Variable neighbourhood decomposition search for 0-1 mixed integer programs

In this paper we propose a new hybrid heuristic for solving 0-1 mixed integer programs based on the principle of variable neighbourhood decomposition search. It combines variable neighbourhood search with a general-purpose CPLEX MIP solver. We perform systematic hard variable fixing (or diving) following the variable neighbourhood search rules. The variables to be fixed are chosen according to their distance from the corresponding linear relaxation solution values. If there is an improvement, variable neighbourhood descent branching is performed as the local search in the whole solution space. Numerical experiments have proven that exploiting boundary effects in this way considerably improves solution quality. With our approach, we have managed to improve the best known published results for 8 out of 29 instances from a well-known class of very di±cult MIP problems. Moreover, computational results show that our method outperforms the CPLEX MIP solver, as well as three other recent most successful MIP solution methods

A scalable dynamic parking allocation framework

International audienceCities suffer from high traffic c ongestion of which one of the main causes is the unorganized pursuit for available parking. Apart from traffic congestion, the blind search for a parking slot causes financial and environmental losses. We consider a general parking allocation scenario in which the GPS data of a set of vehicles, such as the current locations and destinations of the vehicles, are available to a central agency which will guide the vehicles toward a designated parking lot, instead of the entered destination. In its natural form, the parking allocation problem is dynamic, i.e., its input is continuously updated. Therefore, standard static allocation and assignment rules do not apply in this case. In this paper, we propose a framework capable of tackling these real-time updates. From a methodological point of view, solving the dynamic version of the parking allocation problem represents a quantum leap compared with solving the static version. We achieve this goal by solving a sequence of 0-1 programming models over the planning horizon, and we develop several parking policies. The proposed policies are empirically compared on real data gathered from three European cities: Belgrade, Luxembourg, and Lyon. The results show that our framework is scalable and can improve the quality of the allocation, in particular when parking capacities are low

The parking allocation problem for connected vehicles

In this paper, we propose a parking allocation model that takes into account the basic constraints and objectives of a problem where parking lots are assigned to vehicles. We assume vehicles are connected and can exchange information with a central intelligence. Vehicle arrival times can be provided by a GPS device, and the estimated number of available parking slots, at each future time moment and for each parking lot is used as an input. Our initial model is static and may be viewed as a variant of the generalized assignment problem. However, the model can be rerun, and the algorithm can handle dynamic changes by frequently solving the static model, each time producing an updated solution. In practice this approach is feasible only if reliable quality solutions of the static model are obtained within a few seconds since the GPS can continuously provide new input regarding the vehicle’s positioning and its destinations. We propose a 0–1 programming model to compute exact solutions, together with a variable neighborhood search-based heuristic to obtain approximate solutions for larger instances. Computational results on randomly generated instances are provided to evaluate the performance of the proposed approaches.</p

The parking allocation problem for connected vehicles

International audienceIn this paper, we propose a parking allocation model that takes into account the basic constraints and objectives of a problem where parking lots are assigned to vehicles. We assume vehicles are connected and can exchange information with a central intelligence. Vehicle arrival times can be provided by a GPS device, and the estimated number of available parking slots, at each future time moment and for each parking lot is used as an input. Our initial model is static and may be viewed as a variant of the generalized assignment problem. However, the model can be rerun, and the algorithm can handle dynamic changes by frequently solving the static model, each time producing an updated solution. In practice this approach is feasible only if reliable quality solutions of the static model are obtained within a few seconds since the GPS can continuously provide new input regarding the vehicle’s positioning and its destinations. We propose a 0–1 programming model to compute exact solutions, together with a variable neighborhood search-based heuristic to obtain approximate solutions for larger instances. Computational results on randomly generated instances are provided to evaluate the performance of the proposed approaches

