Pickup And Delivery Problem Research Articles

Solving pick-up and delivery problems via deep reinforcement learning based symmetric neural optimization

Recently, there has been a growing trend to use deep reinforcement learning (DRL) to solve NP-hard combinatorial optimization problems such as routing problem, where a policy learned by a deep neural network guides the sequential construction of solutions. Despite their success, most of the previous studies omit the symmetry between the partitions of instances and between solutions, which makes them less effective in handling the more practical scenarios with symmetric features, such as pick-up and delivery problems (PDPs). PDPs are more challenging and practical than traditional routing problems because the correlation between pick-up nodes and delivery nodes in the former is multiple one-to-one and not simple as the correlation in the latter. Besides, most DRL-based methods cannot take both computational cost and the quality of solutions into account. To resolve this issue, we propose the Symmetric Neural Optimization for Pick-up and Delivery Problems (PD-SNO) to solve the pick-up and delivery traveling salesman problem (PDTSP) and the multi-commodity one-to-one pick-up and delivery traveling salesman problem (m-PDTSP), respectively. The PD-SNO leverages the symmetries between different partitions of instances to effectively capture the relationship between symmetric node sets (i.e., pick-up nodes and delivery nodes); the PD-SNO also leverages the symmetry between different trajectories of solution to guide the construction of solutions and training of policy. We evaluate the performance of our PD-SNO, and the results show that it outperforms various representative baselines, including traditional methods (both exact and heuristic algorithms) and state-of-the-art DRL-based methods (both construction and improvement types) on synthetic datasets. Then, we further assess the generalization performance of our PD-SNO on benchmark datasets. Finally, we research the independent effectiveness of our designs through ablation studies.

Efficient Neural Collaborative Search for Pickup and Delivery Problems.

In this paper, we introduce Neural Collaborative Search (NCS), a novel learning-based framework for efficiently solving pickup and delivery problems (PDPs). NCS pioneers the collaboration between the latest prevalent neural construction and neural improvement models, establishing a collaborative framework where an improvement model iteratively refines solutions initiated by a construction model. Our NCS collaboratively trains the two models via reinforcement learning with an effective shared-critic mechanism. In addition, the construction model enhances the improvement model with high-quality initial solutions via curriculum learning, while the improvement model accelerates the convergence of the construction model through imitation learning. Besides the new framework design, we also propose the efficient Neural Neighborhood Search (N2S), an efficient improvement model employed within the NCS framework. N2S exploits a tailored Markov decision process formulation and two customized decoders for removing and then reinserting a pair of pickup-delivery nodes, thereby learning a ruin-repair search process for addressing the precedence constraints in PDPs efficiently. To balance the computation cost between encoders and decoders, N2S streamlines the existing encoder design through a light Synthesis Attention mechanism that allows the vanilla self-attention to synthesize various features regarding a route solution. Moreover, a diversity enhancement scheme is further leveraged to ameliorate the performance during the inference of N2S. Our NCS and N2S are both generic, and extensive experiments on two canonical PDP variants show that they can produce state-of-the-art results among existing neural methods. Remarkably, our NCS and N2S could surpass the well-known LKH3 solver especially on the more constrained PDP variant.

A many-to-many pick-up and delivery problem under stochastic battery depletion of electric vehicles

ABSTRACT The study extends the traditional pick-up and delivery problems (PDPs) to address the specific challenges of urban logistics and electric vehicle (EV) adoption. These challenges include the limited range of EVs, energy consumption along the route, and uncertainty in traffic conditions. To overcome the limited range of EVs, the study includes battery swapping stations to ensure sufficient energy to complete delivery routes. Vehicle energy consumption is considered to reduce range anxiety and optimize energy use. The study also considers the unpredictability of traffic conditions that affect energy consumption and delivery schedules. To address these concerns, the study proposes an approximate Quadratic Chance-Constrained Mixed-Integer Programming (QC-MIP) model with a linear approximation, a constructive heuristic and a meta-heuristic. These quantitative models incorporate comprehensive EV energy estimation approaches, enabling more accurate energy predictions. The proposed approaches provide valuable insights and strategies for improving energy efficiency and delivery performance in urban logistics environments.

