedule). The activity list may induce a search space of representations much larger then the space of schedules because the same schedule can correspond to many different activity list representations. We indicate how the activity set list representation can significantly reduce the search space, and how to move more efficiently through it. Furthermore, this new representation never excludes the optimal solution and it has many interesting properties. An evaluation of the search space reduction induced by this representation is made for the most used library of instances in the literature. The activity set list representation may be used to construct a new category of more efficient solution procedures for the problem.

An algorithm for enumerating all nondominated vectors of multiple objectiveinteger linear programs is presented. The method tests different regionswhere candidates can be found using an auxiliary binary problem for trackingthe regions already explored. An experimental comparision with our previousefforts shows the method has relatively good time performance.

This paper considers large shift scheduling problems with different shiftstart times and lengths, fractionable breaks and work stretch durationrestrictions. Two solution approaches are proposed to solve the problemsover a multiple-day planning horizon. The first approach is based on alocal branching strategy and the second one is based on a temporaldecomposition of the problem. Local branching is veryefficient in finding good feasible solutions when compared to a classicalbranch-and-bound procedure. However, the decomposition approach has theadvantage of yielding feasible solutions in short computing times, even for difficult instances.

Dans cet article nous proposons une nouvelleméthode d'initialisation du problème de transportclassique. Cette méthode est basée sur le principe d'uneaffectation seulement si nécessaire. Elle donne de bonsrésultats etsouvent la solution optimale.

The problem is to modify the capacities of the arcs from a network so that a given feasible flow becomes a maximum flow and the maximum change of the capacities on arcs is minimum. A very fast O(m⋅log(n)) time complexity algorithm for solving this problem is presented, where m is the number of arcs and n is the number of nodes of the network. The case when both, lower and upper bounds of the flow can be modified so that the given feasible flow becomes a maximum flow is also discussed. The algorithm proposed can be adapted to solve this problem, too. The inverse minimum flow problem considering l ∞ norm is also studied.

This article deals with the vehicle routing problem with timewindows (VRPTW). This problem consists in determining a least-costset of trips to serve customers during specific time windows. Theproposed solution method is a memetic algorithm (MA), a geneticalgorithm hybridised with a local search. Contrary to most paperson the VRPTW, which minimize first the number of vehicles, ourmethod is also able to minimize the total distance travelled. Theresults on 56 classical instances are compared to those of thebest metaheuristics. The efficiency of the MA is similar for theclassical criterion, but it becomes the best algorithm availablefor the total distance, being much faster and improving 20best-known solutions.