Genetic Algorithms with Neural Cost Predictor for Solving Hierarchical Vehicle Routing Problems

When vehicle routing decisions are intertwined with higher-level decisions, the resulting optimization problems pose significant challenges for computation. Examples are the multi-depot vehicle routing problem (MDVRP), where customers are assigned to depots before delivery, and the capacitated location routing problem (CLRP), where the locations of depots should be determined first. A simple and straightforward approach for such hierarchical problems would be to separate the higher-level decisions from the complicated vehicle routing decisions. For each higher-level decision candidate, we may evaluate the underlying vehicle routing problems to assess the candidate. As this approach requires solving vehicle routing problems multiple times, it has been regarded as impractical in most cases. We propose a novel deep-learning-based approach called Genetic Algorithm with Neural Cost Predictor (GANCP) to tackle the challenge and simplify algorithm developments. For each higher-level decision candidate, we predict the objective function values of the underlying vehicle routing problems using a pre-trained graph neural network without actually solving the routing problems. In particular, our proposed neural network learns the objective values of the HGS-CVRP open-source package that solves capacitated vehicle routing problems. Our numerical experiments show that this simplified approach is effective and efficient in generating high-quality solutions for both MDVRP and CLRP and has the potential to expedite algorithm developments for complicated hierarchical problems. We provide computational results evaluated in the standard benchmark instances used in the literature

Approches générales de résolution pour les problèmes multi-attributs de tournées de véhicules et confection d'horaires

