Summary:
Electric vehicle technology promises to reduce the cost and environmental impact of logistics operations. Therefore, there is a lot of research going on in this area. At the operational level, the Electric Vehicle Routing Problem (EVRP) has recently been introduced and deals with forming efficient vehicle routing plans while satisfying a range of battery-related constraints. This article presents a comprehensive literature review on EVRP and its extensions. In this context, we review136 published papers that consider battery electric vehicle routing. EVRP is clearly defined, variations on the basic EVRP are discussed, a mathematical formula and a model for several simple variations of the problem are given, and the developed solution is discussed in detail. Furthermore, the EVRP benchmark set is introduced, and finally, interesting future research directions are discussed.
1. Citation:
Electric vehicles promise to reduce transportation costs and pollution impacts compared to fossil fuel-based engines. However, compared with the refueling operation of fossil fuel-based vehicles, the limited cruising range, long charging time and limited charging facility availability make charging operation a more critical issue (Jing et al., 2016; Juan et al., 2016 ; Margaritis et al., 2016 ; Pelletier et al., 2016 ). The Electric Vehicle Routing Problem (EVRP) is an extension of the traditional Vehicle Routing Problem (VRP) that specifically deals with finding optimal routes for electric vehicles, taking into account battery constraints and charging operations (Keskin & Atay, 2016; Schiffer & Walther, 2017; Schneider et al., 2014 ).
As the logistics community becomes more interested in incorporating electric vehicles into its fleets, academic research on EVRP is also increasing, as shown in Figure 1. .This paper conducts a comprehensive survey of EVRP by considering 136 journal papers (JP), conference proceedings (CP), theses (TH), and technical reports (TR). Table 1 gives an overview of the journals that have published 84 academic papers.
The purpose of this survey is to conduct a comprehensive literature review on EVRP and its extensions. First, existing studies are classified according to four criteria: objective function, energy consumption calculation, additional constraints considered, and fleet type. Then, the mathematical formula of EVRP and its basic changes are introduced. Finally, existing solutions proposed for EVRP and useful problem datasets are reviewed and introduced. The contributions of this article to the literature are as follows.
- A comprehensive and detailed survey is presented by analyzing 136 publications. To date, a literature review on electric vehicles (including EVRP) or EVRP has been conducted by Pelletier et al. (2016), Juan et al. (2016), Dammak and Dhouib (2019), Erdeli ́ c and Cari ́ c (2019), Ghorbani et al. (2020) and Qin et al. (2021). However, only a few papers on EVRP have been reviewed. Table 2 shows the papers reviewed in this study and indicates overlap with other papers reviewed. As can be seen from Table 2, the 62 analyzed papers were not included in any existing literature review studies.
- A systematic classification is introduced.
- Summarizes existing solutions and analyzes the performance of seven different solutions by comparing results on a popular dataset.
- Potential research directions are pointed out by discussing existing research gaps.
The remainder of this article is organized as follows. Section 2 introduces the details of EVRP. Section 3 gives a classification of the considered EVRP papers in terms of four criteria (objective function, energy consumption calculation, constraints, fleet type). Section 4 introduces the mathematical formulation of EVRP and its frequently encountered variations. Section 5 summarizes and categorizes the solutions to EVRP. In Section 6, a basic problem set based on the well-known vehicle routing problem is specified. Furthermore, by comparing different solution methods, the best-known solutions for the most popular benchmark datasets are pointed out. Finally, Section 7 gives conclusions and future research prospects.
