A tabu search based memetic algorithm for the max-mean dispersion problem

Given a set V of n   elements and a distance matrix [dij]n×n[dij]n×n among elements, the max-mean dispersion problem (MaxMeanDP) consists in selecting a subset M from V such that the mean dispersion (or distance) among the selected elements is maximized. Being a useful model to formulate several relevant applications, MaxMeanDP is known to be NP-hard and thus computationally difficult. In this paper, we present a tabu search based memetic algorithm for MaxMeanDP which relies on solution recombination and local optimization to find high quality solutions. One key contribution is the identification of the fast neighborhood induced by the one-flip operator which takes linear time. Computational experiments on the set of 160 benchmark instances with up to 1000 elements commonly used in the literature show that the proposed algorithm improves or matches the published best known results for all instances in a short computing time, with only one exception, while achieving a high success rate of 100%. In particular, we improve 53 previous best results (new lower bounds) out of the 60 most challenging instances. Results on a set of 40 new large instances with 3000 and 5000 elements are also presented. The key ingredients of the proposed algorithm are investigated to shed light on how they affect the performance of the algorithm

A multi-start biased-randomized algorithm for the capacitated dispersion problem

The capacitated dispersion problem is a variant of the maximum diversity problem in which a set of elements in a network must be determined. These elements might represent, for instance, facilities in a logistics network or transmission devices in a telecommunication network. Usually, it is considered that each element is limited in its servicing capacity. Hence, given a set of possible locations, the capacitated dispersion problem consists of selecting a subset that maximizes the minimum distance between any pair of elements while reaching an aggregated servicing capacity. Since this servicing capacity is a highly usual constraint in real-world problems, the capacitated dispersion problem is often a more realistic approach than is the traditional maximum diversity problem. Given that the capacitated dispersion problem is an NP-hard problem, whenever large-sized instances are considered, we need to use heuristic-based algorithms to obtain high-quality solutions in reasonable computational times. Accordingly, this work proposes a multi-start biased-randomized algorithm to efficiently solve the capacitated dispersion problem. A series of computational experiments is conducted employing small-, medium-, and large-sized instances. Our results are compared with the best-known solutions reported in the literature, some of which have been proven to be optimal. Our proposed approach is proven to be highly competitive, as it achieves either optimal or near-optimal solutions and outperforms the non-optimal best-known solutions in many cases. Finally, a sensitive analysis considering different levels of the minimum aggregate capacity is performed as well to complete our study.Peer ReviewedPostprint (published version

El problema de la dispersión máxima en un entorno multi-objetivo

El problema de la diversidad máxima o dispersión máxima (MDP - Maximum Diversity Problem) presenta un gran número de aplicaciones prácticas que surgen de la búsqueda de los elementos mas disímiles de un conjunto de datos. Este tipo de problema utiliza modelos de diversidad y definiciones de distancia o disimilitud (observar que en el contexto de este trabajo distancia y disimilitud son considerados sinónimos) como forma de medir que tan diferentes son los elementos de un conjunto dado. Como diversos expertos pueden preferir diferentes definiciones de distancia para problemas específicos, se propone resolver el MDP con un enfoque multi-objetivo, considerando por primera vez, la utilización simultánea de múltiples definiciones de distancia. En este nuevo contexto multi-objetivo, este trabajo propone la utilización de un algoritmo evolutivo multi-objetivo (el reconocido NSGA-II), presentando varios casos de prueba que demuestran la eficiencia del algoritmo propuesto en comparación con la búsqueda exhaustiva.XIV Workshop Bases de Datos y Minería de Datos (WBDDM).Red de Universidades con Carreras en Informática (RedUNCI

El problema de la dispersión máxima en un entorno multi-objetivo

El problema de la diversidad máxima o dispersión máxima (MDP - Maximum Diversity Problem) presenta un gran número de aplicaciones prácticas que surgen de la búsqueda de los elementos mas disímiles de un conjunto de datos. Este tipo de problema utiliza modelos de diversidad y definiciones de distancia o disimilitud (observar que en el contexto de este trabajo distancia y disimilitud son considerados sinónimos) como forma de medir que tan diferentes son los elementos de un conjunto dado. Como diversos expertos pueden preferir diferentes definiciones de distancia para problemas específicos, se propone resolver el MDP con un enfoque multi-objetivo, considerando por primera vez, la utilización simultánea de múltiples definiciones de distancia. En este nuevo contexto multi-objetivo, este trabajo propone la utilización de un algoritmo evolutivo multi-objetivo (el reconocido NSGA-II), presentando varios casos de prueba que demuestran la eficiencia del algoritmo propuesto en comparación con la búsqueda exhaustiva.XIV Workshop Bases de Datos y Minería de Datos (WBDDM).Red de Universidades con Carreras en Informática (RedUNCI