Real-World Pickup and Delivery Problem with Transfers

The pickup and delivery problem with transfers generalizes the classical pickup and delivery problem (PDP) by allowing the vehicles to exchange request loads at designated transfer points. Transfers often lead to substantial reductions in transportation costs, yet they come with a significant burden of additional computational complexity. Even meta-heuristic methods are thus limited to instances of at most lower hundreds of requests leaving the desirable benefits unreachable for larger instances. Our approach bypasses the complexities inherent to current methods by deciding about the transfers apriori and thus reducing the problem to a PDP instance. To make as informed decisions as possible, we analyze a broader set of characteristics that may be used to carry out the apriori decisions. We opt to derive and examine multiple such PDP instances to cover different transfer choices. Our analysis of the derived PDP instances then allows their efficient processing in parallel. The proposed framework addresses a large-scale freight transportation problem with real-world characteristics and transfers where typical instances count over 1,200 requests and 300 vehicles. We show the potential of the proposed framework on both real-world and synthetic instances with up to 1,500 requests. The experiments demonstrate that substantial savings may be achieved within favorable runtimes even for very large instances.

Joint resource optimization and trajectory design for energy minimization in UAV-assisted mobile-edge computing systems

This paper studies an unmanned aerial vehicle (UAV)-assisted mobile-edge computing (MEC) system, where a rotary-wing UAV equipped with computing platforms is used to assist ground users (GUs) with insufficient computing resource. Each GU offloads part of the task to the UAV for computation through the uplink, and the remaining computation task is computed by itself. Then, UAV will return the results to the corresponding GU via downlink. Considering the results for each GU is not only used by itself, but may also be sent to other GUs for data fusion, we thus design two specific scenarios in this paper: (1) homologous UAV-assisted MEC scenario, i.e. UAV receives the computation task of GUs and then returns the results to the identical GUs, and (2) non-homologous UAV-assisted MEC scenario, i.e., UAV receives the computation task of source GUs and returns the results to the corresponding destination GUs. For these two scenarios, we propose an energy minimization problem by jointly optimizing task partition, the time slot length and UAV trajectory. In particular, we use the path discretization approach to convert the problem as a problem form which is finite variables. Since the problem is non-convex, we use successive convex approximation (SCA) techniques to tackle the non-convexity. Considering the initial trajectory has an important affect on the experimental result, then a specific trajectory initialization design via combining with the Pickup-and-Delivery Problem (PDP) is proposed. Numerical results proof our proposed design is superior compared with the benchmark cases.

MAPDP: Cooperative Multi-Agent Reinforcement Learning to Solve Pickup and Delivery Problems

Cooperative Pickup and Delivery Problem (PDP), as a variant of the typical Vehicle Routing Problems (VRP), is an important formulation in many real-world applications, such as on-demand delivery, industrial warehousing, etc. It is of great importance to efficiently provide high-quality solutions of cooperative PDP. However, it is not trivial to provide effective solutions directly due to two major challenges: 1) the structural dependency between pickup and delivery pairs require explicit modeling and representation. 2) the cooperation between different vehicles is highly related to the solution exploration and difficult to model. In this paper, we propose a novel multi-agent reinforcement learning based framework to solve the cooperative PDP (MAPDP). First, we design a paired context embedding to well measure the dependency of different nodes considering their structural limits. Second, we utilize cooperative multi-agent decoders to leverage the decision dependence among different vehicle agents based on a special communication embedding. Third, we design a novel cooperative A2C algorithm to train the integrated model. We conduct extensive experiments on a randomly generated dataset and a real-world dataset. Experiments result shown that the proposed MAPDP outperform all other baselines by at least 1.64\% in all settings, and shows significant computation speed during solution inference.

The pickup and delivery problem with transshipments: Critical review of two existing models and a new formulation

The pickup and delivery problem with transshipments (PDP-T) is generalized from the classical pickup and delivery problem (PDP) by allowing the transfer of requests between vehicles. After considering the time window constraints, the PDP-T is further generalized to the pickup and delivery problem with time windows and transshipments (PDPTW-T). In this paper, we review two state-of-the-art models for the PDP-T and PDPTW-T. We point out the possible issues existing in the models and provide our revisions. In addition, we develop a new mixed-integer linear programming formulation to solve the PDP-T and PDPTW-T. The performance of the proposed model is evaluated by solving 340 generated PDP-T instances and 360 open-access PDPTW-T instances. Computational results show that the proposed model outperforms the existing models in terms of solution quality and computing time. PTP-T instances with up to 25 requests and 2 transfer stations are solved to optimality by using the proposed model. As a comparison, the best-known benchmarks in the literature are instances with 5 requests and 1 transfer station. In addition, the computing time is significantly reduced. In our experiments, the average computational time for solving PDP-T is reduced by 96%. For PDPTW-T instances, the solvable scale is increased from 3 requests and 4 transfer stations to 5 requests and 4 transfer stations. The average computing time is reduced by 40%.