Thèse réalisée en cotutelle entre l'Université de Montréal et l'Université de Technologie de TroyesLe problème de tournées de véhicules (VRP) implique de planifier les itinéraires d'une flotte de véhicules afin de desservir un ensemble de clients à moindre coût. Ce problème d'optimisation combinatoire NP-difficile apparait dans de nombreux domaines d'application, notamment en logistique, télécommunications, robotique ou gestion de crise dans des contextes militaires et humanitaires. Ces applications amènent différents contraintes, objectifs et décisions supplémentaires ; des "attributs" qui viennent compléter les formulations classiques du problème. Les nombreux VRP Multi-Attributs (MAVRP) qui s'ensuivent sont le support d'une littérature considérable, mais qui manque de méthodes généralistes capables de traiter efficacement un éventail significatif de variantes. Par ailleurs, la résolution de problèmes "riches", combinant de nombreux attributs, pose d'importantes difficultés méthodologiques. Cette thèse contribue à relever ces défis par le biais d'analyses structurelles des problèmes, de développements de stratégies métaheuristiques, et de méthodes unifiées. Nous présentons tout d'abord une étude transversale des concepts à succès de 64 méta-heuristiques pour 15 MAVRP afin d'en cerner les "stratégies gagnantes". Puis, nous analysons les problèmes et algorithmes d'ajustement d'horaires en présence d'une séquence de tâches fixée, appelés problèmes de "timing". Ces méthodes, développées indépendamment dans différents domaines de recherche liés au transport, ordonnancement, allocation de ressource et même régression isotonique, sont unifiés dans une revue multidisciplinaire. Un algorithme génétique hybride efficace est ensuite proposé, combinant l'exploration large des méthodes évolutionnaires, les capacités d'amélioration agressive des métaheuristiques à voisinage, et une évaluation bi-critère des solutions considérant coût et contribution à la diversité de la population. Les meilleures solutions connues de la littérature sont retrouvées ou améliorées pour le VRP classique ainsi que des variantes avec multiples dépôts et périodes. La méthode est étendue aux VRP avec contraintes de fenêtres de temps, durée de route, et horaires de conducteurs. Ces applications mettent en jeu de nouvelles méthodes d'évaluation efficaces de contraintes temporelles relaxées, des phases de décomposition, et des recherches arborescentes pour l'insertion des pauses des conducteurs. Un algorithme de gestion implicite du placement des dépôts au cours de recherches locales, par programmation dynamique, est aussi proposé. Des études expérimentales approfondies démontrent la contribution notable des nouvelles stratégies au sein de plusieurs cadres méta-heuristiques. Afin de traiter la variété des attributs, un cadre de résolution heuristique modulaire est présenté ainsi qu'un algorithme génétique hybride unifié (UHGS). Les attributs sont gérés par des composants élémentaires adaptatifs. Des expérimentations sur 26 variantes du VRP et 39 groupes d'instances démontrent la performance remarquable de UHGS qui, avec une unique implémentation et paramétrage, égalise ou surpasse les nombreux algorithmes dédiés, issus de plus de 180 articles, révélant ainsi que la généralité ne s'obtient pas forcément aux dépends de l'efficacité pour cette classe de problèmes. Enfin, pour traiter les problèmes riches, UHGS est étendu au sein d'un cadre de résolution parallèle coopératif à base de décomposition, d'intégration de solutions partielles, et de recherche guidée. L'ensemble de ces travaux permet de jeter un nouveau regard sur les MAVRP et les problèmes de timing, leur résolution par des méthodes méta-heuristiques, ainsi que les méthodes généralistes pour l'optimisation combinatoire.The Vehicle Routing Problem (VRP) involves designing least cost delivery routes to service a geographically-dispersed set of customers while taking into account vehicle-capacity constraints. This NP-hard combinatorial optimization problem is linked with multiple applications in logistics, telecommunications, robotics, crisis management in military and humanitarian frameworks, among others. Practical routing applications are usually quite distinct from the academic cases, encompassing additional sets of specific constraints, objectives and decisions which breed further new problem variants. The resulting "Multi-Attribute" Vehicle Routing Problems (MAVRP) are the support of a vast literature which, however, lacks unified methods capable of addressing multiple MAVRP. In addition, some "rich" VRPs, i.e. those that involve several attributes, may be difficult to address because of the wide array of combined and possibly antagonistic decisions they require. This thesis contributes to address these challenges by means of problem structure analysis, new metaheuristics and unified method developments. The "winning strategies" of 64 state-of-the-art algorithms for 15 different MAVRP are scrutinized in a unifying review. Another analysis is targeted on "timing" problems and algorithms for adjusting the execution dates of a given sequence of tasks. Such methods, independently studied in different research domains related to routing, scheduling, resource allocation, and even isotonic regression are here surveyed in a multidisciplinary review. A Hybrid Genetic Search with Advanced Diversity Control (HGSADC) is then introduced, which combines the exploration breadth of population-based evolutionary search, the aggressive-improvement capabilities of neighborhood-based metaheuristics, and a bi-criteria evaluation of solutions based on cost and diversity measures. Results of remarkable quality are achieved on classic benchmark instances of the capacitated VRP, the multi-depot VRP, and the periodic VRP. Further extensions of the method to VRP variants with constraints on time windows, limited route duration, and truck drivers' statutory pauses are also proposed. New route and neighborhood evaluation procedures are introduced to manage penalized infeasible solutions w.r.t. to time-window and duration constraints. Tree-search procedures are used for drivers' rest scheduling, as well as advanced search limitation strategies, memories and decomposition phases. A dynamic programming-based neighborhood search is introduced to optimally select the depot, vehicle type, and first customer visited in the route during local searches. The notable contribution of these new methodological elements is assessed within two different metaheuristic frameworks. To further advance general-purpose MAVRP methods, we introduce a new component-based heuristic resolution framework and a Unified Hybrid Genetic Search (UHGS), which relies on modular self-adaptive components for addressing problem specifics. Computational experiments demonstrate the groundbreaking performance of UHGS. With a single implementation, unique parameter setting and termination criterion, this algorithm matches or outperforms all current problem-tailored methods from more than 180 articles, on 26 vehicle routing variants and 39 benchmark sets. To address rich problems, UHGS was included in a new parallel cooperative solution framework called "Integrative Cooperative Search (ICS)", based on problem decompositions, partial solutions integration, and global search guidance. This compendium of results provides a novel view on a wide range of MAVRP and timing problems, on efficient heuristic searches, and on general-purpose solution methods for combinatorial optimization problems

Revisión de la literatura del problema de ruteo de vehículos en un contexto de transporte verde

