The double traveling salesman problem with partial last-in-first-out loading constraints

In this paper, we introduce the double traveling salesman problem with partial last-in-first-out loading constraints (DTSPPL). It is a pickup-and-delivery single-vehicle routing problem, where all pickup operations must be performed before any delivery operation because the pickup-and-delivery areas are geographically separated. The vehicle collects items in the pickup area and loads them into its container, a horizontal stack. After performing all pickup operations, the vehicle begins delivering the items in the delivery area. Loading and unloading operations must obey a partial last-in-first-out (LIFO) policy, that is, a version of the LIFO policy that may be violated within a given reloading depth. The objective of the DTSPPL is to minimize the total cost, which involves the total distance traveled by the vehicle and the number of items that are unloaded and then reloaded due to violations of the standard LIFO policy. We formally describe the DTSPPL through two integer linear programming (ILP) formulations and propose a heuristic algorithm based on the biased random-key genetic algorithm (BRKGA) to find high-quality solutions. The performance of the proposed solution approaches is assessed over a broad set of instances. Computational results have shown that both ILP formulations have been able to solve only the smaller instances, whereas the BRKGA obtained good-quality solutions for almost all instances, requiring short computational times

Large neighborhood search for the double traveling salesman problem with multiple stacks

This paper considers a complex real-life short-haul/long haul pickup and delivery application. The problem can be modeled as double traveling salesman problem (TSP) in which the pickups and the deliveries happen in the first and second TSPs respectively. Moreover, the application features multiple stacks in which the items must be stored and the pickups and deliveries must take place in reserve (LIFO) order for each stack. The goal is to minimize the total travel time satisfying these constraints. This paper presents a large neighborhood search (LNS) algorithm which improves the best-known results on 65% of the available instances and is always within 2% of the best-known solutions

On the complexity of the multiple stack TSP, kSTSP

The multiple Stack Travelling Salesman Problem, STSP, deals with the collect and the deliverance of n commodities in two distinct cities. The two cities are represented by means of two edge-valued graphs (G1,d2) and (G2,d2). During the pick-up tour, the commodities are stored into a container whose rows are subject to LIFO constraints. As a generalisation of standard TSP, the problem obviously is NP-hard; nevertheless, one could wonder about what combinatorial structure of STSP does the most impact its complexity: the arrangement of the commodities into the container, or the tours themselves? The answer is not clear. First, given a pair (T1,T2) of pick-up and delivery tours, it is polynomial to decide whether these tours are or not compatible. Second, for a given arrangement of the commodities into the k rows of the container, the optimum pick-up and delivery tours w.r.t. this arrangement can be computed within a time that is polynomial in n, but exponential in k. Finally, we provide instances on which a tour that is optimum for one of three distances d1, d2 or d1+d2 lead to solutions of STSP that are arbitrarily far to the optimum STSP

Mathematical models and heuristic algorithms for routing problems with multiple interacting components.