Workload Equity in Vehicle Routing Problems: A Survey and Analysis

Over the past two decades, equity aspects have been considered in a growing number of models and methods for vehicle routing problems (VRPs). Equity concerns most often relate to fairly allocating workloads and to balancing the utilization of resources, and many practical applications have been reported in the literature. However, there has been only limited discussion about how workload equity should be modeled in VRPs, and various measures for optimizing such objectives have been proposed and implemented without a critical evaluation of their respective merits and consequences. This article addresses this gap with an analysis of classical and alternative equity functions for biobjective VRP models. In our survey, we review and categorize the existing literature on equitable VRPs. In the analysis, we identify a set of axiomatic properties that an ideal equity measure should satisfy, collect six common measures, and point out important connections between their properties and those of the resulting Pareto-optimal solutions. To gauge the extent of these implications, we also conduct a numerical study on small biobjective VRP instances solvable to optimality. Our study reveals two undesirable consequences when optimizing equity with nonmonotonic functions: Pareto-optimal solutions can consist of non-TSP-optimal tours, and even if all tours are TSP optimal, Pareto-optimal solutions can be workload inconsistent, i.e. composed of tours whose workloads are all equal to or longer than those of other Pareto-optimal solutions. We show that the extent of these phenomena should not be underestimated. The results of our biobjective analysis are valid also for weighted sum, constraint-based, or single-objective models. Based on this analysis, we conclude that monotonic equity functions are more appropriate for certain types of VRP models, and suggest promising avenues for further research.Comment: Accepted Manuscrip

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

Reactive scheduling to treat disruptive events in the MRCPSP

Esta tesis se centra en diseñar y desarrollar una metodología para abordar el MRCPSP con diversas funciones objetivo y diferentes tipos de interrupciones. En esta tesis se exploran el MRCPSP con dos funciones objetivo, a saber: (1) minimizar la duración del proyecto y (2) maximizar el valor presente neto del proyecto. Luego, se tiene en cuenta dos tipos diferentes de interrupciones, (a) interrupción de duración, e (b) interrupción de recurso renovable. Para resolver el MRCPSP, en esta tesis se proponen tres estrategias metaheurísticas: (1) algoritmo memético para minimizar la duración del proyecto, (2) algoritmo adaptativo de forrajeo bacteriano para maximizar el valor presente neto del proyecto y (3) algoritmo de optimización multiobjetivo de forrajeo bacteriano (MBFO) para resolver el MRCPSP con eventos de interrupción. Para juzgar el rendimiento del algoritmo memético y de forrajeo bacteriano propuestos, se ha llevado a cabo un extenso análisis basado en diseño factorial y diseño Taguchi para controlar y optimizar los parámetros del algoritmo. Además se han puesto a prueba resolviendo las instancias de los conjuntos más importantes en la literatura: PSPLIB (10,12,14,16,18,20 y 30 actividades) y MMLIB (50 y 100 actividades). También se ha demostrado la superioridad de los algoritmos metaheurísticos propuestos sobre otros enfoques heurísticos y metaheurísticos del estado del arte. A partir de los estudios experimentales se ha ajustado la MBFO, utilizando un caso de estudio.DoctoradoDoctor en Ingeniería Industria

Integration of production, maintenance and quality : Modelling and solution approaches