Heuristiques hybrides pour la résolution de problèmes en variables 0-1 mixtes

The 0-1 mixed integer programs represent many difficult real problems. The subject of this thesis is the proposition of hybrid methods to obtain good solutions in reasonable time for these problems. The algorithms presented in this thesis are tested on the multidimensional knapsack problem. It consists on the maximisation of a linear function with the respect of a set of linear constraints. In the first chapter of this thesis, we give a few concepts used to solve optimisation problems. We also present some problems of the knapsack problem family. We then present in the second chapter a state of the art to solve the multidimensional knapsack problem. We propose in the third chapter a first hybrid method. It combines a dynamic programming approach with a tabu search algorithm in a global intensification process. Some reduction rules are also integrated in the dynamic programming phase to try to reduce the size of the problem. The second approach is described in the chapter 4. It combines a scatter search algorithm with tabu search and path relinking components to enhance the process. We present an experimental study to assess the impact of some elements of the algorithm. We finally present in the chapter 5 some heuristics using jointly the linear programming relaxation and the mixed integer linear programming relaxation to solve the 0-1 integer programs. A set of computational results is presented for each approach. The last one improves some best-known values on a set of available instances of multidimensional knapsack problem.Les problèmes d'optimisation en variables 0-1 mixtes permettent de modéliser de nombreux problèmes réels difficiles à résoudre. Cette thèse s'intéresse à la mise en oeuvre de méthodes de résolution hybrides pour obtenir des solutions de bonne qualité en des temps raisonnables pour ces problèmes. L'ensemble des algorithmes présentés dans cette thèse est testé sur le problème du sac-à-dos multidimensionnel. Il consiste à maximiser une fonction linéaire en respectant un ensemble de contraintes linéaires. Après une présentation de quelques concepts fondamentaux utilisés en recherche opérationnelle pour résoudre les problèmes d'optimisation, nous présentons dans le premier chapitre différents problèmes de la famille du sac-à-dos. Nous abordons dans le second chapitre un ensemble de méthodes efficaces existantes pour résoudre le problème du sac-à-dos multidimensionnel. Nous proposons dans le chapitre 3 une première méthode hybride qui combine la programmation dynamique et la recherche tabou au sein d'un processus dit d'intensification globale. Des concepts de réduction sont également intégrés dans la programmation dynamique de manière à essayer de réduire la taille du problème. La seconde approche décrite dans le chapitre 4 combine la recherche dispersée avec des éléments de la recherche tabou et des chemins reliants pour affiner la recherche. Une étude expérimentale est menée pour mesurer l'impact de différents composants de l'algorithme. Nous terminons dans le chapitre 5 par une méthode utilisant conjointement la relaxation en continu et la relaxation en nombres entiers mixtes pour résoudre efficacement les problèmes en variables 0-1. Un ensemble de résultats numériques est présenté pour chacune de ces méthodes. La dernière approche permet d'améliorer quelques meilleures valeurs connues sur des instances existantes du problème du sac-à-dos multidimensionnel