Programa de P?s-Gradua??o em Ci?ncia da Computa??o. Departamento de Ci?ncia da Computa??o, Instituto de Ci?ncias Exatas e Biol?gicas, Universidade Federal de Ouro Preto.Muitos problemas de otimiza??o com aplica??es reais t?m v?rios componentes de intera??o. Cada um deles pode ser um problema pertencente ? classe N P-dif?cil, e eles podem estar em conflito um com o outro, ou seja, a solu??o ?tima para um componente n?o representa necessariamente uma solu??o ?tima para os outros componentes. Isso pode ser um desafio devido ? influ?ncia que cada componente tem na qualidade geral da solu??o. Neste trabalho, foram abordados quatro problemas de roteamento complexos com v?rios componentes de intera??o: o Double Vehicle Routing Problem with Multiple Stacks (DVRPMS), o Double Traveling Salesman Problem with Partial Last-InFirst-Out Loading Constraints (DTSPPL), o Traveling Thief Problem (TTP) e Thief Orienteering Problem (ThOP). Enquanto os DVRPMS e TTP j? s?o bem conhecidos na literatura, os DTSPPL e ThOP foram recentemente propostos a fim de introduzir e estudar variantes mais realistas dos DVRPMS e TTP, respectivamente. O DTSPPL foi proposto a partir deste trabalho, enquanto o ThOP foi proposto de forma independente. Neste trabalho s?o propostos modelos matem?ticos e/ou algoritmos heur?sticos para a solu??o desses problemas. Dentre os resultados alcan?ados, ? poss?vel destacar que o modelo matem?tico proposto para o DVRPMS foi capaz de encontrar inconsist?ncias nos resultados dos algoritmos exatos previamente propostos na literatura. Al?m disso, conquistamos o primeiro e o segundo lugares em duas recentes competi??es de otimiza??o combinat?ria que tinha como objetivo a solu??o de uma vers?o bi-objetiva do TTP. Em geral, os resultados alcan?ados por nossos m?todos de solu??es mostraram-se melhores do que os apresentados anteriormente na literatura considerando cada problema investigado neste trabalho.I would like to express my greatest thanks to my parents, Jo?o Batista and Adelma, and my sister, Jaqueline, for their wise counsel. They have always supported me and given me the strength to continue towards my goals. To Bruna Vilela, I am grateful for her fondness, for always listening to my complaints, and for celebrating with me my personal and academic achievements. I love you all demais da conta1 ! Throughout the writing of this thesis, I have received great assistance. I would like to acknowledge my advisors, Prof. Ph.D. Marcone J. F. Souza, and Prof. Ph.D. Andr? G. Santos, for their support and guidance over these years. I would also like to thank all the authors who have contributed to the research papers produced from this work, in particular, to Prof. Ph.D. Markus Wagner for his great collaboration in some of my projects. I would like to thank Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior (CAPES), and Universidade Federal de Ouro Preto (UFOP) for funding this project. I thank the Universidade Federal de Vi?osa (UFV) for receiving me as a collaborating researcher over these last two years. I could not but offer up my thanks to the HassoPlattner-Institut (HPI) Future SOC Lab, the Divis?o de Suporte ao Desenvolvimento Cient?fico e Tecnol?gico (DCT/UFV), and the Programa de P?s-gradua??o em Ci?ncia da Computa??o (PPGCC/UFOP) for enabling this research by providing access to their computing infrastructure

The pickup and delivery traveling salesman problem with handling costs

This paper introduces the pickup and delivery traveling salesman problem with handling costs (PDTSPH). In the PDTSPH, a single vehicle has to transport loads from origins to destinations. Loading and unloading of the vehicle is operated in a last-in-first-out (LIFO) fashion. However, if a load must be unloaded that was not loaded last, additional handling operations are allowed to unload and reload other loads that block access. Since the additional handling operations take time and effort, penalty costs are associated with them. The aim of the PDTSPH is to find a feasible route such that the total costs, consisting of travel costs and penalty costs, are minimized. We show that the PDTSPH is a generalization of the pickup and delivery traveling salesman problem (PDTSP) and the pickup and delivery traveling salesman problem with LIFO loading (PDTSPL). We propose a large neighborhood search (LNS) heuristic to solve the problem. We compare our LNS heuristic against best known solutions on 163 benchmark instances for the PDTSP and 42 benchmark instances for the PDTSPL. We provide new best known solutions on 52 instances for the PDTSP and on 15 instances for the PDTSPL, besides finding the optimal or best known solution on 102 instances for the PDTSP and on 23 instances for the PDTSPL. The LNS finds optimal or near-optimal solutions on instances for the PDTSPH. Results show that PDTSPH solutions provide large reductions in handling compared to PDTSP solutions, increasing the travel distance by only a small percentage

Heuristic Solution Approaches to the Double TSP with Multiple Stacks

This paper introduces the Double Travelling Salesman Problem with Multiple Stacks and presents three different metaheuristic approaches to its solution. The Double TSP with Multiple Stacks is concerned with determining the shortest route performing pickups and deliveries in two separated networks (one for pickups and one for deliveries) using only one container. Repacking is not allowed, instead each item can be positioned in one of several rows in the container, such that each row can be considered a LIFO stack, but no mutual constraints exist between the rows. Two different neighbourhood structures are developed for the problem and used with each of the heuristics. Finally some computational results are given along with lower bounds on the objective value.

