This paper presents an approach to learn the local-search heuristics that iteratively improves the solution of Vehicle Routing Problem (VRP). A local-search heuristics is composed of a destroy operator that destructs a candidate solution, and a following repair operator that rebuilds the destructed one into a new one. The proposed neural network, as trained through actor-critic framework, consists of an encoder in form of a modified version of Graph Attention Network where node embeddings and edge embeddings are integrated, and a GRU-based decoder rendering a pair of destroy and repair operators. Experiment results show that it outperforms both the traditional heuristics algorithms and the existing neural combinatorial optimization for VRP on medium-scale data set, and is able to tackle the large-scale data set (e.g., over 400 nodes) which is a considerable challenge in this area. Moreover, the need for expertise and handcrafted heuristics design is eliminated due to the fact that the proposed network learns to design the heuristics with a better performance. Our implementation is available online.
University of Auckland（奥克兰大学）；vWorkApp Inc.（vWorkApp公司）
In this thesis we present a new algorithm for the Vehicle Routing Problem called the Enhanced Bees Algorithm. It is adapted from a fairly recent algorithm, the Bees Algorithm, which was developed for continuous optimisation problems. We show that the results obtained by the Enhanced Bees Algorithm are competitive with the best meta-heuristics available for the Vehicle Routing Problem (within 0.5% of the optimal solution for common benchmark problems). We show that the algorithm has good runtime performance, producing results within 2% of the optimal solution within 60 seconds, making it suitab…
The Multi-Depot Vehicle Routing Problem (MDVRP) is a real-world model of the simplistic Vehicle Routing Problem (VRP) that considers how to satisfy multiple customer demands from numerous depots. This paper introduces a hybrid 2-stage approach based on two population-based algorithms - Ant Colony Optimization (ACO) that mimics ant behaviour in nature and the Imperialist Competitive Algorithm (ICA) that is based on geopolitical relationships between countries. In the proposed hybrid algorithm, ICA is responsible for customer assignment to the depots while ACO is routing and sequencing the custo…
The Dynamic Vehicle Routing Problem with Time Windows (DVRPTW) is an extension of the well-known Vehicle Routing Problem (VRP), which takes into account the dynamic nature of the problem. This aspect requires the vehicle routes to be updated in an ongoing manner as new customer requests arrive in the system and must be incorporated into an evolving schedule during the working day. Besides the vehicle capacity constraint involved in the classical VRP, DVRPTW considers in addition time windows, which are able to better capture real-world situations. Despite this, so far, few studies have focused…
National Research University Higher School of Economics（国立研究型大学高等经济学院）
Vehicle Routing Problem is a well-known problem in logistics and transportation, and the variety of such problems is explained by the fact that it occurs in many real-life situations. It is an NP-hard combinatorial optimization problem and finding an exact optimal solution is practically impossible. In this work, Site-Dependent Truck and Trailer Routing Problem with hard and soft Time Windows and Split Deliveries is considered (SDTTRPTWSD). In this article, we develop a heuristic with the elements of Tabu Search for solving SDTTRPTWSD. The heuristic uses the concept of neighborhoods and visits…
Huazhong University of Science and Technology（华中科技大学）；Huawei Noah’s Ark Lab（华为诺亚方舟实验室）
Vehicle routing is a well-known optimization research topic with significant practical importance. Among different approaches to solving vehicle routing, heuristics can produce a satisfactory solution at a reasonable computational cost. Consequently, much effort has been made in the past decades to develop vehicle routing heuristics. In this article, we systematically survey the existing vehicle routing heuristics, particularly on works carried out in recent years. A classification of vehicle routing heuristics is presented, followed by a review of their methodologies, recent developments, and…
In this paper we present an extension of the Nested Rollout Policy Adaptation algorithm (NRPA), namely the Generalized Nested Rollout Policy Adaptation (GNRPA), as well as its use for solving some instances of the Vehicle Routing Problem. We detail some results obtained on the Solomon instances set which is a conventional benchmark for the Vehicle Routing Problem (VRP). We show that on all instances, GNRPA performs better than NRPA. On some instances, it performs better than the Google OR Tool module dedicated to VRP.