5.Solution
As an extension of the well-known VRP, EVRP also handles planning visits to charging stations while confirming customer orders on a route. Since VRP is an NP-hard problem and EVRP is a generalization of VRP, EVRP can also be considered as NP-hard in a strong sense (Desaulniers et al., 2016; Ferro et al., 2018; Roberti & Wen, 2016 ; S. Zhang et al., 2018). Furthermore, adding the constraints described in the previous sections makes the solution of the problem quite complex (Afroditi et al., 2014; Desaulniers et al., 2016; Goeke & Schneider, 2015). The solution methods proposed in the literature can be divided into exact and heuristic methods. However, due to the complexity of the problem, the number of studies using exact methods as a solution is very small. Tahami et al. (2020) proposed a branch-cut algorithm to solve the famous EVRP. Desaulniers et al. (2016) introduced an accurate branch price and cut algorithm to solve four variants of EVRP: under the full charging policy, each route can only be charged at most once; under the full charging policy, each route can be charged at most Can be charged once; under some charging policies, each route can be charged once. Similarly, Pierotti (2017) used branch price and cut algorithm to solve EVRPTW with heterogeneous charging stations. Ceselli et al. (2021) provide a branch-and-cut and price algorithm for EVRP with multiple charges. The algorithm proposed therein relies on a path-based formulation. Lee (2020) introduced a branch and price method to optimally solve an extended version of EVRP with nonlinear charging times. Wu and Zhang (2021) also considered branch and price methods to solve dual-echelon EVRP. In addition to these methods, commercial solvers are often used to find optimal solutions for EVRP and its extensions. Paz et al. (2018) and Küçüko ̆ glu and ̈ Oztürk (2016) extended EVRPTW with different assumptions and solved their small-scale problems (including 5, 10 and 15 client nodes) using CPLEX, a commercial solver. CPLEX has also been used to solve different EVRP variants (see, for example, Hulagu and Çelikoglu (2019), Keskin, Akhavan-Tabatabaei et al. (2019), Lin et al. (2016)). Aksoy et al. used another commercial solver GUROBI for EVRP. (2018), Chen et al. (2016), Cubides et al. (2019), Froger et al. (2017), Froger et al. (2018), Froger et al. (2019), Granada-Echeverri et al. (2020), Moghaddam (2015), Montoya et al. (2015), Schiffer and Walther (2017), and Wang et al. (2019).
In addition to exact solution methods, metaheuristic algorithms are also widely used as solution methods for EVRP. Table 7 gives an overview of the metaheuristic algorithms used in the reviewed papers: Ant Colony Optimization (ACO), Cuckoo Search (CS), Differential Evolution Algorithm (DEA), Genetic Algorithm (GA), Iterative Local Search ( ILS), Large Neighborhood Search/Adaptive Large Neighborhood Search (LNS/ALNS), Memory Algorithm (MA), Simulated Annealing (SA), Tarub Search/Adaptive Tarub Search/Granular Tarub Search (TS/ATS) /GTS) and variable neighborhood search. The last column of Table 7 also lists additional procedures integrated with the metaheuristic algorithm. Furthermore, a pair of metaheuristic algorithms marked in a row in Table 7 represents a hybrid structure of these two algorithms. Based on the algorithms given in Table 7, Figure 4 presents the relative occurrence of these methods. As can be seen from Table 7 and Figure 4, LNS/ALNS, VNS/AVNS, GA and TS/ATS/GTS are the most common metaheuristic methods in EVRP.
For heuristic-based solution methods, one of the fundamental issues that directly affects the search performance is the representation of the solution. Like classic VRP, envelope-ordered integer arrays are usually used to represent solutions in existing solution methods (Goeke & Schneider, 2015; Küçüko ̆glu & ̈ Oztürk, 2016; Roberti & Wen, 2016; Schiffer & Walther, 2018a; Schneider et al., 2014). For VRP, an integer array consisting of customer locations is rich in earliest arrival, earliest departure, latest arrival and latest departure times, allowing the development of efficient local search algorithms (Mitrovi ́ c-Mini ́ c & Laporte, 2004). However, EVRP's solution also requires charging visits to stations in the route plan. Since there is no limit to the number of charging station visits on a route, a vehicle can visit neither a charging station nor one or more charging stations. Furthermore, it is even possible to have multiple charging station visits between a pair of customer nodes. Furthermore, the capacity of the charging station is another key decision if a partial charging policy is followed. Especially for EVRP with time window restrictions, the charging time of the charging station needs to be well planned to meet the customer's time window restrictions. Therefore, feasible route construction is much more difficult for EVRP than for VRP. In order to develop feasible route plans in terms of battery capacity, two main approaches exist in the literature: heuristics and optimal charging station insertion methods.