Le problème de tournées de véhicules avec cueillettes, livraisons, fenêtres de temps et contraintes de manutention

RÉSUMÉ : Les problèmes de tournées de véhicules avec cueillettes et livraisons consistent à trouver des tournées réalisables minimisant le nombre de véhicules utilisés et la distante totale parcourue, et permettant de compléter toutes les requêtes. Une requête est définie par un point de cueillette et un point de livraison, et une quantité de marchandise à transporter du point de cueillette au point de livraison. Ce faisant, une tournée est dite réalisable si la charge du véhicule ne dépasse pas sa capacité et si, pour chaque requête, on visite le point de cueillette avant le point de livraison avec le même véhicule. Dans la dernière décennie, la communauté de recherche opérationnelle s’est attaquée à des problèmes de plus en plus complexes qui tiennent compte de contraintes opérationnelles difficiles à traiter. Cette thèse s’insère dans cette tendance. Cette thèse propose des modèles et des algorithmes pour résoudre deux variantes du problème de tournées de véhicules avec cueillettes et livraisons : le problème de tournées de véhicules avec cueillettes, livraisons, fenêtres de temps et contrainte de chargement dernier entré premier sorti (last-in-first-out – LIFO) (pickup and delivery problem with time Windows and LIFO loading – PDPTWL) et le problème de tournées de véhicules avec fenêtres de temps et plusieurs piles (pickup and delivery problem with time windows and multiple stacks – PDPTWMS). Dans le PDPTWL, la contrainte de chargement dernier entré premier sorti stipule qu’aucune manutention non nécessaire n’est faite lors de la livraison d’un item : un item peut seulement être livré s’il est situé sur le dessus de la pile. Dans le PDPTWMS, chaque véhicule contient plusieurs piles qui sont gérées selon une politique de chargement dernier entré premier sorti. Afin de résoudre le PDPTWL, trois algorithmes de génération de colonnes avec plans coupants et un algorithme heuristique sont proposés. Le premier algorithme de génération de colonnes incorpore la contrainte de chargement dans le problème maître, alors que le second l’incorpore dans le sous-problème. Pour ce faire, un algorithme d’étiquetage et un critère de dominance spécialisés sont proposés. Le troisième algorithme de génération de colonnes est une combinaison des deux premiers algorithmes. Des inégalités valides connues sont adaptées pour le PDPTWL. Des instances ayant jusqu’à 75 requêtes sont résolues par ces trois algorithmes exacts en une heure de temps de calcul. L’algorithme heuristique, quant à lui, permet de traiter plus rapidement des instances de plus grande taille. D’abord, un ensemble de solutions initiales est construit avec un algorithme glouton. Puis, pour chaque solution, un algorithme de recherche locale est utilisé afin de diminuer en priorité le nombre de véhicules et ensuite la distance totale parcourue. Puis, deux stratégies sont utilisées pour créer des solutions enfants. La première choisit aléatoirement des tournées de l’ensemble de solutions alors que la deuxième utilise un opérateur de croisement. Pour les deux stratégies, un algorithme de recherche locale est ensuite utilisé. Finalement, les enfants sont ajoutés à l’ensemble de solutions et les meilleurs survivants sont conservés. L’ensemble de solutions est géré afin de garder uniquement les solutions variées de meilleure qualité par rapport au coût total. Des instances ayant jusqu’à 300 requêtes sont résolues par cette heuristique en deux heures de temps de calcul. Afin de résoudre le PDPTWMS, deux algorithmes de génération de colonnes avec plans coupants sont proposés. Le premier algorithme de génération de colonnes incorpore la contrainte de chargement avec plusieurs piles dans le sous-problème. Pour ce faire, un algorithme d’étiquetage et un critère de dominance spécialisés sont proposés. Le deuxième algorithme incorpore partiellement la contrainte de chargement avec plusieurs piles dans le sous-problème et ajoute, au besoin, des contraintes au problème maître lorsque la solution trouvée ne respecte pas la contrainte de chargement avec plusieurs piles. Des instances avec une, deux et trois piles et ayant jusqu’à 75 requêtes sont résolues par ces deux algorithmes exacts en deux heures de temps de calcul.----------ABSTRACT : In the pickup and delivery problem, vehicles based at a depot are used to satisfy a set of requests which consists of transporting goods (or items) from a specific pickup location to a specific delivery location. We consider an unlimited fleet of identical vehicles with multiple homogeneous compartments of limited capacity. A vehicle route is feasible if the load in each compartment of the vehicle does not exceed its capacity and each completed request is first picked up at its pickup location and then delivered at its corresponding delivery location. The pickup and delivery problem consists of determining a set of least-cost feasible routes in which the number of vehicles is first minimized. In the last decade, the operations research community has tackled more complex problems that consider real-life constraints. This thesis follows this trend. This thesis proposes models and algorithms for two variants of the pickup and delivery problem: the pickup and delivery problem with time windows and last-in-first-out (LIFO) loading constraints (PDPTWL) and the pickup and delivery problem with time windows and multiple stacks (PDPTWMS). In the first problem, the LIFO loading rule ensures that no handling is required prior to unloading an item from a vehicle: an item can only be delivered if it is the last one in the stack. In the second problem, each vehicle contains multiple stacks that are operated in a LIFO fashion. To solve the PDPTWL, three exact branch-price-and-cut algorithms and one metaheuristic algorithm are developed. The first branch-price-and-cut algorithm incorporates the LIFO constraints in the master problem. The second branch-price-and-cut algorithm handles the LIFO constraints directly in the shortest path pricing problem and applies a dynamic programming algorithm relying on an ad hoc dominance criterion. The third branch-price-andcut algorithm is a hybrid between the first two. Known valid inequalities are adapted to the PDPTWL. Instances with up to 75 requests are solved within one hour of computational time. The metaheuristic is capable of handling larger instances much faster. First, a set of initial solutions is generated with a greedy randomized adaptive search procedure. For each of these solutions, local search is applied in order to first decrease the total number of vehicles and then the total traveled distance. Two different strategies are used to create offspring. The first selects vehicle routes from the solution pool. The second selects two parents to create an offspring with a crossover operator. For both strategies, local search is then performed on the child solution. Finally, the offspring is added to the population and the best survivors are kept. The population is managed so as to maintain good quality solutions with respect to total cost and population diversity. Instances with up to 300 requests are solved within two hours of computational time. To solve the PDPTWMS, two exact branch-price-and-cut algorithms are proposed. The first branch-price-and-cut algorithm handles the multiple stacks policy in the shortest path pricing problem and applies a dynamic programming algorithm relying on an ad hoc dominance criterion. The second branch-price-and-cut algorithm incorporates the multiple stacks Policy partly in the shortest path pricing problem and adds additional inequalities to the master problem when infeasible LIFO multiple stacks are encountered. Instances with one, two and three stacks involving up to 75 requests are solved within two hours of computational time

