The electric vehicle routing problem and its variations: A literature review

Electric vehicles are environmental transportation modes that are widely applied in green logistics systems. To guarantee the energy efficiency, the impacts of customer service modes and recharging strategies need to be integrated into the optimization of electric logistics resource. This paper proposes an electric vehicle routing problem with mixed backhauls, time windows, and recharging strategies (EVRPMBTW-RS), minimizing the total travel cost with sophisticated constraints on the time-dependent pickup and delivery requests, limited recharging station capacity, and battery remaining capacity of electric vehicles. Mixed service sequences of linehaul and backhaul customers is allocated for the routing planning, with the synchronous optimization of recharging strategies including the selection of recharging stations and determination of recharging time. A time-discretized multi-commodity network flow model is constructed based on an extended space–time-state modeling framework, which is formulated as a quadratic 0–1 programming model by using the augmented Lagrangian relaxation technique. After the dualization and linearized transformation, we decompose the model into a sequence of least-cost path subproblems based on the alternating direction multiplier method (ADMM). The subproblems are alternately minimized and solved using the time-dependent forward dynamic programming algorithm. The solution quality can be guaranteed through calculating the optimality gap between the best lower bound and upper bound for each iteration. The proposed solution approach is examined on examples of a simple 7-node network and real-world Yizhuang road network. This paper provides a theoretical foundation for the route optimization method of electric logistics vehicles, and contributes to improve the operational efficiency of electric logistics systems.

Optimizing electric vehicle routing problems with mixed backhauls and recharging strategies in multi-dimensional representation network

In this paper, a battery swap station location and routing problem with time windows and a mixed fleet of electric and conventional vehicles (BSS–MF–LRPTW) is proposed. This problem is motivated by a real-life logistics application by extending the existing electric vehicle battery swap stations location routing problem (BSS–EV–LRP). The BSS–MF–LRPTW aims to simultaneously determine the locations of battery swap stations (BSSs) and the routing plan of a mixed fleet under the driving range, the load capacity limitation, and time windows. An integer programming (IP) model is developed for the proposed BSS–MF–LRPTW. As there are a large number of variables and complicating constraints of the IP model, we break it up into the master problem and the subproblem, based on Danzig–Wolfe decomposition. To enhance the tractability of the problem, we follow up with a heuristic branch-and-price algorithm with an adaptive selection scheme (HBP-ASS), which integrates the exact policy with a heuristic strategy. The HBP-ASS develops heuristic versions of the dynamic programming algorithm by designing seven operators for heuristic label extension and dominance. An adaptive selection scheme is presented to decide which operator is employed. The performance of the proposed HBP-ASS is evaluated based on an extensive computational study. The results show that the HBP-ASS can obtain the exact solution to small-scale instances much more quickly than commercial branch-and-bound/cut solvers such as CPLEX. Also, for all tested cases, the HBP-ASS can find better solutions to large-scale instances within a shorter time than the existing heuristics – adaptive large neighborhood search. Furthermore, sensitivity analyses are carried out to provide managerial insights.

Solving the battery swap station location-routing problem with a mixed fleet of electric and conventional vehicles using a heuristic branch-and-price algorithm with an adaptive selection scheme

The growth of environmental awareness and more robust enforcement of numerous regulations to reduce greenhouse gas (GHG) emissions have directed efforts towards addressing current environmental challenges. Considering the Vehicle Routing Problem (VRP), one of the effective strategies to control greenhouse gas emissions is to convert the fossil fuel-powered fleet into Environmentally Friendly Vehicles (EFVs). Given the multitude of constraints and assumptions defined for different types of VRPs, as well as assumptions and operational constraints specific to each type of EFV, many variants of environmentally friendly VRPs (EF-VRP) have been introduced. In this paper, studies conducted on the subject of EF-VRP are reviewed, considering all the road transport EFV types and problem variants, and classifying and discussing with a single holistic vision. The aim of this paper is twofold. First, it determines a classification of EF-VRP studies based on different types of EFVs, i.e., Alternative-Fuel Vehicles (AFVs), Electric Vehicles (EVs) and Hybrid Vehicles (HVs). Second, it presents a comprehensive survey by considering each variant of the classification, technical constraints and solution methods arising in the literature. The results of this paper show that studies on EF-VRP are relatively novel and there is still room for large improvements in several areas. So, to determine future insights, for each classification of EF-VRP studies, the paper provides the literature gaps and future research needs.