Complexity Analysis of Green Pickup-and-Delivery Problems on Ring Structures

In a Green Pickup-and Delivery problem (GPD), green vehicles (e.g., electric or hybrid cars) are used for routing in the problem domain, and these vehicles are particularly constrained with limited fuel capacity, thus shorter traveling range. A refueling infrastructure providing wide-area coverage, meanwhile, has not been fully developed to this end. A recent study reveals that vehicle routing inessence with green constraints only, is at least weakly NP-hard, motivating us to pursue a deeper understanding of the underlying computational challenge associated with this “green” intractability. In this paper we perform complexity analysis on several GPD subproblems (namely, RINGs), that is, theproblems whose task-graphs are under a ring structure. Using measures of width/length of rings, we delineate clearly two complexity boundaries: one between weakly and strongly NP-complete, and the other between tractable and intractable in general. Our results bring new insights for the research anddevelopment (current and active, but with limited success only to this point) of heuristics or algorithmsfor solving GPDs

CiteSpace-Based Bibliometric Review of Pickup and Delivery Problem from 1995 to 2021

In this paper, we adopt the bibliometric analysis software CiteSpace to analyze the research status quo and evolution trend of pickup and delivery problem (PDP), an important real-world issue occurring in logistics and transportation. We obtain 819 documents with the topic of PDP that were published in the Web of Science core collection during the period 1995–2021, and acquire their basic situation of posting trend and category distribution. Next, we employ CiteSpace to draw scientific knowledge maps and perform the corresponding visualization analysis, which mainly include the following aspects: (a) collaboration analysis of author, country, and institution; (b) co-citation analysis of author, journal, and reference; (c) citation burst detection of keyword; (d) co-citation clustering analysis of reference. The results show that PDP research has gradually become interdisciplinary and highly comprehensive, and the evolution trend of hot topics also reflects that the research directions involve multiple academic disciplines and professional areas ranging from algorithm design to logistics management. The changing knowledge components reveal the fact that the development of PDP research is highly related to the diversity and uncertainty of realistic logistics industry contexts. Study in this paper provides comprehensive understandings of PDP research for scholars and logistics practitioners, inspiring its further investigation.

The pickup and delivery problem with alternative locations and overlapping time windows

Online second-hand marketplaces have seen a vast increase in transactions in recent years, although sending and receiving parcels can be an inconvenience for private buyers and sellers in C2C settings. To facilitate transportation providers expanding their product portfolio with alternative concepts, we consider the pickup and delivery problem (PDP) with alternative locations and overlapping time windows. The transportation requests have to be served by a fleet of homogeneously capacitated vehicles. Each request may have multiple roaming pickup locations throughout the day with non-overlapping time windows (since the product cannot be in two places at once). A request may also have many roaming delivery locations, and additionally an alternative recipient with their own set of roaming locations. As such, several persons in different locations can be available simultaneously to accept a delivery. Recipients could also use 24-hour locker boxes if these are conveniently located.We propose a solution approach based on a multi-start, adaptive, large neighborhood search with problem specific operators, to solve the pickup and delivery problem with alternative locations. We compare our algorithm with similar problems from the literature and examine in detail different scenarios based on real data provided by an Austrian logistics provider. In particular, we explore the benefits of locker boxes, roaming locations, alternative recipients, and mixed customer profiles based on different preferences concerning data sharing and convenience. We found that an increase in flexibility and convenience for the customers translates into cost savings up to almost 30% for the carriers.

VRP variants applicable to collecting donations and similar problems: A taxonomic review

This paper presents a taxonomic review of Vehicle Routing Problem (VRP) with Time Windows (VRPTW), Pick-up and Delivery Problem (PDP), and Periodic Vehicle Routing Problem (PVRP). We focus on the problems of collection goods and similar. The applications of these models are typical like found in the literature; however, not applications specifically about collecting donations were found. Because of concern for the environment, social equity, and business efficiency, specific research fields related to green and reverse logistics have arisen; thus, optimization of waste (second-hand goods, food, recyclable/no recyclable waste, etc.) collection routes gain interest. In the literature reviewed, we found several VRP models of goods collection applied to picks-up of returned items, End-of-Life (EOL) products, Municipal Solid Waste collection (MSW), and Waste Collection Problem (WCP). The primary purpose of this paper is to structure the taxonomy of VRPTW, PDP and PVRP problems applicable to collecting donations according to its features, solution methods, and mathematical formulation. Likewise, provide the reader with an outline orderly and differentiated from the VRP models associated with pick up items and delivery orders (VRPPD), backhauling customers (VRPB), collection waste, and similar problems to propose our problem. For clarity, Appendix A includes the acronym used in these types of problems. This paper is part of a larger research project called “CVRPTW model applied to collecting food donations,” intending to contribute to a new perspective on the routing problems little explored.