Heuristic charging station insertion methods search the inserted solution space in a straightforward manner. The most common method is to apply removal and insertion procedures to the charging station continuously. This has been successfully applied to EVRP in many studies (Felipe et al., 2014; Goeke and Schneider, 2015; Keskin & Çatay, 2015; 2016; Schiffer and Walter, 2018a; Schneider et al., 2014). This procedure requires a solution representative consisting of the customer and the charging station. For the removal operation, multiple stops are removed from the route based on heuristic rules, such as random selection, selection of sites that result in high travel distance, selection of sites that result in higher battery usage, etc. Similarly, insert charging stations into routes to restore battery viability.
As an alternative to the heuristic charging station insertion method, forward marking algorithms based on dynamic programming have been applied in some studies (see, for example, the study by Hiermann et al.). (2014), Hiermann et al. (2016), Jie et al. (2019), Küçüko ̆ glu et al. (2019), Pierotti (2017), and Roberti and Wen (2016)). The labeling algorithm works through a solution consisting only of customer locations and attempts to optimally insert charging stations into the route while maintaining feasibility in terms of battery capacity or other constraints such as time windows. The algorithm starts with an initial label of a warehouse node (battery full) and creates a feasible set of labels at each step by inserting possible charging stations between customer nodes. This algorithm provides an optimal set of charging station insertions for a given customer node route (Roberti & Wen, 2016). Compared with the heuristic charging station insertion method, the labeling algorithm is much more time-consuming. However, given enough computation time, this labeling algorithm often produces better solutions than using heuristic methods. Similar to the study by Roberti and Wen (2016), Kullman et al. (2017), and Kullman et al. (2018) introduced a dynamic decision-making procedure for a single electric vehicle routing problem with uncertain charging station availability. The computational complexity of inserting charging stations for a given customer-only route has not been previously determined. However, this problem is most likely to be NP-hard in the strong sense, because the insertion problem is similar to the resource-constrained shortest path problem, whose purpose is to find a minimum cost-oriented path from the source to the destination while satisfying the resource constraints. (Horv ́ath & Kis, 2016; Strehler et al., 2017).
6.Dataset
The most widely used EVRP dataset was introduced by Schneider et al. (2014), consists of small and large instances with up to 100 customer locations. All these instances are generated based on Solomon's (1987) benchmark dataset of VRPTW. The VRPTW data set is divided into three categories based on geographical distribution: random customer distribution (R), clustered customer distribution (C), and a mixture of R and C categories (RC). Furthermore, in terms of scheduling scope, these categories are divided into two groups, where R1, C1, and RC1 form the first group with a shorter scheduling scope, while R2, C2, and RC2 form the second group with a longer scheduling scope. Based on VRPTW instances, Schneider et al. (2014) proposed a set of 56 large-size instances, including 100 customer locations and 21 charging stations, and a set of 36 small-size instances, including 5, 10, and 15 customer locations. . Charging stations in each instance are identified as follows. One of the charging stations is located at the warehouse node. The remaining charging stations are randomly distributed, assuming that each customer can use up to two charging stations to arrive from the warehouse. On the other hand, the battery capacity of electric vehicles is determined by taking into account the maximum of the following two values: the charging required for 60% of the average route length of the best-known VRPTW solution of this instance, and the distance between the customer and the station Twice the charge required for the longest arc distance. Finally, the time window data were regenerated using the procedure described in Solomon (1987) to obtain feasible instances.