In the efficient management of the supply chain the optimal management of transport of consumables and finished products appears. The costs associated with transport have direct impact on the final value consumers must pay, which in addition to requiring competitive products also demand that they are generated in environmentally friendly organizations. Aware of this reality, this document is intended to be a starting point for Master’s and Doctoral degree students who want to work in a line of research recently proposed: green routing. The state of the art of the vehicle routing problem is presented in this paper, listing its variants, models and methodologies for solution. Furthermore, the proposed interaction between variants of classical routing problems and environmental effects of its operations, known in the literature as Green- VRP is presented. The goal is to generate a discussion in which mathematical models and solution strategies that can be applied within organizations that consider within their objectives an efficient and sustainable operation are posed.En el gerenciamiento eficiente de la cadena de suministro aparece la gestión óptima del transporte de insumos y productos terminados. Los costos asociados al transporte tienen impacto directo sobre el valor final que deben pagar los consumidores, que además de requerir productos competitivos también exigen que los mismos sean generados en organizaciones amigables con el medioambiente. Consientes de esa realidad este documento pretende ser un punto de partida para estudiantes de maestría y doctorado que quieran trabajar en una línea de investigación propuesta recientemente: el ruteo verde. En este trabajo se muestra un estado del arte del problema de ruteo de vehículos, enumerando sus variantes, modelos y metodologías de solución. Además, se presenta la interacción que se ha propuesto entre variantes clásicas de los problemas de ruteo y los efectos ambientales de su operación, denominados en la literatura como Green-VRP. El objetivo es generar una discusión donde se planteen modelos matemáticos y estrategias de solución que puedan ser aplicadas en organizaciones que consideren dentro de sus objetivos una operación eficiente y sustentable

REVISIÓN DE LA LITERATURA DEL PROBLEMA DE RUTEO DE VEHÍCULOS EN UN CONTEXTO DE TRANSPORTE VERDE

In the efficient management of the supply chain the optimal management of transport of consumables and finished products appears. The costs associated with transport have direct impact on the final value consumers must pay, which in addition to requiring competitive products also demand that they are generated in environmentally friendly organizations. Aware of this reality, this document is intended to be a starting point for Master's and Doctoral degree students who want to work in a line of research recently proposed: green routing. The state of the art of the vehicle routing problem is presented in this paper, listing its variants, models and methodologies for solution. Furthermore, the proposed interaction between variants of classical routing problems and environmental effects of its operations, known in the literature as Green-VRP is presented. The goal is to generate a discussion in which mathematical models and solution strategies that can be applied within organizations that consider within their objectives an efficient and sustainable operation are posed. En el gerenciamiento eficiente de la cadena de suministro aparece la gestión óptima del transporte de insumos y productos terminados. Los costos asociados al transporte tienen impacto directo sobre el valor final que deben pagar los consumidores, que además de requerir productos competitivos también exigen que los mismos sean generados en organizaciones amigables con el medioambiente. Consientes de esa realidad este documento pretende ser un punto de partida para estudiantes de maestría y doctorado que quieran trabajar en una línea de investigación propuesta recientemente: el ruteo verde. En este trabajo se muestra un estado del arte del problema de ruteo de vehículos, enumerando sus variantes, modelos y metodologías de solución. Además, se presenta la interacción que se ha propuesto entre variantes clásicas de los problemas de ruteo y los efectos ambientales de su operación, denominados en la literatura como Green-VRP. El objetivo es generar una discusión donde se planteen modelos matemáticos y estrategias de solución que puedan ser aplicadas en organizaciones que consideren dentro de sus objetivos una operación eficiente y sustentable. Document type: Articl

Two-step Meta-heuristic Approach for a Vehicle Assignment Problem – Case from İstanbul/Turkey

In this paper, a two-step meta-heuristic approach is proposed for vehicle assignment problem with geometric shape-based clustering and genetic algorithm. First, the geometric shape-based clustering method is used and then the solution of this method is given to the genetic algorithm as initial solution. The solution process is continued by genetic algorithm. There are 282 bus lines in İstanbul European side. Those buses should be assigned to six bus garages. The proposed method is used to determine the minimum distance between the bus lines and garages by assigning buses to garages. According to the computational results, the proposed algorithm has better clustering performance in terms of the distance from each bus-line start point to each bus garage in the cluster. The crossover rate changing method is also applied as a trial in order to improve the algorithm performance. Finally, the outputs that are generated by different crossover rates are compared with the results of the k-Nearest Neighbour algorithm to prove the effectiveness of the study.</p

