A relax-and-repair heuristic for the Swap-Body Vehicle Routing Problem

International audienceIn this paper we address the Swap-Body Vehicle Routing Problem, a variant of the Truck and Trailer Routing Problem. It was introduced in the VeRoLog Challenge 2014. We develop a solution approach that we coin Relax-and-Repair. It consists in solving a relaxed version of the SB-VRP and deriving a feasible solution by repairing the relaxed one. We embed this approach within a population-based heuristic. During computation we store all feasible routes in order to derive better solutions by solving a set-partitioning problem. In order to take advantages of nowadays multi-core machines, our algorithm is designed as a collaborative parallel population-based heuristic. Experimental results show that our relax-and-repair algorithm is very competitive and point the impact of each phase on the quality of the obtained solutions. The advantage of our approach is that it can be adapted to solve complex industrial routing problems

The multi-depot VRP with vehicle interchanges

In real-world logistic operations there are a lot of situations that can be exploited to get better operational strategies. It is important to study these new alternatives, because they can represent significant cost reductions to the companies working with physical distribution. This thesis defines the Multi-Depot Vehicle Routing Problem with Vehicle Interchanges (MDVRPVI). In this problem, both vehicle capacities and duration limits on the routes of the drivers are imposed. To favor a better utilization of the available capacities and working times, it is allowed to combine pairs of routes at predefined interchange locations. The objective of this thesis is to analyze and solve the Multi-Depot Vehicle Routing Problem adding the possibility to interchange vehicles at predefined points. With this strategy, it is possible to reduce the total costs and the number of used routes with respect to the classical approach: The Multi-Depot Vehicle Routing Problem (MDVRP). It should be noted that the MDVRP is more challenging and sophisticated than the single-depot Vehicle Routing Problem (VRP). Besides, most exact algorithms for solving the classical VRP are difficult to adapt in order to solve the MDVRP (Montoya-Torres et al., 2015). From the complexity point of view, the MDVRPVI is NP-Hard, since it is an extension of the classical problem, which is already NP-Hard. We present a tight bound on the costs savings that can be attained allowing interchanges. Three integer programming formulations are proposed based on the classical vehicle-flow formulations of the MDVRP. One of these formulations was solved with a branch-and-bound algorithm, and the other two formulations, with branch-and-cut algorithms. Due to its great symmetry, the first formulation is only able to solve small instances. To increase the dimension of the instances used, we proposed two additional formulations that require one or more families of constraints of exponential size. In order to solve these formulations, we had to design and implement specific branch-and-cut algorithms. For these algorithms we implemented specific separation methods for constraints that had not previously been used in other routing problems. The computational experience performed evidences the routing savings compared with the solutions obtained with the classical approach and allows to compare the efficacy of the three solution methods proposed.En les operacions logístiques del món real es donen situacions que poden ser explotades per obtenir millors estratègies operacionals. És molt important estudiar aquestes noves alternatives, perquè poden representar una reducció significativa de costos per a les companyies que treballen en distribució de mercaderies. En aquesta tesi es defineix el Problema d'Enrutament de Vehicles amb Múltiples Dipòsits i Intercanvi de Vehicles (MDVRPVI). En aquest problema, es consideren tant la capacitat dels vehicles com els límits de duració de les rutes dels conductors. Per tal de millorar la utilització de les capacitats i temps de treball disponibles, es permet combinar parelles de rutes en punts d'intercanvi predefinits. L'objectiu d'aquesta tesi és analitzar i resoldre el problema d'Enrutament de Vehicles amb Múltiples Dipòsits, on es permet l'intercanvi de vehicles. Amb aquesta estratègia, és possible reduir els costos totals i el nombre de les rutes utilitzades respecte l'enfocament clàssic: el problema d'Enrutament de Vehicles amb Múltiples Dipòsits (MDVRP). Cal assenyalar que el MDRVP és més desafiant i sofisticat que el problema d'Enrutament de Vehicles d'un únic dipòsit (VRP). A més, molts algoritmes exactes per resoldre el VRP clàssic son complicats d'adaptar per resoldre el MDVRP (Montoya-Torres et al., 2015). Des del punt de vista de la complexitat, el MDRVPVI és NP-Dur, perquè és una extensió del problema clàssic, que també ho és. Presentem una cota ajustada de l'estalvi en els costos de distribució que es pot obtenir permetent els intercanvis. Es proposen tres formulacions de programació sencera basades en la formulació clàssica “vehicle-flow” del MDVRP. La primera formulació, degut a la seva grandària i la seva simetria, només permet resoldre instàncies molt petites. Per augmentar la dimensió de les instàncies abordables, es proposen dues formulacions addicionals que requereixen una o vàries famílies de restriccions de mida exponencial. Per això, per tal de resoldre el problema amb aquestes formulacions, ha calgut dissenyar i implementar sengles algorismes de tipus branch-and-cut. En aquests algorismes s'han implementat mètodes de separació específics per a les restriccions que no s'havien utilitzat prèviament en altres problemes de rutes. L’experiència computacional realitzada evidencia els estalvis obtinguts comparació amb les solucions corresponents l'enfocament clàssic. També es compara l’eficàcia dels tres mètodes propostes a l'hora de resoldre el problema.Postprint (published version

