On green routing and scheduling problem

The vehicle routing and scheduling problem has been studied with much interest within the last four decades. In this paper, some of the existing literature dealing with routing and scheduling problems with environmental issues is reviewed, and a description is provided of the problems that have been investigated and how they are treated using combinatorial optimization tools

An improving dynamic programming algorithm to solve the shortest path problem with time windows

International audienceAn efficient use of dynamic programming requires a substantial reduction of the number of labels. We propose in this paper an efficient way of reducing the number of labels saved and dominance computing time. Our approach is validated by experiments on shortest path problem with time windows instances

Solutions diversification in a column generation algorithm

International audienceColumn generation algorithms have been specially designed for solving mathematical programs with a huge number of variables. Unfortunately, this method suffers from slow convergence that limits its efficiency and usability. Several accelerating approaches are proposed in the literature such as stabilization-based techniques. A more classical approach, known as "intensification, consists in inserting a set of columns instead of only the best one. Unfortunately, this intensication typically overloads the master problem, and generates a huge number of useless variables. This article covers some characteristics of the generated columns from theoretical and experimental points of view. Two selection criteria are compared. The first one is based on column reduced cost and the second on column structure. We conclude our study with computational experiments on two kinds of problems: the acyclic vehicle routing problem with time windows and the one-dimensional cutting stock. problem

Dantzig-Wolfe and Lagrangian decompositions in integer linear programming

International audienceWe propose in this paper a new Dantzig-Wolfe master model based on Lagrangian decomposition. We establish the relationship with classical Dantzig-Wolfe decomposition master problem and propose an alternative proof of the dominance of Lagrangian decomposition on Lagrangian relaxation dual bound. As illustration, we give the corresponding models and numerical results for two standard mathematical programs: the 0-1 bidimensional knapsack problem and the generalized assignment problem

Sur l'accélération de la convergence de la génération de colonnes

29 pagesThe use of the method of column generation was intensified during the last decades, in particular for the resolution of huge discrete problems in order to obtain a lagrangian bound. It is also integrated in a branch and bound method (branch-and-price) where it is used for the computation of the evaluation function at each node of the research tree. The efficiency of this method is very related to the resolution of the subproblems and to the quality of the columns generated at each iteration. Like iterative methods, it suffers from the long tail effect, particularly when it is used to solve degenerated problems. The scheme of column generation offers several possibilities for improvements. We present in this report some of these possibilities suggested in the literature, which are based on varied principles according to whether one operates on the primal or dual plan, or that acceleration relates to the resolution of the master problem, the subproblem or the whole process, or his hybridization with other resolution methods. At the end of this report, we focus our study on reoptimization techniques, which prove to be promising for the acceleration of column generation, particularly when the total time of resolution is dominated by that of the subproblems

Diversification and reoptimization procedures in column generation for the resolution of the acyclic vehicle routing problem with time windows

International audienceThis paper focuses on accelerating strategies in a Column Generation (CG) algorithm. In order to decrease the total number of generated columns and then, master problems resolution time, pricing problems solutions are made of task-disjoint columns. This can be achieved by diversification methods. Another way to improve CG computing time is to use reoptimization approaches to solve efficiently the pricing problems. We show in this work that diversification approaches are more efficient when applied on the first iterations to build efficiently a good approximation of pricing problems convex hull and that reoptimization methods are more efficient when applied on the last iterations when the dual variables are close. We combine a diversification technique and a reoptimization procedure in a CG scheme to improve the global resolution time. This study is validated on the Vehicle Routing Problem with Time Windows (VRPTW), defined on acyclic networks

Amélioration des performances du schéma de la génération de colonnes (application aux problèmes de tournées de véhicules)

La génération de colonnes est une méthode dédiée à la résolution de problèmes d'optimisation combinatoire de grande taille. Les méthodes utilisant cette approche de résolution ont souvent des problèmes de convergence, particulièrement quand elles sont utlisées pour résoudre des problèmes pratiques, de grandes dimensions. Nous nous intéressons dans cette thèse à l'accéleration de la méthode de génération de colonnes. Nous proposons des téchniques de diversification pour diminuer le nombre total de colonnes généreés ainsi que le temps de résolution des problèmes maîtres.Nous nous intéressons également à la résolution éfficace des sous-problèmes en utilisant des techniques de réoptimisation, mais aussi en proposant des améliorations de la méthode de programmation dynamique. Les approches sont validées expérimentalement sur le problème de tournées de véhicules avec fénêtre de temps.Columgeneration algorithms are instrumental in many areas of applied optimization where linear programs with an enormous number of variables need to be solued. Although success fully used in many applications, this method suffers from well-known "instability" issues, that somewhat limit its efficiency. This work focuses on accelerating strategies in a column generation algorithm. We propose some diversifiication methods in order to decrease the total number of generated columns and then master problems resolution time. We interest also to solving efficiently the pricing problems, by proposing an improning approch based on reoptimization principle and a new variant of the dynamic programming algorithm. The effectiveness of these approches is validated on vehicule routing problem with time windowsPARIS13-BU Sciences (930792102) / SudocSudocFranceF

Méthodes de décomposition pour l'optimisation discrète

30 pagesMany practical problems are modelled by integer programs. The difficulty of their resolution lies in the characterization of the feasible domain. Face to this difficulty, the researchers directed themselves towards approximations of this domain by decomposing the problem. The decomposition generally results in the relaxation of the integrality conditions on a subset of constraints. Decomposition methods differ from the bound quality and from the resolution methods used like their complexity. We present in this report some of these methods, analyze their strong and weak points and finally, establish a synthesis showing the relation between some methods considered to be different