Algorithmes de branch-and-cut bi-objectif appliqués au problème du sac-à-dos en variables binaires: ensembles bornants surrogate, stratégies de branchement dynamiques, génération et exploitation d'inégalités de couverture

In this work, we are interested in solving multi-objective combinatorial optimization problems. These problems have received a large interest in the past decades. In order to solve exactly and efficiently these problems, which are particularly difficult, the designed algorithms are often specific to a given problem. In this thesis, we focus on the branch-and-bound method and propose an extension by a branch-and-cut method, in bi-objective context. Knapsack problems are the case study of this work. Three main axis are considered: the definition of new upper bound sets, the elaboration of a dynamic branching strategy and the generation of valid inequalities. The defined upper bound sets are based on the surrogate relaxation, using several multipliers. Based on the analysis of the different multipliers, algorithms are designed to compute efficiently these surrogate upper bound sets. The dynamic branching strategy arises from the comparison of different static branching strategies from the literature. It uses reinforcement learning methods. Finally, cover inequalities are generated and introduced, all along the solving process, in order to improve it. Those different contributions are experimentally validated and the obtained branch-and-cut algorithm presents encouraging results.Dans ce travail, nous nous intéressons à la résolution de problèmes d'optimisation combinatoire multi-objectif. Ces problèmes ont suscité un intérêt important au cours des dernières décennies. Afin de résoudre ces problèmes, particulièrement difficiles, de manière exacte et efficace, les algorithmes sont le plus souvent spécifiques au problème traité. Dans cette thèse, nous revenons sur l'approche dite de branch-and-bound et nous en proposons une extension pour obtenir un branch-and-cut, dans un contexte bi-objectif. Les problèmes de sac-à-dos sont utilisés comme support pour ces travaux. Trois axes principaux sont considérés : la définition de nouveaux ensembles bornants, l'élaboration d'une stratégie de branchement dynamique et la génération d'inégalités valides. Les ensembles bornants définis sont basés sur la relaxation surrogate, utilisant un ensemble de multiplicateurs. Des algorithmes sont élaborés, à partir de l'étude des différents multiplicateurs, afin de calculer efficacement les ensembles bornants surrogate. La stratégie de branchement dynamique émerge de la comparaison de différentes stratégies de branchement statiques, issues de la littérature. Elle fait appel à une méthode d'apprentissage par renforcement. Enfin, des inégalités de couverture sont générées et introduites, tout au long de la résolution, dans le but de l'accélérer. Ces différents apports sont validés expérimentalement et l'algorithme de branch-and-cut obtenu présente des résultats encourageants

A branch-and-bound method for the bi-objective simple line assembly balancing problem

International audienceThe design of a production system is a strategic level decision. One of the key problems to solve is the line balancing problem that determines the efficiency of a production or assembly line. This class of problem has been widely studied in the literature. It determines important features, such as the number of stations, the takt time or the working conditions. Most of the variants of this problem consider only one objective function, but nowadays companies have to take into account different criteria. In this study, we consider a bi-objective variant of the simple assembly line balancing problem. We present a generic branch-and-bound method to solve exactly this problem. The objective functions are to minimise the takt time and the number of stations. To do so, bounds and bound sets are developed. The resulting method is numerically tested and compared to an ϵ-constraint method. These experiments show that the bi-objective branch-and-bound algorithm outperforms an ϵ-constraint method using a state-of-the-art single objective algorithm for more than 80% of the instances. Finally, we propose an analysis of the cases where the branch-and-bound method is outperformed

Evaluating the scalability of reconfigurable manufacturing systems at the design phase

International audienceTo face market volatility, reconfigurable manufacturing systems (RMS) aim to efficiently and cost-effectively react to changes. We focus on one characteristic of RMS: the scalability (ability to adapt the volume of throughput). In the literature, the only few indicators for scalability are not always formally defined and usually only consider a partial view of scalability. Moreover, most of them are actually more suited for the configuration planning rather than for the design. However, the design of the RMS has a high impact on its scalability. We propose the first combinatorial definition of this problem and a new measure to fully assess the scalability of a system at the design phase. This measure, based on a multi-objective approach, can assess the scalability of single-product manufacturing systems, analysing all configurations that it can implement. We present numerical experiments to compare this indicator with a state-of-the-art scalability indicator and with some classical production line design indicators, and we show that future research should focus on scalability as a specific criterion to optimise during the design of an RMS. In addition, the results obtained allow us to infer some managerial insights on the best levers to use when performing a reconfiguration for scalability purpose

Bounds and bound sets for the bi-objective simple assembly line balancing problem

International audienceThis paper focuses on the use of bounds and bound sets in the solving of a bi-objective version of the simple assembly line balancing problem. The two objective functions considered are the takt time and the number of stations. We propose a bi-objective solution method, returning all solutions that present an interesting tradeoff between the two objectives. We present bounds and bound sets and introduce them in a branch-and-bound method. The algorithm is demonstrated on a didactic instance