Recent studies in using deep learning to solve routing problems focus on construction heuristics, the solutions of which are still far from optimality. Improvement heuristics have great potential to narrow this gap by iteratively refining a solution. However, classic improvement heuristics are all guided by hand-crafted rules which may limit their performance. In this paper, we propose a deep reinforcement learning framework to learn the improvement heuristics for routing problems. We design a self-attention based deep architecture as the policy network to guide the selection of next solution.…
Due to the practical importance of vehicle routing problems (VRP), there exists an ever-growing body of research in algorithms and (meta)heuristics for solving such problems. However, the diversity of VRP domains creates the separate problem of modeling such problems -- describing the domain entities (and, in particular, the planning decisions), the set of valid planning decisions, and the preferences between different plans. In this paper, we review the approaches for modeling vehicle routing problems. To make the comparison more straightforward, we formulate several criteria for evaluating m…
The article describes an investigation of the effectiveness of genetic algorithms for multi-objective combinatorial optimization (MOCO) by presenting an application for the vehicle routing problem with soft time windows. The work is motivated by the question, if and how the problem structure influences the effectiveness of different configurations of the genetic algorithm. Computational results are presented for different classes of vehicle routing problems, varying in their coverage with time windows, time window size, distribution and number of customers. The results are compared with a simp…
Middlesex University（密德萨斯大学）；Deusto Institute of Technology (DeustoTech)（德乌斯托技术学院（DeustoTech））；University of Deusto（德乌斯托大学）
A real-world newspaper distribution problem with recycling policy is tackled in this work. In order to meet all the complex restrictions contained in such a problem, it has been modeled as a rich vehicle routing problem, which can be more specifically considered as an asymmetric and clustered vehicle routing problem with simultaneous pickup and deliveries, variable costs and forbidden paths (AC-VRP-SPDVCFP). This is the first study of such a problem in the literature. For this reason, a benchmark composed by 15 instances has been also proposed. In the design of this benchmark, real geographica…
The Australian National University（澳大利亚国立大学）；Data61
In the classic Vehicle Routing Problem (VRP) a fleet of of vehicles has to visit a set of customers while minimising the operations' costs. We study a rich variant of the VRP featuring split deliveries, an heterogeneous fleet, and vehicle-commodity incompatibility constraints. Our goal is twofold: define the cheapest routing and the most adequate fleet. To do so, we split the problem into two interdependent components: a fleet design component and a routing component. First, we define two Mixed Integer Programming (MIP) formulations for each component. Then we discuss several improvements in t…
SNCF, the French public train company, is experimenting to develop new types of transportation services by tackling vehicle routing problems. While many deep learning models have been used to tackle efficiently vehicle routing problems, it is difficult to take into account time related constraints. In this paper, we solve the Capacitated Vehicle Routing Problem with Time Windows (CVRPTW) and the Capacitated Pickup and Delivery Problem with Time Windows (CPDPTW) with a constructive iterative Deep Learning algorithm. We use an Attention Encoder-Decoder structure and design a novel insertion heur…
We consider a wide family of vehicle routing problem variants with many complex and practical constraints, known as rich vehicle routing problems, which are faced on a daily basis by C.H. Robinson (CHR). Since CHR has many customers, each with distinct requirements, various routing problems with different objectives and constraints should be solved. We propose a set partitioning framework with a number of route generation algorithms, which have shown to be effective in solving a variety of different problems. The proposed algorithms have outperformed the existing technologies at CHR on 10 benc…
The article presents a framework for the resolution of rich vehicle routing problems which are difficult to address with standard optimization techniques. We use local search on the basis on variable neighborhood search for the construction of the solutions, but embed the techniques in a flexible framework that allows the consideration of complex side constraints of the problem such as time windows, multiple depots, heterogeneous fleets, and, in particular, multiple optimization criteria. In order to identify a compromise alternative that meets the requirements of the decision maker, an intera…
School of Technology, University of Campinas（坎皮纳斯大学技术学院）
The number of optimization techniques in the combinatorial domain is large and diversified. Nevertheless, real-world based benchmarks for testing algorithms are few. This work creates an extensible real-world mail delivery benchmark to the Vehicle Routing Problem (VRP) in a planar graph embedded in the 2D Euclidean space. Such problem is multi-objective on a roadmap with up to 25 vehicles and 30,000 deliveries per day. Each instance models one generic day of mail delivery, allowing both comparison and validation of optimization algorithms for routing problems. The benchmark may be extended to …
School of Technology, University of Campinas（坎皮纳斯大学技术学院）