A Hybrid Heuristic for a Broad Class of Vehicle Routing Problems with Heterogeneous Fleet

We consider a family of Rich Vehicle Routing Problems (RVRP) which have the particularity to combine a heterogeneous fleet with other attributes, such as backhauls, multiple depots, split deliveries, site dependency, open routes, duration limits, and time windows. To efficiently solve these problems, we propose a hybrid metaheuristic which combines an iterated local search with variable neighborhood descent, for solution improvement, and a set partitioning formulation, to exploit the memory of the past search. Moreover, we investigate a class of combined neighborhoods which jointly modify the sequences of visits and perform either heuristic or optimal reassignments of vehicles to routes. To the best of our knowledge, this is the first unified approach for a large class of heterogeneous fleet RVRPs, capable of solving more than 12 problem variants. The efficiency of the algorithm is evaluated on 643 well-known benchmark instances, and 71.70\% of the best known solutions are either retrieved or improved. Moreover, the proposed metaheuristic, which can be considered as a matheuristic, produces high quality solutions with low standard deviation in comparison with previous methods. Finally, we observe that the use of combined neighborhoods does not lead to significant quality gains. Contrary to intuition, the computational effort seems better spent on more intensive route optimization rather than on more intelligent and frequent fleet re-assignments

Hybrid Metaheuristics for the Clustered Vehicle Routing Problem

The Clustered Vehicle Routing Problem (CluVRP) is a variant of the Capacitated Vehicle Routing Problem in which customers are grouped into clusters. Each cluster has to be visited once, and a vehicle entering a cluster cannot leave it until all customers have been visited. This article presents two alternative hybrid metaheuristic algorithms for the CluVRP. The first algorithm is based on an Iterated Local Search algorithm, in which only feasible solutions are explored and problem-specific local search moves are utilized. The second algorithm is a Hybrid Genetic Search, for which the shortest Hamiltonian path between each pair of vertices within each cluster should be precomputed. Using this information, a sequence of clusters can be used as a solution representation and large neighborhoods can be efficiently explored by means of bi-directional dynamic programming, sequence concatenations, by using appropriate data structures. Extensive computational experiments are performed on benchmark instances from the literature, as well as new large scale ones. Recommendations on promising algorithm choices are provided relatively to average cluster size.Comment: Working Paper, MIT -- 22 page

A Comparative Study of the PSO and GA for the m-MDPDPTW

The m-MDPDPTW is the multi-vehicles, multi-depots pick-up and delivery problem with time windows. It is an optimization vehicles routing problem which must meet requests for transport between suppliers and customers for the purpose of satisfying precedence, capacity and time constraints. This problem is a very important class of operational research, which is part of the category of NP-hard problems. Its resolution therefore requires the use of evolutionary algorithms such as Genetic Algorithms (GA) or Particle Swarm Optimization (PSO). We present, in this sense, a comparative study between two approaches based respectively on the GA and the PSO for the optimization of m-MDPDPTW. We propose, in this paper, a literature review of the Vehicle Routing Problem (VRP) and the Pick-up and Delivery Problem with Time Windows (PDPTW), present our approaches, whose objective is to give a satisfying solution to the m-MDPDPTW minimizing the total distance travelled. The performance of both approaches is evaluated using various sets instances from [10] PDPTW benchmark data problems. From our study, in the case of m-MDPDPTW problem, the proposed GA reached to better results compared with the PSO algorithm and can be considered the most appropriate model to solve our m-MDPDPTW problem

SOLUCIÓN DEL MDVRP USANDO EL ALGORITMO DE BÚSQUEDA LOCAL ITERADA

En este artículo se propone una metodología para resolver el problema de ruteo considerando múltiples depósitos (MDVRP).  El modelo contempla situaciones con y sin restricción de distancia.  En el proceso de búsqueda se aceptan soluciones infactibles por sobrecarga en vehículos, depósitos y longitud de ruta, las cuales son llevadas como penalidades en la función objetivo.  Para su solución es implementado el algoritmo de Búsqueda Local Iterada (Iterated Local Search).  En la construcción de la solución inicial se usan heurísticas basadas en técnicas de clusterización.  La metodología es verificada usando casos de prueba de la literatura, los resultados obtenidos y tiempos de cómputo son comparados con los registros existentes