A Survey on Environmentally Friendly Vehicle Routing Problem and a Proposal of Its Classification

A column generation tailored to electric vehicle routing problem with nonlinear battery depreciation

We study a new problem named the Time-dependent Electric Vehicle Routing Problem (TDEVRP) which involves routing a fleet of electric vehicles to serve a set of customers and determining the vehicle’s speed and departure time at each arc of the routes with the purpose of minimizing a cost function. We propose an integer linear programming (ILP) model to formulate the TDEVRP and show that the state-of-the-art commercial optimizer (CPLEX) can only solve instances of very limited sizes (with no more than 15 customers). We thus propose an iterated variable neighbourhood search (IVNS) algorithm to find near-optimal solutions for larger instances. The key ingredients of IVNS include a fast evaluation method that allows local search moves to be evaluated in constant time O ( 1 ) , a variable neighbourhood descent (VND) procedure to optimize the node sequences, and a departure time and speed optimization procedure(DSOP) to optimize the speed and departure time on each arc of the routes. The proposed algorithm demonstrates excellent performances on a set of newly created instances. In particular, it can achieve optimal or near-optimal solutions for all small-size instances (with no more than 15 customers) and is robust for large-size instances where the gap between the average and the best solution value is consistently lower than 2.38%. Additional experimental results on 40 benchmark instances of the closely related Time-Dependent Pollution Routing Problem indicate that the proposed IVNS algorithm also performs very well and even discovers 39 new best-known solutions (improved upper bounds).

The Time-dependent Electric Vehicle Routing Problem: Model and solution

Earth observation satellites (EOSs) are taking a large number of pictures with increasing resolution which produce massive image data. Satellite data transmission becomes the bottleneck part in the process of EOS resource management. In this paper, we study the earth observation satellite integrated scheduling problem (EOSIS) where the imaging activities and download activities are considered integratively. We propose an integer linear programming model to formulate the problem. Due to the NP-hardness of the problem, we propose an efficient local search heuristic (ELSH) to solve problems of large size. ELSH uses a dedicated local search method to guarantee algorithm performance and efficient constraint handling mechanisms to guarantee algorithm efficiency. Numerical experimental results show that the algorithm demonstrates excellent performance on a set of benchmark instances. The ELSH achieves optimal results for all small-size instances (with 50 targets, two satellites, and three ground stations), and is very robust for large instances with up to 2000 targets. Moreover, the proposed ELSH easily dominates the state-of-the-art algorithm.

An Efficient Local Search Heuristic for Earth Observation Satellite Integrated Scheduling

Autonomy increases the ability of earth observing satellites by allowing them to acquire more images. This is enabled by an efficient planning and scheduling algorithm which is able to make quick decisions onboard. Due to the NP-hardness of the agile earth observing satellite (AEOS) onboard scheduling problem, heuristic and metaheuristic algorithms seem to be appropriate to cope with increasingly enlarged problems. Also, the algorithms need to be intelligent enough to deal with dynamically changing situations onboard. Such algorithms are missing in the literature and we make the first attempt to propose a learning-based approach (LBA) for the AEOS onboard scheduling problem. LBA adopts an offline training - onboard scheduling paradigm where it trains a classifier using massive historical data offline on the ground and embeds this classifier to an onboard greedy construction algorithm. At each construction step, the greedy algorithm uses the classifier to test the potential of a task and arranges its observation time if it is accepted by the classifier. Extensive experimental results show that the proposed LBA is highly suitable for onboard use in terms of both solution quality and response time. In particular, LBA easily dominates state-of-the-art algorithms by producing very high quality solutions for large-size problems (with over 100 tasks) in seconds.

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Renjie He

Papers

The Time-dependent Electric Vehicle Routing Problem: Model and solution

An Efficient Local Search Heuristic for Earth Observation Satellite Integrated Scheduling

A Learning-Based Approach for Agile Satellite Onboard Scheduling