A column generation and Combinatorial Benders Decomposition algorithm for the Selective Dial-A-Ride-Problem

In Pickup-and-Delivery Problems (PDP), one must design a set of vehicle routes that visit matching pickup and delivery locations. The Selective Dial-A-Ride Problem (SDARP) is a PDP which aims to serve as many pickup–delivery pairs as possible, where each pair has a time window and a maximum ride time. This paper introduces Extended Fragments to solve the SDARP. Extended Fragments stem from a subclass of vehicle routes which can be directly enumerated. An Extended Fragment formulation for the SDARP is proposed and solved using Combinatorial Benders Decomposition, augmented by a time discretisation and a novel variable-fixing technique. This algorithm, along with other recent ‘fragment’-based methods for PDP, is an a priori column generation method, combined with Combinatorial Benders Decomposition. The new method solves the existing benchmark for the SDARP, including 11 previously-unsolved instances.

A GRASP-ALNS combination for robust pickup and delivery problem

One of the well-studied routing issues is the Pickup and Delivery Problem (PDP). It aims to route a fleet of vehicles based on a depot to satisfy a set of transport requests subject to numerous constraints. In real-life cases, the satisfaction of those requests over a given time slot (1 day for example) may become impossible while respecting all problem constraints. Therefore, the studied variant is characterised by the selective aspect which consists of choosing a subset of demands to be honoured. In addition, travel times between sites may be uncertain and may vary according to several scenarios. The robustness consists then at finding a solution which remains feasible over all scenarios. Therefore, the goal of this study is to introduce lexicographic and metaheuristic approaches to solve the Robust Selective PDP (RSPDP). Numerous tests have been done on new instances for the considered variant, in order to show the efficiency of proposed approaches.

Heterogeneous Attentions for Solving Pickup and Delivery Problem via Deep Reinforcement Learning

Recently, there is an emerging trend to apply deep reinforcement learning to solve the vehicle routing problem (VRP), where a learnt policy governs the selection of next node for visiting. However, existing methods could not handle well the pairing and precedence relationships in the pickup and delivery problem (PDP), which is a representative variant of VRP. To address this challenging issue, we leverage a novel neural network integrated with a heterogeneous attention mechanism to empower the policy in deep reinforcement learning to automatically select the nodes. In particular, the heterogeneous attention mechanism specifically prescribes attentions for each role of the nodes while taking into account the precedence constraint, i.e., the pickup node must precede the pairing delivery node. Further integrated with a masking scheme, the learnt policy is expected to find higher-quality solutions for solving PDP. Extensive experimental results show that our method outperforms the state-of-the-art heuristic and deep learning model, respectively, and generalizes well to different distributions and problem sizes.

A Large Neighborhood Search for the Pickup and Delivery Problem with Time Windows, Split Loads and Transshipments

In the pickup and delivery problem (PDP) a fleet of capacitated vehicles must be routed in order to satisfy a set of customer requests. In this article, we address a variant of the one-to-one PDP where each customer location can be visited several times and load may be transshipped from one vehicle to another at specific locations. The goal is to minimize the sum of travel costs and transshipment costs. The corresponding problem is called the PDP with time windows, split loads and transshipments. We present an arc-based mixed-integer formulation for the problem and propose a large neighbourhood search metaheuristic for solving it. Extensive computational experiments using both benchmark instances from the literature and instances based on real-world data illustrate the performance of the solution method and give insights regarding the benefits of combining split loads and transshipments.

A Compact Arc-Based ILP Formulation for the Pickup and Delivery Problem with Divisible Pickups and Deliveries

We consider the capacitated single vehicle one-to-one pickup and delivery problem with divisible pickups and deliveries (PDPDPD). In this problem, we do not make the standard assumption of one-to-one pickup and delivery problems (PDPs) that each location has only one transportation request. Instead we assume there are multiple requests per location that may be performed individually. This may result in multiple visits to a location. We provide a new compact arc-based integer linear programming (ILP) formulation for the PDPDPD by deriving time-consistency constraints that identify the order in which selected outgoing arcs from a node are actually traversed. The formulation can also easily be applied to the one-to-one PDP by restricting the number of times that a node can be visited. Numerical results on standard one-to-one PDP test instances from the literature show that our compact formulation is almost competitive with tailor-made solution methods for the one-to-one PDP. Moreover, we observe that significant cost savings of up to 15% on average may be obtained by allowing divisible pickups and deliveries in one-to-one PDPs. It turns out that divisible pickups and deliveries are not only beneficial when the vehicle capacity is small, but also when this capacity is unrestrictive.