The multi-depot VRP with vehicle interchanges

In real-world logistic operations there are a lot of situations that can be exploited to get better operational strategies. It is important to study these new alternatives, because they can represent significant cost reductions to the companies working with physical distribution. This thesis defines the Multi-Depot Vehicle Routing Problem with Vehicle Interchanges (MDVRPVI). In this problem, both vehicle capacities and duration limits on the routes of the drivers are imposed. To favor a better utilization of the available capacities and working times, it is allowed to combine pairs of routes at predefined interchange locations. The objective of this thesis is to analyze and solve the Multi-Depot Vehicle Routing Problem adding the possibility to interchange vehicles at predefined points. With this strategy, it is possible to reduce the total costs and the number of used routes with respect to the classical approach: The Multi-Depot Vehicle Routing Problem (MDVRP). It should be noted that the MDVRP is more challenging and sophisticated than the single-depot Vehicle Routing Problem (VRP). Besides, most exact algorithms for solving the classical VRP are difficult to adapt in order to solve the MDVRP (Montoya-Torres et al., 2015). From the complexity point of view, the MDVRPVI is NP-Hard, since it is an extension of the classical problem, which is already NP-Hard. We present a tight bound on the costs savings that can be attained allowing interchanges. Three integer programming formulations are proposed based on the classical vehicle-flow formulations of the MDVRP. One of these formulations was solved with a branch-and-bound algorithm, and the other two formulations, with branch-and-cut algorithms. Due to its great symmetry, the first formulation is only able to solve small instances. To increase the dimension of the instances used, we proposed two additional formulations that require one or more families of constraints of exponential size. In order to solve these formulations, we had to design and implement specific branch-and-cut algorithms. For these algorithms we implemented specific separation methods for constraints that had not previously been used in other routing problems. The computational experience performed evidences the routing savings compared with the solutions obtained with the classical approach and allows to compare the efficacy of the three solution methods proposed.En les operacions logístiques del món real es donen situacions que poden ser explotades per obtenir millors estratègies operacionals. És molt important estudiar aquestes noves alternatives, perquè poden representar una reducció significativa de costos per a les companyies que treballen en distribució de mercaderies. En aquesta tesi es defineix el Problema d'Enrutament de Vehicles amb Múltiples Dipòsits i Intercanvi de Vehicles (MDVRPVI). En aquest problema, es consideren tant la capacitat dels vehicles com els límits de duració de les rutes dels conductors. Per tal de millorar la utilització de les capacitats i temps de treball disponibles, es permet combinar parelles de rutes en punts d'intercanvi predefinits. L'objectiu d'aquesta tesi és analitzar i resoldre el problema d'Enrutament de Vehicles amb Múltiples Dipòsits, on es permet l'intercanvi de vehicles. Amb aquesta estratègia, és possible reduir els costos totals i el nombre de les rutes utilitzades respecte l'enfocament clàssic: el problema d'Enrutament de Vehicles amb Múltiples Dipòsits (MDVRP). Cal assenyalar que el MDRVP és més desafiant i sofisticat que el problema d'Enrutament de Vehicles d'un únic dipòsit (VRP). A més, molts algoritmes exactes per resoldre el VRP clàssic son complicats d'adaptar per resoldre el MDVRP (Montoya-Torres et al., 2015). Des del punt de vista de la complexitat, el MDRVPVI és NP-Dur, perquè és una extensió del problema clàssic, que també ho és. Presentem una cota ajustada de l'estalvi en els costos de distribució que es pot obtenir permetent els intercanvis. Es proposen tres formulacions de programació sencera basades en la formulació clàssica “vehicle-flow” del MDVRP. La primera formulació, degut a la seva grandària i la seva simetria, només permet resoldre instàncies molt petites. Per augmentar la dimensió de les instàncies abordables, es proposen dues formulacions addicionals que requereixen una o vàries famílies de restriccions de mida exponencial. Per això, per tal de resoldre el problema amb aquestes formulacions, ha calgut dissenyar i implementar sengles algorismes de tipus branch-and-cut. En aquests algorismes s'han implementat mètodes de separació específics per a les restriccions que no s'havien utilitzat prèviament en altres problemes de rutes. L’experiència computacional realitzada evidencia els estalvis obtinguts comparació amb les solucions corresponents l'enfocament clàssic. També es compara l’eficàcia dels tres mètodes propostes a l'hora de resoldre el problema

Mathematical Methods and Operation Research in Logistics, Project Planning, and Scheduling

