Electric Vehicle Routing Research Articles

Delivery routing for electric vehicles with en-route mobile battery swapping

Amid increasing environmental concerns, electric vehicles (EVs) are gaining traction as a sustainable transportation alternative. However, the widespread adoption of EVs is hindered by range limitations, inadequate charging infrastructure, and unpredictable access to charging facilities. The battery swapping van (BV) has been proposed as an innovative approach to actively offer on-demand charging at designated locations. This study leverages the novel BV concept and proposes a novel electric vehicle routing model with time windows and en-route mobile battery swapping (EVRPTW-EMBS). This achieves flexible mobile battery swapping services provided by BVs to EVs that are either en route or at customer sites. A tailored heuristic algorithm called CIP-TDP-ILNS is adopted, combining improved large neighborhood search (ILNS) with tree-template dynamic programming (TDP) and cluster-aided integer programming (CIP) to reduce the search space and enhance solving efficiency. Through extensive testing, the CIP-TDP-ILNS algorithm exhibits robust performance, yielding up to 16% cost reductions for the EVRPTW-EMBS compared to the benchmark model. The findings of this study suggest that (1) the EVRPTW-EMBS system is particularly beneficial for servicing clients with wider time windows, and (2) the optimal balance between the quantity of batteries carried and their capacity should be tailored to the logistics network’s size.

Layered Graph Models for the Electric Vehicle Routing Problem With Nonlinear Charging Functions

AbstractElectric vehicle routing problems (EVRPs) involve the routing of a fleet of electric vehicles (EVs) to visit a set of customers while typically minimizing the total travel and charging time. Due to their limited autonomy, EVs may need to recharge their batteries en‐route at charging stations (CSs). Thus, routing decisions also include which CSs to visit, and how much energy to charge during those visits. These decisions are compounded by the fact that charging times follow a nonlinear charging function with respect to the EV's state of charge (SoC). We propose a layered graph representation for the EVRP with nonlinear charging functions (EVRP‐NL). Specifically, the layers correspond to discretized SoC values. Therefore, the arcs' energy consumption is approximated to match those values. We develop two compact formulations based on the layered graph. Furthermore, we introduced two charging policies that facilitate aligning charging duration with practical considerations. Computational results demonstrate the effectiveness of our formulations. Our best formulation effectively handles instances with up to 40 customers. On those instances, compared to the state‐of‐the‐art compact formulation, our formulation solves 13 more instances to optimality with less than half of the computational time. Considering instances solved by both formulations to optimally, the approximation entailed by our formulation yields a 0.94% deviation on average. Since our best performing formulation is compact, it may be readily used by a broad audience. Furthermore, as the majority of algorithms for the EVPR and its variants are heuristics, our formulation could be beneficial in evaluating the performance of these methods.

An End-to-End Deep Reinforcement Learning Framework for Electric Vehicle Routing Problem

An End-to-End Deep Reinforcement Learning Framework for Electric Vehicle Routing Problem

Electric delivery vehicle routing problem optimization model with time-varying traffic congestion

In order to plan a reasonable scheme for the fleet travel and minimize the energy consumption of electric vehicles during traffic congestion periods, while relieving the mileage anxiety of delivery personnel, the pure electric delivery vehicle routing problem considering time-varying traffic congestion was studied. Firstly , a novel mixed integer programming model (TD-EVRP) is established to step for its extended model of EVRP, which especially characterizes the time-varying traffic congestion state and measures the energy consumption of electric delivery vehicles. This model also refines its constraints including customer time window, vehicle load, and vehicle charging requirements. Secondly, a traffic congestion avoidance strategy is introduced into the model, which allows vehicles to park and charge at customer points during peak traffic periods in order to actively avoid unnecessary energy consumption caused by traffic congestion. Finally, the improved ant colony algorithm is designed to acquire the optimal solution.

CMSA based on set covering models for packing and routing problems

AbstractMany packing, routing, and knapsack problems can be expressed in terms of integer linear programming models based on set covering. These models have been exploited in a range of successful heuristics and exact techniques for tackling such problems. In this paper, we show that integer linear programming models based on set covering can be very useful for their use within an algorithm called “Construct, Merge, Solve & Adapt”(CMSA), which is a recent hybrid metaheuristic for solving combinatorial optimization problems. This is because most existing applications of CMSA are characterized by the use of an integer programming solver for solving reduced problem instances at each iteration. We present applications of CMSA to the variable-sized bin packing problem and to the electric vehicle routing problem with time windows and simultaneous pickups and deliveries. In both applications, CMSA based on a set covering model strongly outperforms CMSA when using an assignment-type model. Moreover, state-of-the-art results are obtained for both considered optimization problems.