Many solution programs use the EVRPTW dataset introduced by Schneider et al. (2014). Therefore, this section also presents the best solutions for examples from existing studies and compares the solution quality of different solutions. Table 8 shows existing results based on the small-scale example studied by Schneider et al. (2014), Küçükŏglu and Oztürk (2016), and Schiffer and Walter (2017). Schneider et al. (2014) compared their proposed VNS/TS algorithm with the exact solution obtained by CPLEX in two hours. Two other studies presented by Küçükŏglu and Oztürk (2016) and Schiffer and Walther (2017) present the optimal solutions obtained by CPLEX and GUROBI solvers respectively. According to the exact solution results shown in Table 8, each study found the same solution for most instances. However, the results presented by Küçükŏglu and Oztürk (2016) obtained the minimum average objective function value with shorter CPU time by using a better formula. On the other hand, VNS/TS is able to obtain the same results as or better than the optimal bounded integer solution of the exact solver in shorter processing time.
For large-sized instances, Table 9 shows the results of seven different solution methods and lists the best solution for each instance. It should be noted that for this table, the first goal of EVRPTW proposed by Schneider et al. (2014) is to minimize the total number of electric vehicles used on the route. The secondary goal is to minimize the total driving distance of an electric vehicle. Therefore, a solution with a smaller number of routes can be determined to be a better solution than another solution with a smaller total travel distance. Regarding the quality of the solution, the ALNS algorithm proposed by Goeke and Schneider (2015) is the best algorithm compared with the other six solution methods. In addition to the results shown in Table 9, Schiffer and Walther (2018a) and Kancharla and Ramadurai (2018) established shorter distances for EVRPTW. However, these results were not considered in this study because the authors did not give the total number of electric vehicles used for the route.
Since the calculations are performed in different technical environments given in Table 10, it is difficult to make a fair comparison between algorithms. Computation of the branch-and-price algorithm proposed by Hiermann et al. (2016) were conducted under a time limit of 8 h, and for most cases the results were obtained at the end of the time limit. For other algorithms, the average CPU time is similar except for the ALNS algorithm proposed by Goeke and Schneider (2015), which is better than
The calculation of EVRPTW mentioned above and its results take into account the full charging policy of the station charging operation. Some papers discuss partial charging policies applied to the problem dataset of Schneider et al. (2014) to test their method. Since partial charging requires less operating time for electric vehicles than full charging, EVRPTW's problem dataset can be used without any issues. Following the partial charging policy, Keskin and Çatay (2016) proposed 33 optimal solutions for small EVRPTW instances by using CPLEX with a two-hour time limit. Furthermore, the authors applied their ALNS algorithm to both small and large instances and reported an average saving of 1.64% in total distance compared to the EVRPTW solution. Additionally, a reduction in the number of electric vehicles in use has been observed in some instances. Schiffer and Walther (2017) also found similar results for small-sized EVRPTWs with partial charges. However, they were able to obtain the optimal solution for 32 instances despite higher average CPU time. The authors also extended the data set of Schneider et al. (2014) for another extended version of EVRP, called the robust electric positioning routing problem with time windows and partial charging (Schiffer and Walther, 2018a; Schiffer and Walther, 2018b). This dataset was used in another study by Schiffer et al. (2018) to test the ALNS introduced for the location routing problem with in-route facilities.
The data set of Schneider et al. (2014) was also used for EVRPTW with heterogeneous fleets. For this extension, Hiermann et al. (2014) and Hiermann et al. (2016) modified the original instance by incorporating different EV types into the problem data using the instance set defined by Liu and Shen (1999) for the time-windowed hybrid vehicle routing problem. The same extension was also considered by Küçüko ̆ glu and ̈ Oztürk (2016). The authors modified the original small-size EVRPTW dataset by using real technical information on eight different electric vehicles. According to their calculations using CPLEX, using a heterogeneous fleet can achieve an average reduction of 5.55% in total distance. Desaulniers et al. (2016) modified the data set of Schneider et al. (2014) for their proposed four variants of EVRPTW, described in the previous section. The authors present a detailed solution to the problem solved by the branch price and cut algorithm.
