A Multi-Objective Genetic Algorithm for the Vehicle Routing with Time Windows and Loading Problem

This work presents the Vehicle Routing with Time Windows and Loading Problem (VRTWLP) as a multi-objective optimization problem, implemented within a Genetic Algorithm. Specifically, the three dimensions of the problem to be optimized – the number of vehicles, the total travel distance and volume utilization – are considered to be separated dimensions of a multi-objective space. The quality of the solution obtained using this approach is evaluated and compared with results of other heuristic approaches previously developed by the author. The most significant contribution of this work is our interpretation of VRTWLP as a Multi-objective Optimization Problem

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

Sequential Routing-Loading Algorithm for Optimizing One-Door Container Closed-Loop Logistics Operations

One-door container type of vehicle is the main tool for urban logistics in Indonesia which may take the form of truck, car, or motorcycle container. The operations would be more effective when it is performed through pickup-delivery or forward-reverse at a time. However, there is difficulty to optimize the operation of routing and container loading processes in such a system. This article is proposing an improvement for algorithm for sequential routing- loading process which had been tested in the small datasets but not yet tested in the case of big data set and vehicle routing problem with time windows. The improvement algorithm is tested in big data set with the input of the vehicle routing problem with time windows (VRP-TW) using the solution optimization of the Simulated Annealing process with restart point procedure (SA-R) for the routing optimization and Genetic Algorithm (GA) to optimize the container loading algorithm. The large data sets are hypothetical generated data for 800-2500 single-sized products, 4 types of container capacity, and 100-400 consumer spots. As result, the performance of the proposed algorithm in terms of cost is influenced by the number of spots to be visited by the vehicle and the vehicle capacity. Limitations and further analysis are also described in this article

Large neighbourhood search with adaptive guided ejection search for the pickup and delivery problem with time windows

An effective and fast hybrid metaheuristic is proposed for solving the pickup and delivery problem with time windows. The proposed approach combines local search, large neighbourhood search and guided ejection search in a novel way to exploit the benefits of each method. The local search component uses a novel neighbourhood operator. A streamlined implementation of large neighbourhood search is used to achieve an effective balance between intensification and diversification. The adaptive ejection chain component perturbs the solution and uses increased or decreased computation time according to the progress of the search. While the local search and large neighbourhood search focus on minimising travel distance, the adaptive ejection chain seeks to reduce the number of routes. The proposed algorithm design results in an effective and fast solution method that finds a large number of new best known solutions on a well-known benchmark data set. Experiments are also performed to analyse the benefits of the components and heuristics and their combined use in order to achieve a better understanding of how to better tackle the subject problem

The pickup and delivery problem with time windows and handling operations

This paper introduces the pickup and delivery problem with time windows and handling operations. In this problem, the loading compartment of a vehicle is modeled as a linear LIFO stack. When an item is picked up, it is positioned on top of the stack. When it is on top of the stack, it can be delivered without additional handling. Otherwise, items on top must be unloaded before the delivery and reloaded afterwards, which requires time. We define two rehandling policies. For both policies, rehandling is only allowed at delivery locations and there is no specific reloading order for the rehandled items. Under the first policy, only compulsory rehandling is allowed. Under the second policy, in addition to compulsory rehandling, preventive rehandling is allowed. For each policy, we propose a branch-price-and-cut algorithm with an ad hoc dominance criterion for the labeling algorithm used to generate routes. Computational results are reported on benchmark instances for the pickup and delivery problem with time windows. (C) 2016 Elsevier Ltd. All rights reserved

The split delivery vehicle routing problem with three-dimensional loading constraints

 The Split Delivery Vehicle Routing Problem with three-dimensional loading constraints (3L-SDVRP) combines vehicle routing and three-dimensional loading with additional packing constraints. In the 3L-SDVRP splitting deliveries of customers is basically possible, i.e. a customer can be visited in two or more tours. We examine essential problem features and introduce two problem variants. In the first variant, called 3L-SDVRP with forced splitting, a delivery is only split if the demand of a customer cannot be transported by a single vehicle. In the second variant, termed 3L-SDVRP with optional splitting, splitting customer deliveries can be done any number of times. We propose a hybrid algorithm consisting of a local search algorithm for routing and a genetic algorithm and several construction heuristics for packing. Numerical experiments are conducted using three sets of instances with both industrial and academic origins. One of them was provided by an automotive logistics company in Shanghai; in this case some customers per instance have a total freight volume larger than the loading space of a vehicle. The results prove that splitting deliveries can be beneficial not only in the one-dimensional case but also when goods are modeled as three-dimensional items

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

Search for optimal routes on roads applying metaheuristic algorithms

The design of efficient routes for vehicles visiting a significant number of destinations is a critical factor for the competitiveness of many companies. The design of such routes is known as the vehicle routing problem. Indeed, efficient vehicle routing is one of the most studied problems in the areas of logistics and combinatorial optimization. The present study presents a memetic algorithm that evolves using a mechanism inspired by virus mutations. Additionally, the algorithm uses Taboo Search as an intensification mechanism