Optimization of Many Objective Pickup and Delivery Problem with Delay Time of Vehicle Using Memetic Decomposition Based Evolutionary Algorithm

The pickup and delivery problem (PDP) is a very common and important problem, which has a large number of real-world applications in logistics and transportation. In PDP, customers send transportation requests to pick up an object from one place and deliver it to another place. This problem is under the focus of researchers since the last two decades with multiple variations. In the literature, different variations of PDP with different number of objectives and constraints have been considered. Depending on the number of objectives, multi and many-objective evolutionary algorithms have been applied to solve the problem and to study the conflicts between objectives. In this paper, PDP is formulated as a many-objective pickup and delivery problem (MaOPDP) with delay time of vehicle having six criteria to be optimized. To the best of our knowledge, this variation of PDP has not been considered in the literature. To solve the problem, this paper proposes a memetic I-DBEA (Improved Decomposition Based Evolutionary Algorithm), which is basically the modification of an existing many-objective evolutionary algorithm called I-DBEA. To demonstrate the superiority of our approach, a set of experiments have been conducted on a variety of small, medium and large-scale problems. The quality of the results obtained by the proposed approach is compared with five existing multi and many-objective evolutionary algorithms using three different multi-objective evaluation measures such as hypervolume (HV), inverted generational distance (IGD) and generational distance (GD). The experimental results demonstrate that the proposed algorithm has significant advantages over several state-of-the-art algorithms in terms of the quality of the obtained solutions.

Optimisation of the multi-depots pick-up and delivery problems with time windows and multi-vehicles using PSO algorithm

Many sectors in the transport industry are concerned about the vehicle routing problem (VRP), hence the growing interest of researchers for this type of problem and its variants. This is due essentially to its many real applications in logistics for the transport of goods. The originality and contribution of our work is that we have dealt a problem that combines several variants: multiple vehicles (m), multiple depots (MD), pickup and delivery problem (PDP) with time windows (TW). Hence the notation of our problem: m-MDPDPTW. In this paper, we present the m-MDPDPTW, which is an optimisation problem belonging to the category of NP Hard problems. This problem must meet requests for transport between customers and suppliers satisfying precedence, capacity and time constraints. The goal is to find the best solution, which is the best route minimising the total travelled distance. To solve and optimise our m-MDPDPTW, we have developed a new algorithm based on the particle swarm optimisation (PSO) method. The performance of this new approach is tested on data set instances of Li and Lim's benchmark problems in which we have added multiple depot locations. Comparing with prior works, our proposed approach gave better results by decreasing the distance for several studied instances.

A quantum genetic algorithm for pickup and delivery problems with coalition formation

With the “last mile” of the delivery process being the most expensive phase, autonomous package delivery systems are gaining traction as they aim for faster and cheaper delivery of goods to city, urban and rural destinations. This interest is further fueled by the emergence of e-commerce, where many applications can benefit from autonomous package delivery solutions. However, the environment stochasticity, variability and task complexity for autonomous operation make it difficult to deploy such systems in real-world applications without the incorporation of advanced machine learning and optimization algorithms. Moving away from designing a “one size fits all” agent to solve the outdoor package delivery problem and considering ad-hoc teams of agents trained within a data-driven framework could provide the answer. In this work, we propose a delivery scheduling algorithm for heterogeneous multi-agent systems using the pickup and delivery problem (PDP) formulation. Specifically, a 3-index mixed integer program-based PDP that allows coalition formation (PDP-CF) among agents is derived to allow multi-agent PDP schedules. We propose a quantum genetic algorithm to solve for the schedule since it is can better handle the large computational complexity of PDP-CF. Multiple PDP scenario simulations show the merits of the proposed approach.

A comparison of two meta-heuristics for the pickup and delivery problem with transshipment

In the Pickup and Delivery Problems (PDP), a set of routes satisfying requests between pickup and delivery nodes has to be found. This problem has applications in cargo transportation, mail deliveries, passenger transportation ... Recently, a new problem has arisen, the Pickup and Delivery Problem with Transshipment (PDPT), where requests can be transferred from a vehicle to another one in special nodes called transshipment nodes. In this paper, we propose two meta-heuristics to solve the PDPT. The first one is a Large Neighbourhood Search (LNS). The second one is a Genetic Algorithm (GA) which, as far as we know, has not yet been proposed to solve the PDPT. The objective of this paper is to compare the GA and the LNS with existing algorithms from the literature. To perform this comparison, benchmark instances from the literature are used. The GA outperforms the LNS and the existing solutions in the literature.