A Two-Stage Approach for Electric Vehicle Routing Problem with Time Windows and Heterogeneous Recharging Stations

A Two-Stage Approach for Electric Vehicle Routing Problem with Time Windows and Heterogeneous Recharging Stations

Evolving routing policies for electric vehicles by means of genetic programming

AbstractIn recent years, the growing interest in environmental sustainability has led to Electric Vehicle Routing Problems (EVRPs) attracting more and more attention. EVRPs involve the use of electric vehicles, which have additional constraints, such as range and recharging time, compared to conventional Vehicle Routing Problems (VRPs). The complexity and dynamic nature of solving VRPs often lead to the introduction of Routing Policies (RPs), simple heuristics that incrementally build routes. However, manually designing efficient RPs proves to be a challenging and time-consuming task. Therefore, there is a pressing need to explore the application of hyper-heuristics, in particular Genetic Programming (GP), to automatically generate new RPs. Since this method has not yet been investigated in the literature in the context of EVRPs, this study explores the applicability of GP to automatically generate new RPs for EVRP. To this end, three RP variants (serial, semiparallel, and parallel) are introduced in this study, along with a set of domain-specific terminal nodes to optimise three criteria: the number of vehicles, energy consumption, and total tardiness. The experimental analysis shows that the serial variant performs best in terms of energy consumption and number of vehicles, while the parallel variant is most effective in minimising the total tardiness. A comprehensive analysis of the proposed method is conducted to determine its convergence properties and the impact of the proposed terminal nodes on performance and to describe several generated RPs. The results show that the automatically generated RPs perform commendably compared to traditional methods such as metaheuristics and exact methods, which usually require significantly more runtime. More specifically, depending on the scenario in which they are used, the generated RPs achieve results that are about 20%-37% worse compared to the best known results for the number of vehicles in almost negligible time, in just some milliseconds.

Prize-collecting Electric Vehicle routing model for parcel delivery problem

Electric Vehicle (EV)-based parcel delivery is getting much more popular these days due to EVs being eco-friendly and sustainable. One well-known problem in the literature to study last-mile delivery via EVs is the Electric Vehicle Routing Problem (EVRP). One limitation of EVRP is that it assumes all customers must be visited directly by EVs. This forces companies to purchase or utilize additional EVs, increasing operational costs for EV utilization and routing. To overcome this limitation, the present work introduces the Prize-collecting EVRP with Time Windows (PC-EVRP-TW), utilizing multiple EVs for the home-delivery service of high-priority customers (customers with high loyalty or premium memberships), leaving the rest for the next day or outsourcing to a third-party shipper. It also ensures a minimum number of served demands to maintain service quality. PC-EVRP-TW is modeled by mixed-integer linear programming and solved by a problem-specific hybrid metaheuristic aiming to minimize EVs’ route and usage cost and maximize collected profits (prizes) while satisfying EVs’ load and battery capacity, task completion, and time window constraints. Analyses were performed on the optimal solution of PC-EVRP-TW. The results show that the company could achieve significant route cost savings, up to 22% compared to EVRP-TW. Additionally, remarkable reductions in EV usage costs, 6%, 16%, and 18%, were observed for various-size instances of PC-EVRP-TW. These findings highlight the potential for practitioners and managers to realize substantial cost savings and optimize EV usage by selectively serving a prioritized subset of customers daily, particularly when facing high utilization costs and the inability to serve all customers directly.

The Electric Vehicle Routing and Overnight Charging Scheduling Problem on a Multigraph