Heuristiques hybrides pour la résolution de problèmes en variables 0-1 mixtes

Les problèmes d optimisation en variables 0-1 mixtes permettent de modéliser de nombreux problèmes réels difficiles à résoudre. Cette thèse s intéresse à la mise en œuvre de méthodes de résolution hybrides pour obtenir des solutions de bonne qualité en des temps raisonnables pour ces problèmes. L ensemble des algorithmes présentés dans cette thèse est testé sur le problème du sac-à-dos multidimensionnel qui consiste à maximiser une fonction linéaire en respectant un ensemble de contraintes linéaires. Nous présentons dans le premier chapitre différents problèmes de la famille du sac-à-dos. Nous abordons dans le second chapitre un ensemble de méthodes efficaces existantes pour résoudre le problème du sac-à-dos multidimensionnel. Nous proposons dans le chapitre 3 une première méthode hybride qui combine la programmation dynamique et la recherche tabou au sein d un processus dit d intensification globale. Des concepts de réduction sont intégrés dans la programmation dynamique pour essayer de réduire la taille du problème. La seconde approche décrite dans le chapitre 4 combine la recherche dispersée avec des éléments de la recherche tabou et des chemins reliants pour affiner la recherche. Une étude expérimentale est menée pour mesurer l impact de différents composants de l algorithme. Le chapitre 5 présente une approche utilisant conjointement la relaxation en continu et la relaxation en nombres entiers mixtes pour résoudre efficacement les problèmes en variables 0-1. Un ensemble de résultats numériques est présenté pour chacune des méthodes. La dernière permet d améliorer quelques meilleures valeurs connues sur des instances existantes de sac-à-dos multidimensionnel.The 0-1 mixed integer programs represent many difficult real problems. The subject of this thesis is the proposition of hybrid methods to obtain good solutions in reasonable time for these problems. All the algorithms presented in this thesis are tested on the ultidimensional knapsack problem. It consists on the maximisation of a linear function with the respect of a set of linear constraints. In the first chapter of this thesis, we give a few concepts used to solve optimisation problems. We also present some problems of the knapsack problem family. We then present in the second chapter a state of the art to solve the multidimensional knapsack problem. We propose in the third chapter a first hybrid method. It combines a dynamic programming approach with a tabu search algorithm in a global intensification process. Some reduction rules are also integrated in the dynamic programming phase to try to reduce the size of the problem. The second approach is described in the chapter 4. It combines a scatter search algorithm with tabu search and path relinking components to enhance the process. We present an experimental study to assess the impact of some elements of the algorithm. We finally present in the chapter 5 some heuristics using jointly the linear programming relaxation and the mixed integer linear programming relaxation to solve the 0-1 integer programs. A set of computational results is presented for each approach. The last one improves some best-known values on a set of available instances of multidimensional knapsack problemVALENCIENNES-BU Sciences Lettres (596062101) / SudocSudocFranceF

A survey of effective heuristics and their application to a variety of knapsack problems

We present a family of knapsack problems (KPs) while highlighting their particular applications. Though most of the problems are derived from the classical KP, the differences arise in the addition or modification of the constraints or in the way the objective function is defined. Appropriate techniques that were found to be successful in solving these problems are briefly reviewed. Hybrid methods that combine the strengths of different methods such as exact and heuristics are also briefly discussed. Some research avenues that we believe to be useful and challenging are also pointed out

Three-stage hybrid-flowshop model for cross-docking

International audienceThis paper deals with the optimization of a cross-docking system. It is modeled as a three-stage hybrid flowshop, in which shipments and orders are represented as batches. The first stage corresponds to the receiving docks, the second stage corresponds to the sorting stations, and the third stage corresponds to the shipping docks. The objective of the problem is to find a schedule that minimizes the completion time of the latest batch. In order to obtain good quality feasible solutions, we have developed several heuristic schemes depending on the main stage considered, and several rules to order the batches in this stage. Then, we propose a branch-and-bound algorithm that takes into account the decomposition of the problem into three stages. To evaluate the heuristics and to reduce the tree size during the branch-and-bound computation, we also propose lower bounds. Finally, the computational experiments are presented to demonstrate the efficiency of our heuristics. The results show that the exact approach can solve instances containing up to 9–10 batches in each stage (i.e., up to 100 jobs). In addition, our heuristics were evaluated over instances with up to 3000 jobs, and they can provide good quality feasible solutions in a few seconds (i.e., less than 2 s per heuristic)

Variable Neighbourhood Decent for Parking Allocation Problem

National audienceSearching for available parking lots presents a mayor problem in urban areas.Massive unorganized pursuit for parking provokes traffic congestion, financial losses, negativeenvironmental effects, among others. Most studies on this topic base their research on simulations due to the large set of non-deterministic input. In this paper we propose an approachwhere each vehicle that is looking for a parking lot is equipped with GPS device. Based on thisassumption, the static Parking allocation problem (PAP) can be modeled as a variant of Generalized assignment problem (GAP). Here we also discuss inclusion of the static model into adynamic real-world circumstances. Moreover, we developed a heuristic based on sequential Variable Neighborhood Decent (VND) to solve static PAP. It uses two neighborhood structures :reallocation and interchange. It appears that the deviation of VND based heuristic, comparedwith the optimal solutions, are always less than 0.1%