Different from the EVRPTW dataset of Schneider et al. (2014), some researchers formed their own datasets for the considered EVRP problem. For example, Felipe et al. (2014) generated a new problem set consisting of 60 instances of EVRP with multiple technologies and partial charges, where the number of customers varied between 100 and 400 and was randomly distributed, Even geographical distribution. Goeke and Schneider (2015) adapted the data set proposed by Demir et al. (2012) targeted the polluted routing problem by adapting it to a routing problem for a mixed fleet of electric and conventional vehicles. The modified dataset consists of nine instance sets, grouped according to problem size, which varies between 10 and 200 customers, with each instance set containing 20 instances. S. Zhang et al. (2018) introduced 40 examples of EVRP, where the research goal was energy minimization of electric vehicles rather than distance minimization. Yang and Sun (2015) used four well-known datasets for the capacity vehicle routing problem for the battery exchange station location and routing problem by assuming that all nodes are candidate battery exchange stations. These questions were also used by Hof et al. (2017). Based on battery swapping technology, Jie et al. (2019) introduced a new two-level capacitor electric vehicle routing problem dataset. Roberti and Wen (2016) introduced another useful dataset for the electric traveling salesman problem with time windows to test their GVNS algorithm. The authors generated two sets of test problems, where the first set consisted of 50 small instances with 20 customer locations, and the second set consisted of 50 large instances with 150 and 200 customer locations. Furthermore, each group was divided into two subsets based on the number of charging stations in the problem (5 and 10). The small and large examples are respectively from the traveling salesman problem with time window instances proposed by Gendreau et al. (1998) and Ohlmann and Thomas (2007). The proposed GVNS is tested on the dataset with full and partial charging strategies. Hof et al. (2017) and Montoya et al. (2017). As one of the recent studies, Karakati C (2021) extended the dataset proposed by Cordeau et al. (2001) by adding charging stations per instance for multi-site EVRPTW , where each charging station has the same charging speed.
7. Conclusion and future research directions
In this study, we provide a comprehensive and up-to-date review of existing research on EVRP. Looking at the electric vehicle route alone, we analyzed 136 different papers, including journal articles, conference proceedings, technical reports, and theses. We discuss these studies from different aspects. The mathematical formula of EVRP and its basic variants are given, the most successful solution methods are introduced, useful problem data sets for EVRP are summarized, and computational tests comparing several successful methods are discussed. Considering the current research on EVRP, the following conclusions and future research directions can be expressed:
-1. As with traditional vehicle routing problems, most EVRP-related studies aim to minimize distance-based performance metrics, while a few studies take into account the total energy consumed or the number of charging stations used. As interest in green logistics concepts grows, objective functions more related to consumed energy or charging operations are also of interest to be studied in EVRP. In practice, however, a logistics company's primary focus is the bottom line. Therefore, a realistic goal in most applications is to minimize the total cost, which includes energy use, driver cost, and vehicle cost. Energy use is a function of distance, speed, vehicle load and vehicle type. Driver costs depend on the total route duration, and special attention should be paid to possible overtime costs. Vehicle costs can be addressed within a primary objective of minimizing the number of vehicles or minimizing the weighted number of vehicles of a specific type. Alternatively, vehicle cost can be expressed as depreciation as a function of distance and vehicle type. These goals can be combined into a single goal expressed in monetary terms.
2. In almost all work, the energy consumed by an electric vehicle over a given distance is determined by using constant energy usage per unit of distance. However, under real-world driving conditions, the energy consumption of electric vehicles is affected by different conditions, such as road conditions, traffic conditions, weather conditions, driver performance, terrain and vehicle load. Therefore, these conditions should be considered to obtain more realistic results for route planning. Additionally, regeneration of energy when going downhill or braking is possible and should be taken into account. In addition, the energy use of an electric vehicle's heating or air conditioning system relative to weather conditions can be analyzed. Because the optimization algorithm will optimize to the limit, some routes will have battery power close to zero by the time they reach a charging station or parking lot. Therefore, ignoring or oversimplifying aspects of energy consumption is likely to lead to routes that are not feasible in practice. Since it is impractical to accurately model energy use in large-scale applications, it might be interesting to study when this infeasibility arises when simplifying certain aspects. This can then be used to determine safe buffers on the battery based on EVRP instance type or even routing characteristics.