Toward scalability evaluation of multi-model lines

International audienceManufacturing companies are nowadays facing the high volatility of market conditions and the need for increased customization, which lead them to consider Reconfigurable Manufacturing Systems (RMS) as a way to react quickly and efficiently to changes in order to remain competitive. Two important characteristics of such systems are the scalability and the customization. Scalability and customization refer to the ability to change the throughput capacity and to the flexibility to produce various models from the same part family, respectively. However, if both characteristics have been studied in the literature in recent years, they are usually considered independently. In this article, we are proposing a new scalability indicator dedicated to the case of multi-model RMS as well as a procedure to generate a set of configurations. An illustrative example is presented to explain the main differences with the single-model case

Ensembles bornants pour un problème d’équilibrage de ligne d’assemblage bi-objectif

International audienceLa production manufacturière est généralement organisée le long de lignes. Celles-ci sontconstituées de stations, organisées en séquence, sur lesquelles un ensemble de tâches doivent êtreréalisées. Les problèmes d’équilibrage de ligne d’assemblage consistent à affecter les tâches auxstations, considérant des contraintes de précédence. Cette affectation détermine non seulementle nombre de stations composant la ligne et le takt time (cadence à laquelle les pièces sortentde la ligne), mais aussi les conditions de travail des opérateurs.De nombreuses variantes du problème d’équilibrage de ligne ont été étudiées [1]. Une desplus étudiée est leSimple assembly line balancing problem(SALBP) [6]. Ce problème considèreune ligne produisant un unique produit et suppose que le temps de traitement des tâches sontdéterministes. Trois versions classiques du problème se retrouvent dans la littérature, différantpar l’objectif optimisé :— SALBP-1 : minimise le nombre de stations, le takt time étant donné— SALBP-2 : minimise le takt time, le nombre de stations étant fixé— SALBP-E : minimise le produit du nombre de stations et du takt time.Le SALBP, qui est parmi les variantes les plus simples, est NP-difficile. Les méthodes derésolution développées pour ce problème ont souvent servi de base pour des variantes pluscomplexes du problème d’équilibrage

A Bi-objective Based Measure for the Scalability of Reconfigurable Manufacturing Systems

International audienceThe reconfigurable manufacturing systems aim to efficiently respond to demand changes. One of the key characteristics of these systems is the scalability, i.e. the ability to modify the volume of the throughput in order to fit to the demand variability. The design of the RMS has a high impact on its scalability. In the literature, there are only few indicators to evaluate the scalability of a system and most of them are a posteriori measures. In this article, we propose a new measure to assess the scalability since the design phase of the RMS. We present experimental results on state-of-the-art instances to validate our approach. They show that the proposed measure evaluates accurately the scalability

Evaluating the scalability of reconfigurable manufacturing systems at the design phase

International audienceTo face market volatility, reconfigurable manufacturing systems (RMS) aim to efficiently and cost-effectively react to changes. We focus on one characteristic of RMS: the scalability (ability to adapt the volume of throughput). In the literature, the only few indicators for scalability are not always formally defined and usually only consider a partial view of scalability. Moreover, most of them are actually more suited for the configuration planning rather than for the design. However, the design of the RMS has a high impact on its scalability. We propose the first combinatorial definition of this problem and a new measure to fully assess the scalability of a system at the design phase. This measure, based on a multi-objective approach, can assess the scalability of single-product manufacturing systems, analysing all configurations that it can implement. We present numerical experiments to compare this indicator with a state-of-the-art scalability indicator and with some classical production line design indicators, and we show that future research should focus on scalability as a specific criterion to optimise during the design of an RMS. In addition, the results obtained allow us to infer some managerial insights on the best levers to use when performing a reconfiguration for scalability purpose

Evaluating the scalability of reconfigurable manufacturing systems at the design phase

International audienceTo face market volatility, reconfigurable manufacturing systems (RMS) aim to efficiently and cost-effectively react to changes. We focus on one characteristic of RMS: the scalability (ability to adapt the volume of throughput). In the literature, the only few indicators for scalability are not always formally defined and usually only consider a partial view of scalability. Moreover, most of them are actually more suited for the configuration planning rather than for the design. However, the design of the RMS has a high impact on its scalability. We propose the first combinatorial definition of this problem and a new measure to fully assess the scalability of a system at the design phase. This measure, based on a multi-objective approach, can assess the scalability of single-product manufacturing systems, analysing all configurations that it can implement. We present numerical experiments to compare this indicator with a state-of-the-art scalability indicator and with some classical production line design indicators, and we show that future research should focus on scalability as a specific criterion to optimise during the design of an RMS. In addition, the results obtained allow us to infer some managerial insights on the best levers to use when performing a reconfiguration for scalability purpose

Surrogate upper bound sets for bi-objective bi-dimensional binary knapsack problems

Abstract The paper deals with the definition and the computation of surrogate upper bound sets for the bi-objective bi-dimensional binary knapsack problem. It introduces the Optimal Convex Surrogate Upper Bound set, which is the tightest possible definition based on the convex relaxation of the surrogate relaxation. Two exact algorithms are proposed: an enumerative algorithm and its improved version. This second algorithm results from an accurate analysis of the surrogate multipliers and the dominance relations between bound sets. Based on the improved exact algorithm, an approximated version is derived. The proposed algorithms are benchmarked using a dataset composed of three groups of numerical instances. The performances are assessed thanks to a comparative analysis where exact algorithms are compared between them, the approximated algorithm is confronted to an algorithm introduced in a recent research work