The number of optimization techniques in the combinatorial domain is large and diversified. Nevertheless, there is still a lack of real benchmarks to validate optimization algorithms. In this work we introduce VRPBench, a tool to create instances and visualize solutions to the Vehicle Routing Problem (VRP) in a planar graph embedded in the Euclidean 2D space. We use VRPBench to model a real-world mail delivery case of the city of Artur Nogueira. Such scenarios were characterized as a multi-objective optimization of the VRP. We extracted a weighted graph from a digital map of the city to create…
Massachusetts Institute of Technology（麻省理工学院）；University of Southampton（南安普顿大学）；Universidade Federal da Paraíba（帕拉伊巴联邦大学）
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 …
The use of electric vehicles (EV) in the last mile is appealing from both sustainability and operational cost perspectives. In addition to the inherent cost efficiency of EVs, selling energy back to the grid during peak grid demand, is a potential source of additional revenue to a fleet operator. To achieve this, EVs have to be at specific locations (discharge points) during specific points in time (peak period), even while meeting their core purpose of delivering goods to customers. In this work, we consider the problem of EV routing with constraints on loading capacity; time window; vehicle-…
Learning how to automatically solve optimization problems has the potential to provide the next big leap in optimization technology. The performance of automatically learned heuristics on routing problems has been steadily improving in recent years, but approaches based purely on machine learning are still outperformed by state-of-the-art optimization methods. To close this performance gap, we propose a novel large neighborhood search (LNS) framework for vehicle routing that integrates learned heuristics for generating new solutions. The learning mechanism is based on a deep neural network wit…
Pontifícia Universidade Católica do Rio de Janeiro（里约热内卢天主教大学）；CIRRELT（企业网络、物流与运输跨大学研究中心）；HEC Montréal（蒙特利尔高等商学院）；University of Vienna（维也纳大学）
Vehicle routing problems have been the focus of extensive research over the past sixty years, driven by their economic importance and their theoretical interest. The diversity of applications has motivated the study of a myriad of problem variants with different attributes. In this article, we provide a concise overview of existing and emerging problem variants. Models are typically refined along three lines: considering more relevant objectives and performance metrics, integrating vehicle routing evaluations with other tactical decisions, and capturing fine-grained yet essential aspects of mo…
Nanyang Technological University（南洋理工大学）；Shandong University（山东大学）；National University of Singapore（新加坡国立大学）
We present a novel deep reinforcement learning method to learn construction heuristics for vehicle routing problems. In specific, we propose a Multi-Decoder Attention Model (MDAM) to train multiple diverse policies, which effectively increases the chance of finding good solutions compared with existing methods that train only one policy. A customized beam search strategy is designed to fully exploit the diversity of MDAM. In addition, we propose an Embedding Glimpse layer in MDAM based on the recursive nature of construction, which can improve the quality of each policy by providing more infor…
Tecnologico de Monterrey（蒙特雷科技大学）；Universidade Federal da Bahia（巴伊亚联邦大学）
We consider an NP-hard selective and periodic inventory routing problem (SPIRP) in a waste vegetable oil collection environment. This SPIRP arises in the context of reverse logistics where a biodiesel company has daily requirements of oil to be used as raw material in its production process. These requirements can be fulfilled by using the available inventory, collecting waste vegetable oil or purchasing virgin oil. The problem consists in determining a period (cyclic) planning for the collection and purchasing of oil such that the total collection, inventory and purchasing costs are minimized…
University of Deusto（德乌斯托大学）；Ikerbasque, Basque Foundation for Science（伊克巴斯克，巴斯克科学基金会）；Universidad de Guadalajara（瓜达拉哈拉大学）
Electric vehicles (EVs) have been adopted in urban areas to reduce environmental pollution and global warming as a result of the increasing number of freight vehicles. However, there are still deficiencies in routing the trajectories of last-mile logistics that continue to impact social and economic sustainability. For that reason, in this paper, a hyper-heuristic (HH) approach called Hyper-heuristic Adaptive Simulated Annealing with Reinforcement Learning (HHASA$_{RL}$) is proposed. It is composed of a multi-armed bandit method and the self-adaptive Simulated Annealing (SA) metaheuristic algo…
Wayne State University（韦恩州立大学）；U.S. Army CCDC Ground Vehicle Systems Center（美国陆军CCDC地面车辆系统中心）
An increase in greenhouse gases emission from the transportation sector has led companies and the government to elevate and support the production of electric vehicles (EV). With recent developments in urbanization and e-commerce, transportation companies are replacing their conventional fleet with EVs to strengthen the efforts for sustainable and environment-friendly operations. However, deploying a fleet of EVs asks for efficient routing and recharging strategies to alleviate their limited range and mitigate the battery degradation rate. In this work, a fleet of electric vehicles is consider…
Korea Advanced Institute of Science and Technology (KAIST)（韩国科学技术院（KAIST））
This paper introduces a new routing problem referred to as the vehicle routing problem with vector profits. Given a network composed of nodes (depot/sites) and arcs connecting the nodes, the problem determines routes that depart from the depot, visit sites to collect profits, and return to the depot. There are multiple stakeholders interested in the mission and each site is associated with a vector whose k-th element represents the profit value for the k-th stakeholder. The objective of the problem is to maximize the profit sum for the least satisfied stakeholder, i.e., the stakeholder with th…