In the electric vehicle (EV) routing and overnight charging scheduling problem, a fleet of EVs must serve the demand of a set of customers with time windows. The problem consists in finding a set of minimum cost routes and determining an overnight EV charging schedule that ensures the routes’ feasibility. Because (i) travel time and energy consumption are conflicting resources, (ii) the overnight charging operations take considerable time, and (iii) the charging infrastructure at the depot is limited, we model the problem on a multigraph where each arc between two vertices represents a path with a different resource consumption trade-off. To solve the problem, we design a branch-price-and-cut algorithm that implements state-of-the-art techniques, including the ng-path relaxation, subset-row inequalities, and a specialized labeling algorithm. We report computational results showing that the method solves to optimality instances with up to 50 customers. We also present experiments evaluating the benefits of modeling the problem on a multigraph rather than on the more classical 1-graph representation. History: Accepted by Andra Lodi, Area Editor for Design and Analysis of Algorithms—Discrete. Funding: This work was supported by the Natural Sciences and Engineering Research Council of Canada through the Discovery grants [Grant RGPIN-2023-03791]. It was also partially funded by HEC Montréal through the research professorship on Clean Transportation Analytics. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.0404 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2023.0404 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

An alternating direction multiplier method with variable neighborhood search for electric vehicle routing problem with time windows and battery swapping stations

This paper studies a real-world electric vehicle routing problem (EVRP). Specifically, it is an EVRP with time windows and battery swapping stations (EVRP_TWBSS). The EVRP_TWBSS considers the routing of electric vehicles (EVs), the determination of each electric vehicle’s battery level, and the selection of battery swapping stations. The criterion of EVRP_TWBSS is to minimize the operating costs. To simplify the structure of model, a time-discrete and multi-commodity flow model based on extended state-space-time network (TMFM_ESSTN) is established. Meanwhile, an alternating direction multiplier method with variable neighborhood search (ADMM_VNS) is presented to address the TMFM_ESSTN. In ADMM_VNS, the augmented lagrangian relaxation (ALR) model constructed from the TMFM_ESSTN is decomposed and linearized to a series of least cost vehicle routing subproblems through the linear augmented lagrangian relaxation (LALR) decomposed technique. Then, each subproblem is iteratively solved by using the dynamic programming and two special designed VNS strategies in ADMM_VNS iterative framework. The solution’s quality can be controlled to a certain extent through monitoring the gap between the lower and upper bounds obtained after each iteration. Test results on instances with different scales and a real-world instance based on partial road network in Kunming City demonstrate that ADMM_VNS can achieve smaller gaps and better solutions than several state-of-the-art algorithms. In which, ADMM_VNS can reduce the optimal gap by up to 2.27 % compared to the other state-of-the-art algorithms in small-scale instances. The gap of ADMM_VNS is calculated based on the lower bound and the upper bound in the large-scale instances and the real-world instance are 10.36 % and 1.57 %, respectively.

Optimal Agent-Based Pickup and Delivery with Time Windows and Electric Vehicles

The traditional methods of transporting goods and people in urban areas using vehicles powered by internal combustion engines are major contributors to pollution. As a result, an increasing number of logistics companies are transitioning to electric vehicles (EVs) for daily operations, replacing traditional engines. This shift opens research avenues regarding the integration of EVs into delivery workflows and how this can contribute to greener cities. This study tackles the EV routing problem, focusing on balancing battery constraints and optimizing routes. We formulated the problem as a pickup and delivery with time windows, incorporating electric energy consumption constraints, and utilized consensus mechanisms in an agent-based simulation context. Our evaluation used 15 scenarios, capturing variations in vehicle configurations, order generation rates, and battery and freight capacities. We compared two order allocation strategies: “Closest Allocation” and “Negotiation” consensus-based allocation. The results confirmed that the consensus-based strategy outperformed the “Closest Allocation” in metrics such as remaining orders, orders not handled in time, total distance traveled, total recharging cost, and total number of recharges. These findings have significant implications for urban planners, logistic companies, and policymakers, demonstrating that an agent-based simulation context for electric vehicles using consensus-based strategies can enhance delivery efficiency and promote sustainability.

Pickup and delivery problem with electric vehicles and time windows considering queues

The electric vehicle, as a green and sustainable technology, has gained tremendous development and application recently in the logistics distribution system. However, the increasing workload and limited infrastructure capacity pose challenges for electric vehicles in the pickup and delivery operating system, including task allocation, electric vehicle routing, and queue scheduling. To address these issues, this paper introduces a pickup and delivery problem with electric vehicles and time windows considering queues, which considers queue scheduling for multiple electric vehicles when operating at the same site. A novel mixed integer linear programming model is proposed to minimize the cost of travel distance and queue time. An adaptive hybrid neighborhood search algorithm is developed to solve the moderately large-scale problem. Experimental results demonstrate the effectiveness of the model and adaptive hybrid neighborhood search algorithm. The competitive performance of the developed algorithm is further confirmed by finding 9 new best solutions for the pickup and delivery problem with electric vehicles and time windows benchmark instances. Moreover, the results and sensitivity analysis of objective weight costs highlight the impact and importance of considering queues in the studied problem and obtain some management insights.

