This study introduces the Territory Design for Dynamic Multi-Period Vehicle Routing Problem with Time Windows (TD-DMPVRPTW), motivated by a real-world application at a food company's distribution center. This problem deals with the design of contiguous and compact territories for delivery of orders from a depot to a set of customers, with time windows, over a multi-period planning horizon. Customers and their demands vary dynamically over time. The problem is modeled as a mixed-integer linear program (MILP) and solved by a proposed heuristic. The heuristic solutions are compared with the proposed MILP solutions on a set of small artificial instances and the food company's solutions on a set of real-world instances. Computational results show that the proposed algorithm can yield high-quality solutions within moderate running times.
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…
Universidad Adolfo Ibáñez（阿道夫·伊瓦涅斯大学）；Universidad Diego Portales（迭戈·波塔莱斯大学）；AGH University of Science and Technology（AGH科技大学）
We develop a heuristic for the Consistent Vehicle Routing Problem with Time Windows (ConVRPTW), which is motivated by a real-world application at a food company's distribution center. Besides standard VRPTW restrictions, ConVRPTW assigns each customer just one driver to fulfill their orders during the whole multi-period planning horizon. For each driver and period, a route is sought to serve all their customers with positive demand. For each customer, the number of periods between consecutive orders and the ordered quantities are highly irregular. This causes difficulties in the daily routing,…
The vehicle routing problem is a well known class of NP-hard combinatorial optimisation problems in literature. Traditional solution methods involve either carefully designed heuristics, or time-consuming metaheuristics. Recent work in reinforcement learning has been a promising alternative approach, but has found it difficult to compete with traditional methods in terms of solution quality. This paper proposes a hybrid approach that combines reinforcement learning, policy rollouts, and a satisfiability solver to enable a tunable tradeoff between computation times and solution quality. Results…
In real life, providing security for a set of large areas by covering the area with Unmanned Aerial Vehicles (UAVs) is a difficult problem that consist of multiple objectives. These difficulties are even greater if the area coverage must continue throughout a specific time window. We address this by considering a Vehicle Routing Problem with Time Windows (VRPTW) variation in which capacity of agents is one and each customer (target area) must be supplied with more than one vehicles simultaneously without violating time windows. In this problem, our aim is to find a way to cover all areas with …
In this paper fuzzy VRPTW with an uncertain travel time is considered. Credibility theory is used to model the problem and specifies a preference index at which it is desired that the travel times to reach the customers fall into their time windows. We propose the integration of fuzzy and ant colony system based evolutionary algorithm to solve the problem while preserving the constraints. Computational results for certain benchmark problems having short and long time horizons are presented to show the effectiveness of the algorithm. Comparison between different preferences indexes have been ob…
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…
University of Maryland（马里兰大学）；University of Southern California（南加州大学）；Verisk（Verisk公司）；ESG UQAM（魁北克大学蒙特利尔分校 ESG 学院）；GERAD（GERAD研究院）；University of California, Irvine（加州大学欧文分校）；Laminaar（Laminaar公司）
Robots performing tasks in warehouses provide the first example of wide-spread adoption of autonomous vehicles in transportation and logistics. The efficiency of these operations, which can vary widely in practice, are a key factor in the success of supply chains. In this work we consider the problem of coordinating a fleet of robots performing picking operations in a warehouse so as to maximize the net profit achieved within a time period while respecting problem- and robot-specific constraints. We formulate the problem as a weighted set packing problem where the elements in consideration are…
Spatial-temporal-demand clustering for solving large-scale vehicle routing problems with time windows
Logistics and Supply Chain Management, School of Management, Technical University of Munich（物流与供应链管理系，管理学院，慕尼黑技术大学）；Munich Data Science Institute (MDSI), Technical University of Munich（慕尼黑数据科学研究所（MDSI），慕尼黑技术大学）
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…