Dans cette thèse, nous analysons le problème de l'intégration de la planification de production et de la maintenance préventive, ainsi que l'élaboration du système de contrôle de la qualité. Premièrement, on considère un système de production composé d'une machine et de plusieurs produits dans un contexte incertain, dont les prix et le coût changent d'une période à l'autre. La machine se détériore avec le temps et sa probabilité de défaillance, ainsi que le risque de passage à un état hors contrôle augmentent. Le taux de défaillance dans un état dégradé est plus élevé et donc, des coûts liés à la qualité s’imposent. Lorsque la machine tombe en panne, une maintenance corrective ou une réparation minimale seront initiées pour la remettre en marche sans influer ses conditions ou le processus de détérioration. L'augmentation du nombre de défaillances de la machine se traduit par un temps d'arrêt supérieur et un taux de disponibilité inférieur. D'autre part, la réalisation des plans de production est fortement influencée par la disponibilité et la fiabilité de la machine. Les interactions entre la planification de la maintenance et celle de la production sont incorporées dans notre modèle mathématique. Dans la première étape, l'effet de maintenance sur la qualité est pris en compte. La maintenance préventive est considérée comme imparfaite. La condition de la machine est définie par l’âge actuel, et la machine dispose de plusieurs niveaux de maintenance avec des caractéristiques différentes (coûts, délais d'exécution et impacts sur les conditions du système). La détermination des niveaux de maintenance préventive optimaux conduit à un problème d’optimisation difficile. Un modèle de maximisation du profit est développé, dans lequel la vente des produits conformes et non conformes, les coûts de la production, les stocks tenus, la rupture de stock, la configuration de la machine, la maintenance préventive et corrective, le remplacement de la machine et le coût de la qualité sont considérés dans la fonction de l’objectif. De plus, un système composé de plusieurs machines est étudié. Dans cette extension, les nombres optimaux d’inspections est également considéré. La fonction de l’objectif consiste à minimiser le coût total qui est la somme des coûts liés à la maintenance, la production et la qualité. Ensuite, en tenant compte de la complexité des modèles préposés, nous développons des méthodes de résolution efficaces qui sont fondées sur la combinaison d'algorithmes génétiques avec des méthodes de recherches locales. On présente un algorithme mimétique qui emploi l’algorithme Nelder-Mead, avec un logiciel d'optimisation pour déterminer les valeurs exactes de plusieurs variables de décisions à chaque évaluation. La méthode de résolution proposée est comparée, en termes de temps d’exécution et de qualités des solutions, avec plusieurs méthodes Métaheuristiques. Mots-clés : Planification de la production, Maintenance préventive imparfaite, Inspection, Qualité, Modèles intégrés, MétaheuristiquesIn this thesis, we study the integrated planning of production, maintenance, and quality in multi-product, multi-period imperfect systems. First, we consider a production system composed of one machine and several products in a time-varying context. The machine deteriorates with time and so, the probability of machine failure, or the risk of a shift to an out-of-control state, increases. The defective rate in the shifted state is higher and so, quality related costs will be imposed. When the machine fails, a corrective maintenance or a minimal repair will be initiated to bring the machine in operation without influencing on its conditions or on the deterioration process. Increasing the expected number of machine failures results in a higher downtime and a lower availability rate. On the other hand, realization of the production plans is significantly influenced by the machine availability and reliability. The interactions between maintenance scheduling and production planning are incorporated in the mathematical model. In the first step, the impact of maintenance on the expected quality level is addressed. The maintenance is also imperfect and the machine conditions after maintenance can be anywhere between as-good-as-new and as-bad-as-old situations. Machine conditions are stated by its effective age, and the machine has several maintenance levels with different costs, execution times, and impacts on the system conditions. High level maintenances on the one hand have greater influences on the improvement of the system state and on the other hand, they occupy more the available production time. The optimal determination of such preventive maintenance levels to be performed at each maintenance intrusion is a challenging problem. A profit maximization model is developed, where the sale of conforming and non-conforming products, costs of production, inventory holding, backorder, setup, preventive and corrective maintenance, machine replacement, and the quality cost are addressed in the objective function. Then, a system with multiple machines is taken into account. In this extension, the number of quality inspections is involved in the joint model. The objective function minimizes the total cost which is the sum of maintenance, production and quality costs. In order to reduce the gap between the theory and the application of joint models, and taking into account the complexity of the integrated problems, we have developed an efficient solution method that is based on the combination of genetic algorithms with local search and problem specific methods. The proposed memetic algorithm employs Nelder-Mead algorithm along with an optimization package for exact determination of the values of several decision variables in each chromosome evolution. The method extracts not only the positive knowledge in good solutions, but also the negative knowledge in poor individuals to determine the algorithm transitions. The method is compared in terms of the solution time and quality to several heuristic methods. Keywords : Multi-period production planning, Imperfect preventive maintenance, Inspection, Quality, Integrated model, Metaheuristic