The vehicle routing problem with simultaneous pickup and delivery and handling costs

In this paper we introduce the vehicle routing problem with simultaneous pickup and delivery and handling costs (VRPSPD-H). In the VRPSPD-H, a fleet of vehicles operates from a single depot to service all customers, which have both a delivery and a pickup demand such that all delivery items originate from and all pickup items go to the depot. The items on the vehicles are organized as a single linear stack where only the last loaded item is accessible. Handling operations are required if the delivery items are not the last loaded ones. We implement a heuristic handling policy approximating the optimal decisions for the handling sub-problem, and we propose two bounds on the optimal policy, resulting in two new myopic policies. We show that one of the myopic policies outperforms the other one in all configurations, and that it is competitive with the heuristic handling policy if many routes are required. We propose an adaptive large neighborhood search (ALNS) metaheuristic to solve our problem, in which we embed the handling policies. Computational results indicate that our metaheuristic finds optimal solutions on instances of up to 15 customers. We also compare our ALNS metaheuristic against best solutions on benchmark instances of two special cases, the vehicle routing problem with simultaneous pickup and delivery (VRPSPD) and the traveling salesman problem with pickups, deliveries and handling costs (TSPPD-H), and on two related problems, the vehicle routing problem with divisible pickup and delivery (VRPDPD) and the vehicle routing problem with mixed pickup and delivery (VRPMPD). We find or improve 39 out of 54 best known solutions (BKS) for the VRPSPD, 36 out of 54 BKS for the VRPDPD, 15 out of 21 BKS for the VRPMPD, and 69 out of 80 BKS for the TSPPD-H. Finally, we introduce and analyze solutions for the variations of the VRPDPD and VRPMPD with handling costs – the VRPDPD-H and the VRPMPD-H, respectively