Vehicle Routing Problems (VRPs) in real-world applications often come with various constraints, therefore bring additional computational challenges to exact solution methods or heuristic search approaches. The recent idea to learn heuristic move patterns from sample data has become increasingly promising to reduce solution developing costs. However, using learning-based approaches to address more types of constrained VRP remains a challenge. The difficulty lies in controlling for constraint violations while searching for optimal solutions. To overcome this challenge, we propose a Reinforcement…
University of Houston（休斯顿大学）；Vanderbilt University（范德堡大学）；Chattanooga Area Regional Transportation Authority（查塔努加地区交通管理局）；Cornell University（康奈尔大学）
Vehicle routing problems (VRPs) can be divided into two major categories: offline VRPs, which consider a given set of trip requests to be served, and online VRPs, which consider requests as they arrive in real-time. Based on discussions with public transit agencies, we identify a real-world problem that is not addressed by existing formulations: booking trips with flexible pickup windows (e.g., 3 hours) in advance (e.g., the day before) and confirming tight pickup windows (e.g., 30 minutes) at the time of booking. Such a service model is often required in paratransit service settings, where pa…
LMask: Learn to Solve Constrained Routing Problems with Lazy Masking
Beijing International Center for Mathematical Research, Peking University（北京大学北京国际数学研究中心）；Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）；Department of Statistics and Data Science, University of Pennsylvania（宾夕法尼亚大学统计与数据科学系）
Nanyang Technological University（南洋理工大学）；Singapore Institute of Manufacturing Technology (SIMTech) A*STAR（新加坡科技研究局制造技术研究院）
With an increasing demand from emerging logistics businesses, Vehicle Routing Problem with Private fleet and common Carrier (VRPPC) has been introduced to manage package delivery services from a supplier to customers. However, almost all of existing studies focus on the deterministic problem that assumes all parameters are known perfectly at the time when the planning and routing decisions are made. In reality, some parameters are random and unknown. Therefore, in this paper, we consider VRPPC with hard time windows and random demand, called Optimal Delivery Planning (ODP). The proposed ODP ai…
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-…
VNU University of Engineering and Technology（越南国立大学工程技术大学）；Université de Montréal（蒙特利尔大学）；CIRRELT（企业物流研究中心）；École Polytechnique de Montréal（蒙特利尔综合理工学院）
We consider a vehicle routing problem which seeks to minimize cost subject to time window and synchronization constraints. In this problem, the fleet of vehicles is categorized into regular and special vehicles. Some customers require both vehicles' services, whose starting service times at the customer are synchronized. Despite its important real-world application, this problem has rarely been studied in the literature. To solve the problem, we propose a Constraint Programming (CP) model and an Adaptive Large Neighborhood Search (ALNS) in which the design of insertion operators is based on so…
VRPAgent: LLM-Driven Discovery of Heuristic Operators for Vehicle Routing Problems
Bielefeld University（比勒菲尔德大学）；Radical Numerics；KAIST（韩国科学技术院）；Peking University（北京大学）；University of Turin（都灵大学）；Stanford University（斯坦福大学）；RIKEN（日本研究机构）；Omelet；University of Vienna（维也纳大学）
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…
University of Toronto（多伦多大学）；Western University（韦仕敦大学）；University of Waterloo（滑铁卢大学）
The past decade has seen a rapid penetration of electric vehicles (EV) in the market, more and more logistics and transportation companies start to deploy EVs for service provision. In order to model the operations of a commercial EV fleet, we utilize the EV routing problem with time windows (EVRPTW). In this research, we propose an end-to-end deep reinforcement learning framework to solve the EVRPTW. In particular, we develop an attention model incorporating the pointer network and a graph embedding technique to parameterize a stochastic policy for solving the EVRPTW. The model is then traine…
Learning to Handle Complex Constraints for Vehicle Routing Problems
Nanyang Technological University（南洋理工大学）；Shandong University（山东大学）；Singapore Management University（新加坡管理大学）；Eindhoven University of Technology（埃因霍温理工大学）
Multi-vehicle routing problem with soft time windows (MVRPSTW) is an indispensable constituent in urban logistics distribution systems. Over the past decade, numerous methods for MVRPSTW have been proposed, but most are based on heuristic rules that require a large amount of computation time. With the current rapid increase of logistics demands, traditional methods incur the dilemma between computational efficiency and solution quality. To efficiently solve the problem, we propose a novel reinforcement learning algorithm called the Multi-Agent Attention Model that can solve routing problem ins…
