Contextual Stochastic Vehicle Routing with Time Windows
School of Management, Technical University of Munich（慕尼黑工业大学管理学院）；Amazon.com, Inc.（亚马逊公司）；Munich Data Science Institute, Technical University of Munich（慕尼黑工业大学慕尼黑数据科学研究所）；Polytechnique Montréal（蒙特利尔理工学院）
Breno Serrano, Alexandre M. Florio, Stefan Minner, Maximilian Schiffer, Thibaut Vidal
We study the vehicle routing problem with time windows (VRPTW) and stochastic travel times, in which the decision-maker observes related contextual information, represented as feature variables, before making routing decisions. Despite the extensive literature on stochastic VRPs, the integration of feature variables has received limited attention in this context. We introduce the contextual stochastic VRPTW, which minimizes the total transportation cost and expected late arrival penalties conditioned on the observed features. Since the joint distribution of travel times and features is unknown, we present novel data-driven prescriptive models that use historical data to provide an approximate solution to the problem. We distinguish the prescriptive models between point-based approximation, sample average approximation, and penalty-based approximation, each taking a different perspective on dealing with stochastic travel times and features. We develop specialized branch-price-and-cut algorithms to solve these data-driven prescriptive models. In our computational experiments, we compare the out-of-sample cost performance of different methods on instances with up to one hundred customers. Our results show that, surprisingly, a feature-dependent sample average approximation outperforms existing and novel methods in most settings.
A Rolling-Space Branch-and-Price Algorithm for the Multi-Compartment Vehicle Routing Problem with Multiple Time Windows
H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, USA（佐治亚理工学院H. Milton Stewart工业与系统工程学院）；Department of Operations and Decision Systems, Université Laval（拉瓦尔大学运营管理与决策系统系）
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…
Many real-world vehicle routing problems involve rich sets of constraints with respect to the capacities of the vehicles, time windows for customers etc. While in recent years first machine learning models have been developed to solve basic vehicle routing problems faster than optimization heuristics, complex constraints rarely are taken into consideration. Due to their general procedure to construct solutions sequentially route by route, these methods generalize unfavorably to such problems. In this paper, we develop a policy model that is able to start and extend multiple routes concurrently…
Amazon Customer Service provides real-time support for millions of customer contacts every year. While bot-resolver helps automate some traffic, we still see high demand for human agents, also called subject matter experts (SMEs). Customers outreach with questions in different domains (return policy, device troubleshooting, etc.). Depending on their training, not all SMEs are eligible to handle all contacts. Routing contacts to eligible SMEs turns out to be a non-trivial problem because SMEs' domain eligibility is subject to training quality and can change over time. To optimally recommend SME…
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…
Learning-Enhanced Neighborhood Selection for the Vehicle Routing Problem with Time Windows
Centrum Wiskunde & Informatica (CWI)（荷兰数学和计算机科学研究学会（CWI））；Institute for Logic, Language and Computation (ILLC), University of Amsterdam（阿姆斯特丹大学逻辑、语言与计算研究所）；DELMIA R&D, Dassault Systèmes B.V.（达索系统DELMIA研发部）
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）
The skip-gram (SG) model learns word representation by predicting the words surrounding a center word from unstructured text data. However, not all words in the context window contribute to the meaning of the center word. For example, less relevant words could be in the context window, hindering the SG model from learning a better quality representation. In this paper, we propose an enhanced version of the SG that leverages context information to produce word representation. The proposed model, Contextual Skip-gram, is designed to predict contextual words with both the center words and the con…
Seoul National University（首尔大学）；Samsung Research（三星研究院）
Capsule networks (CapsNets) have recently gotten attention as a novel neural architecture. This paper presents the sequential routing framework which we believe is the first method to adapt a CapsNet-only structure to sequence-to-sequence recognition. Input sequences are capsulized then sliced by a window size. Each slice is classified to a label at the corresponding time through iterative routing mechanisms. Afterwards, losses are computed by connectionist temporal classification (CTC). During routing, the required number of parameters can be controlled by the window size regardless of the le…
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…
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…
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…
Routing problems are a class of combinatorial problems with many practical applications. Recently, end-to-end deep learning methods have been proposed to learn approximate solution heuristics for such problems. In contrast, classical dynamic programming (DP) algorithms guarantee optimal solutions, but scale badly with the problem size. We propose Deep Policy Dynamic Programming (DPDP), which aims to combine the strengths of learned neural heuristics with those of DP algorithms. DPDP prioritizes and restricts the DP state space using a policy derived from a deep neural network, which is trained…
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）
Deep-learning models have enabled performance leaps in analysis of high-dimensional functional MRI (fMRI) data. Yet, many previous methods are suboptimally sensitive for contextual representations across diverse time scales. Here, we present BolT, a blood-oxygen-level-dependent transformer model, for analyzing multi-variate fMRI time series. BolT leverages a cascade of transformer encoders equipped with a novel fused window attention mechanism. Encoding is performed on temporally-overlapped windows within the time series to capture local representations. To integrate information temporally, cr…