In the last decade, the Industrial Revolution 4.0 brought flexible supply chains and flexible design projects to the forefront. Nevertheless, the recent pandemic, the accompanying economic problems, and the resulting supply problems have further increased the role of logistics and supply chains. Therefore, planning and scheduling procedures that can respond flexibly to changed circumstances have become more valuable both in logistics and projects. There are already several competing criteria of project and logistic process planning and scheduling that need to be reconciled. At the same time, the COVID-19 pandemic has shown that even more emphasis needs to be placed on taking potential risks into account. Flexibility and resilience are emphasized in all decision-making processes, including the scheduling of logistic processes, activities, and projects

A Polyhedral Study of Mixed 0-1 Set

We consider a variant of the well-known single node fixed charge network flow set with constant capacities. This set arises from the relaxation of more general mixed integer sets such as lot-sizing problems with multiple suppliers. We provide a complete polyhedral characterization of the convex hull of the given set

The Dynamic Multi-objective Multi-vehicle Covering Tour Problem

This work introduces a new routing problem called the Dynamic Multi-Objective Multi-vehicle Covering Tour Problem (DMOMCTP). The DMOMCTPs is a combinatorial optimization problem that represents the problem of routing multiple vehicles to survey an area in which unpredictable target nodes may appear during execution. The formulation includes multiple objectives that include minimizing the cost of the combined tour cost, minimizing the longest tour cost, minimizing the distance to nodes to be covered and maximizing the distance to hazardous nodes. This study adapts several existing algorithms to the problem with several operator and solution encoding variations. The efficacy of this set of solvers is measured against six problem instances created from existing Traveling Salesman Problem instances which represent several real countries. The results indicate that repair operators, variable length solution encodings and variable-length operators obtain a better approximation of the true Pareto front

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

From metaheuristics to learnheuristics: Applications to logistics, finance, and computing

Un gran nombre de processos de presa de decisions en sectors estratègics com el transport i la producció representen problemes NP-difícils. Sovint, aquests processos es caracteritzen per alts nivells d'incertesa i dinamisme. Les metaheurístiques són mètodes populars per a resoldre problemes d'optimització difícils en temps de càlcul raonables. No obstant això, sovint assumeixen que els inputs, les funcions objectiu, i les restriccions són deterministes i conegudes. Aquests constitueixen supòsits forts que obliguen a treballar amb problemes simplificats. Com a conseqüència, les solucions poden conduir a resultats pobres. Les simheurístiques integren la simulació a les metaheurístiques per resoldre problemes estocàstics d'una manera natural. Anàlogament, les learnheurístiques combinen l'estadística amb les metaheurístiques per fer front a problemes en entorns dinàmics, en què els inputs poden dependre de l'estructura de la solució. En aquest context, les principals contribucions d'aquesta tesi són: el disseny de les learnheurístiques, una classificació dels treballs que combinen l'estadística / l'aprenentatge automàtic i les metaheurístiques, i diverses aplicacions en transport, producció, finances i computació.Un gran número de procesos de toma de decisiones en sectores estratégicos como el transporte y la producción representan problemas NP-difíciles. Frecuentemente, estos problemas se caracterizan por altos niveles de incertidumbre y dinamismo. Las metaheurísticas son métodos populares para resolver problemas difíciles de optimización de manera rápida. Sin embargo, suelen asumir que los inputs, las funciones objetivo y las restricciones son deterministas y se conocen de antemano. Estas fuertes suposiciones conducen a trabajar con problemas simplificados. Como consecuencia, las soluciones obtenidas pueden tener un pobre rendimiento. Las simheurísticas integran simulación en metaheurísticas para resolver problemas estocásticos de una manera natural. De manera similar, las learnheurísticas combinan aprendizaje estadístico y metaheurísticas para abordar problemas en entornos dinámicos, donde los inputs pueden depender de la estructura de la solución. En este contexto, las principales aportaciones de esta tesis son: el diseño de las learnheurísticas, una clasificación de trabajos que combinan estadística / aprendizaje automático y metaheurísticas, y varias aplicaciones en transporte, producción, finanzas y computación.A large number of decision-making processes in strategic sectors such as transport and production involve NP-hard problems, which are frequently characterized by high levels of uncertainty and dynamism. Metaheuristics have become the predominant method for solving challenging optimization problems in reasonable computing times. However, they frequently assume that inputs, objective functions and constraints are deterministic and known in advance. These strong assumptions lead to work on oversimplified problems, and the solutions may demonstrate poor performance when implemented. Simheuristics, in turn, integrate simulation into metaheuristics as a way to naturally solve stochastic problems, and, in a similar fashion, learnheuristics combine statistical learning and metaheuristics to tackle problems in dynamic environments, where inputs may depend on the structure of the solution. The main contributions of this thesis include (i) a design for learnheuristics; (ii) a classification of works that hybridize statistical and machine learning and metaheuristics; and (iii) several applications for the fields of transport, production, finance and computing