Dubins tours represent a solution of the Dubins Traveling Salesman Problem (DTSP) that is a variant of the optimization routing problem to determine a curvature-constrained shortest path to visit a set of locations such that the path is feasible for Dubins vehicle, which moves only forward and has a limited turning radius. The DTSP combines the NP-hard combinatorial optimization to determine the optimal sequence of visits to the locations, as in the regular TSP, with the continuous optimization of the heading angles at the locations, where the optimal heading values depend on the sequence of v…
This paper develops an inherently parallelised, fast, approximate learning-based solution to the generic class of Capacitated Vehicle Routing Problems with Time Windows and Dynamic Routing (CVRP-TWDR). Considering vehicles in a fleet as decentralised agents, we postulate that using reinforcement learning (RL) based adaptation is a key enabler for real-time route formation in a dynamic environment. The methodology allows each agent (vehicle) to independently evaluate the value of serving each customer, and uses a centralised allocation heuristic to finalise the allocations based on the generate…
Multiobjective Vehicle Routing Optimization with Time Windows: A Hybrid Approach Using Deep Reinforcement Learning and NSGA-II
College of Computer Science and Technology, Nanjing University of Aeronautics and Astronautics（南京航空航天大学计算机科学与技术学院）；Collaborative Innovation Center of Novel Software Technology and Industrialization（新型软件技术与产业化协同创新中心）；Lassonde School of Engineering, York University（约克大学拉森德工程学院）；School of Computer Science and Engineering, Nanyang Technological University（南洋理工大学计算机科学与工程学院）
In task allocation for real-time domains, such as disaster response, a limited number of agents is deployed across a large area to carry out numerous tasks, each with its prerequisites, profit, time window and workload. To maximize profits while minimizing time penalties, agents need to cooperate by forming, disbanding and reforming coalitions. In this paper, we name this problem Multi-Agent Routing and Scheduling through Coalition formation (MARSC) and show that it generalizes the important Team Orienteering Problem with Time Windows. We propose a binary integer program and an anytime and sca…
Nanyang Technological University（南洋理工大学）；Singapore Institute of Manufacturing Technology (SIMTech)（新加坡制造技术研究院（SIMTech））；Agency for Science Technology and Research (A*STAR)（科学、技术与研究局（A*STAR））；Shandong University（山东大学）；Technische Universiteit Delft（代尔夫特理工大学）
We propose a manager-worker framework based on deep reinforcement learning to tackle a hard yet nontrivial variant of Travelling Salesman Problem (TSP), \ie~multiple-vehicle TSP with time window and rejections (mTSPTWR), where customers who cannot be served before the deadline are subject to rejections. Particularly, in the proposed framework, a manager agent learns to divide mTSPTWR into sub-routing tasks by assigning customers to each vehicle via a Graph Isomorphism Network (GIN) based policy network. A worker agent learns to solve sub-routing tasks by minimizing the cost in terms of both to…
SynthCharge: An Electric Vehicle Routing Instance Generator with Feasibility Screening to Enable Learning-Based Optimization and Benchmarking
Industrial and Systems Engineering, University of Miami, Coral Gables, FL, USA（迈阿密大学工业与系统工程系）；Faculty of Engineering, Cyprus International University 99258 Nicosia, North Cyprus, via Mersin 10, Turkey（塞浦路斯国际大学工程学院）；Engineering Management and Systems Engineering, Missouri University of Science and Technology, Rolla, MO, USA（密苏里科学与技术大学工程管理与系统工程系）
Eindhoven University of Technology（埃因霍温理工大学）；Delft University of Technology（代尔夫特理工大学）；McGill University（麦吉尔大学）；Bielefeld University（比勒费尔德大学）；General Electric（通用电气）；Shopify（Shopify（电商平台））；Université de Montréal（蒙特利尔大学）；Polytechnic Institute of Viseu（维塞乌理工学院）；Rockets of Awesome（Rockets of Awesome（游戏公司））；TH Köln（科隆应用技术大学）；University of Málaga（马拉加大学）；Telecom Paris（巴黎电信学院（巴黎高等电信学院））
This paper reports on the first international competition on AI for the traveling salesman problem (TSP) at the International Joint Conference on Artificial Intelligence 2021 (IJCAI-21). The TSP is one of the classical combinatorial optimization problems, with many variants inspired by real-world applications. This first competition asked the participants to develop algorithms to solve a time-dependent orienteering problem with stochastic weights and time windows (TD-OPSWTW). It focused on two types of learning approaches: surrogate-based optimization and deep reinforcement learning. In this p…