The Vehicle Routing Problem (VRP) is the combinatorial optimization problem of designing routes for vehicles to visit customers in such a fashion that a cost function, typically the number of vehicles, or the total travelled distance is minimized. The problem finds applications in industrial scenarios, for example where Automated Guided Vehicles run through the plant to deliver components from the warehouse. This specific problem, henceforth called the Electric Conflict-Free Vehicle Routing Problem (CF-EVRP), involves constraints such as limited operating range of the vehicles, time windows on…
Industry 4.0 is a concept that assists companies in developing a modern supply chain (MSC) system when they are faced with a dynamic process. Because Industry 4.0 focuses on mobility and real-time integration, it is a good framework for a dynamic vehicle routing problem (DVRP). This research works on DVRP. The aim of this research is to minimize transportation cost without exceeding the capacity constraint of each vehicle while serving customer demands from a common depot. Meanwhile, new orders arrive at a specific time into the system while the vehicles are executing the delivery of existing …
The University of Adelaide（阿德莱德大学）；University of Münster（明斯特大学）
In practice, e.g. in delivery and service scenarios, Vehicle-Routing-Problems (VRPs) often imply repeated decision making on dynamic customer requests. As in classical VRPs, tours have to be planned short while the number of serviced customers has to be maximized at the same time resulting in a multi-objective problem. Beyond that, however, dynamic requests lead to the need for re-planning of not yet realized tour parts, while already realized tour parts are irreversible. In this paper we study this type of bi-objective dynamic VRP including sequential decision making and concurrent realizatio…
Motivated by the promising advances of deep-reinforcement learning (DRL) applied to cooperative multi-agent systems we propose a model and learning procedure to solve the Capacitated Multi-Vehicle Routing Problem (CMVRP) with fixed fleet size. Our learning procedure follows a centralized-training and decentralized-execution paradigm. We empirically test our model and showed its capability for producing near-optimal solutions through cooperative actions. In large instances, our model generates better solutions than other commonly used heuristics. Additionally, our model can solve arbitrary inst…
The goal of this paper is to propose and test a new memetic algorithm for the capacitated vehicle routing problem in parallel computing environment. In this paper we consider simple variation of vehicle routing problem in which the only parameter is the capacity of the vehicle and each client only needs one package. We present simple reduction to prove the existence of polynomial-time algorithm for capacity 2. We analyze the efficiency of the algorithm using hierarchical Parallel Random Access Machine (PRAM) model and run experiments with code written in CUDA (for capacities larger than 2).
This paper presents a method for choosing a Particle Swarm Optimization based optimizer for the Dynamic Vehicle Routing Problem on the basis of the initially available data of a given problem instance. The optimization algorithm is chosen on the basis of a prediction made by a linear model trained on that data and the relative results obtained by the optimization algorithms. The achieved results suggest that such a model can be used in a hyper-heuristic approach as it improved the average results, obtained on the set of benchmark instances, by choosing the appropriate algorithm in 82% of signi…
Victoria University of Wellington（惠灵顿维多利亚大学）；Warwick Business School（华威商学院）
Due to its direct relevance to post-disaster operations, meter reading and civil refuse collection, the Uncertain Capacitated Arc Routing Problem (UCARP) is an important optimisation problem. Stochastic models are critical to study as they more accurately represent the real-world than their deterministic counterparts. Although there have been extensive studies in solving routing problems under uncertainty, very few have considered UCARP, and none consider collaboration between vehicles to handle the negative effects of uncertainty. This paper proposes a novel Solution Construction Procedure (S…
The electric vehicle routing problem (EVRP) has garnered great interest from researchers and industrialists in an attempt to move from fuel-based vehicles to healthier and more efficient electric vehicles (EVs). While it seems that the EVRP should not be much different from traditional vehicle routing problems (VRPs), challenges like limited cruising time, long charging times, and limited availability of charging facilities for electric vehicles makes all the difference. Previous works target logistics and delivery-related solutions wherein a homogeneous fleet of commercial EVs have to return …
This paper presents a parallel memetic algorithm for solving the vehicle routing problem with time windows (VRPTW). The VRPTW is a well-known NP-hard discrete optimization problem with two objectives. The main objective is to minimize the number of vehicles serving customers scattered on the map, and the second one is to minimize the total distance traveled by the vehicles. Here, the fleet size is minimized in the first phase of the proposed method using the parallel heuristic algorithm (PHA), and the traveled distance is minimized in the second phase by the parallel memetic algorithm (PMA). I…