An interaction-enhanced co-evolutionary algorithm for electric vehicle routing optimization

Recently, the electric vehicle routing problem (EVRP) has emerged as a significant challenge in the transportation field. Unlike traditional vehicle routing problems, EVRP requires optimizing not only the customer route but also the charging scheme. This implies that routes must be planned while considering the availability of charging stations, and charging decisions must be made based on the specific route structure. Although the dual-population-based co-evolutionary algorithm (DPCA) has been proposed to address this coupling relationship, there is still room for further performance improvement. Therefore, this paper proposes an interaction-enhanced co-evolutionary algorithm (IECA) that facilitates a more effective collaborative search between routing and charging optimizations. For routing optimization, we propose an improved ant colony optimization method with a novel pheromone update approach to generate diverse route solutions. Specifically, we utilize information from the charging population to guide the pheromone update process. In contrast to DPCA, which solely relies on the best solution, we establish interaction among multiple solutions from both the routing and charging populations, which can better contribute the information interaction between two populations. Furthermore, we devise a novel population update strategy that enhances the selection of promising solutions. Experimental results validate the effectiveness of the proposed algorithm by demonstrating its ability to avoid local optima. Moreover, it achieves a reduction of approximately 4% in the average route distance across two public test suites. The source code is available at https://github.com/ShouLiang-Z/IECA.

Municipal solid waste management using electric vehicle by variable neighbourhood search algorithm

Efficient solid waste management is essential for addressing the multifaceted challenges associated with waste disposal, including environmental, economic, technical, and social aspects. Municipal solid waste management (MSWM) incurs significant costs and contributes to environmental pollution primarily due to the collection process. This research presents a comprehensive case study that focuses on optimising the routing of electric vehicles for solid waste collection. Specifically, it addresses the Half-Open Time-Dependent Multi-Depot Electric Vehicle Routing Problem considering Battery Recharging and Swapping (HOTDMDEVRPBRS) in the context of waste collection. This problem aims to optimise the routes taken by electric vehicles across multiple depots, considering constraints such as limited battery capacity, multiple technologies for recharging battery capacity, the impact of truckload on energy consumption, and time-dependent travel times. To tackle this problem, we propose a highly efficient Variable Neighborhood Search (VNS) meta-heuristic algorithm, which outperforms the Simulated Annealing (SA) approach. The proposed algorithm achieves an average improvement of 11.88% in solution quality and reduces execution time by 73% for last-mile delivery. We evaluate the effectiveness of the proposed approach using real-world data from New York's recycling management system. The findings of this study emphasise the potential for enhancing solution quality and operational efficiency in solid waste management.

A Vehicle-to-Grid planning framework incorporating electric vehicle user equilibrium and distribution network flexibility enhancement

The rapid surge in electric vehicle (EV) adoption, coupled with advancements in charging technologies, emphasizes the critical necessity for expanding EV recharging infrastructure. Simultaneously, the Distribution Network (DN) encounters escalating challenges in meeting charging demand during peak traffic periods. Consequently, there is a mounting demand for the deployment of innovative Vehicle-to-Grid (V2G) technologies to augment the DN’s flexibility in power dispatch and alleviate travel costs for EV users. Hence, this paper proposes an EV-user-equilibrium-(UE)-constrained V2G planning framework that enhances flexibility in the DN. The framework aims to ascertain the optimal placement and capacity of EV charging stations (EVCSs) and V2G charging piles within the Transportation Network (TN). It takes into account the equilibrium condition stemming from competitive EV charging and routing behaviors alongside the optimal expansion of DN energy resources to accommodate the electricity supplied by the V2G piles. This study commences by analyzing EV drivers’ travel decisions, considering the influence of charging and V2G pile locations and sizes. Subsequently, we tackle the Traffic Assignment Problem with User Equilibrium (TAP-UE) model to characterize the steady-state traffic flow distribution of EVs. Following this, we formulate the optimization model for the Coordinated Power and Transportation Network (CPTN), which encompasses the optimal expansion of DN facilities and traffic flow regulation under UE conditions. To mitigate the computational complexity associated with the V2G planning model, we introduce a series of linearization methods to obtain a manageable Mixed-Integer Linear Programming (MILP) solution. Finally, to validate the efficacy of our proposed planning framework, we apply it to two test systems, including a real-world case study. Through these case studies, we explore the necessity and potential benefits of V2G technologies.

Two-stage heuristic algorithm with pseudo node-based model for electric vehicle routing problem

Electric vehicle routing problem (EVRP) is a special vehicle routing problem, which owns several specific characteristics of EV technology including the limited charging stations and the limited cruising range of EVs. This paper proposes a two-stage heuristic algorithm for EVRP with a kind of pseudo node, termed EVRPPN-TSH, which not only contributes to the model innovation but also to the algorithm design. In model innovation, the pseudo node is introduced into the EVRP model, forming EVRPPN, to reduce the search space and time complexity for obtaining service orders of customers from O(n) to O(1). Moreover, different from other research works which only use total distance as the fitness function, an improved fitness function is proposed, which takes all the distance, the electricity and capacity constraints compliance into consideration. In algorithm design, we first adopt the two-stage idea, which divides EVRP into the capacitated vehicle routing problem (CVRP) and a fixed route vehicle charging problem (FRVCP). Then we design a two-stage heuristic algorithm, termed as TSH. Specifically, for CVRP, a route division heuristic algorithm and a depot move heuristic algorithm are designed to divide routes. Further, an adjustment strategy with three operators is designed for adjusting the customer order. For FRVCP, an existing heuristic algorithm is adopted and enhanced by a variable extent shaking algorithm to avoid local trapped. Experimental results show that EVRPPN-TSH generally outperforms other state-of-the-art algorithms. Moreover, EVRPPN-TSH can obtain the best-known solution in all the 7 test cases, and update the best-known solution in test case E101 from 834.84 to 834.22.

Heterogeneous Electric Vehicle Routing Problem with Multiple Compartments and Multiple Trips for the Collection of Classified Waste

Heterogeneous Electric Vehicle Routing Problem with Multiple Compartments and Multiple Trips for the Collection of Classified Waste

Electric vehicle routing optimization under 3D electric energy modeling

Electric vehicle routing optimization under 3D electric energy modeling

A resilience-oriented pre-positioning approach for electric vehicle routing and scheduling in coupled energy and transport sectors

High-impact low-probability (HILP) events have occurred more frequently than before and caused severe damage to conventional power systems. Energy hubs (EHs) consist of various distributed energy resources (DERs) for energy generation, conversion and storage across different sectors. The high energy integration of EH systems makes them more robust under extreme events than traditional power systems. In addition, the large penetration of electric vehicles (EVs) has been witnessed in modern energy systems due to their significant benefits in accelerating transport electrification and reducing carbon emissions. Due to the characteristics of mobility and flexibility, EVs can be utilised as mobile energy resources in coupled energy and transport sectors and shift energy between different regions via effective routing and scheduling behaviours. In this context, this paper proposes a resilient-oriented pre-positioning approach for the routing and scheduling of multiple EVs in a coupled energy-transport system, where the energy system includes multiple EHs across both electricity and heat sectors. To simulate real-world scenarios, uncertainties associated with renewable generation, load profiles, and EV commuting time as well as contingencies related to component failures are incorporated into the proposed pre-positioning approach via stochastic programming. Extensive case studies are carried out based on an EH system including three EHs and five EVs, which illustrate that EVs can coordinate with static DERs in the system and perform energy shifting between different EHs via appropriate routing and scheduling behaviours. Additionally, results demonstrate that the proposed pre-positioning approach can achieve higher resilience level and ensure the supply continuity of critical loads.

Machine Learning Applied to Electric Vehicle Routing Problem: Optimizing Costs for a Sustainable Environment

The global move towards Electric Vehicles (EVs) marks a crucial step towards sustainable transportation. However, effectively integrating EVs into the current infrastructure demands more than technological advancements. One of the key challenges is optimizing the routing of EVs to minimize costs and environmental impact. This editorial examines the role of Machine Learning (ML) in addressing the electric vehicle routing problem (ESVRP), highlighting its potential to transform cost optimization and sustainability in transportation. Routing is a fundamental part of transportation logistics, influencing efficiency, cost, and environmental impact. While traditional internal combustion engine vehicles have established routing systems, EVs present unique challenges such as limited battery capacity, longer refueling times, and fewer charging stations. These factors require advanced routing solutions that can dynamically adapt to various constraints.