A Collection of Literature Review on Vehicle Routing Problem and Reflections

: As a variation of vehicle routing problem whose objective is to determine the subset of nodes to be visited, and the order in which they should be visited, in order to maximize the profit collected within a given time, team orienteering problem has received a lot of attention in the last decades. With the growing interest in the logistics community in using electric vehicles as an alternative to conventional fuel vehicles, academic research on electric vehicle problem is increasing. However, there is still a paucity of research on the use of electric vehicles in team orienteering problem. This paper reviews the existing literature on electric vehicle routing problems and team orienteering problems to identify the feasibility of innovations that propose the use of electric vehicles to replace conventional fuel vehicles in team orienteering problems to complete deliveries, and briefly outlines future research plans.


Introduction
In February 2019, the Opinions on Promoting High-quality Development of Logistics and Forming a strong Domestic Market jointly issued by 24 ministries and commissions including the National Development and Reform Commission pointed out that it is necessary to speed up the development of green logistics, continue to promote pollution control efforts of diesel trucks, and encourage enterprises to use low-carbon and environmentally friendly distribution vehicles that meet standards. In order to actively respond to the national call for green logistics and low-carbon life, various logistics and express delivery enterprises have integrated the concept of green development into the actual distribution field.
As the logistics community shows growing interest in using electric vehicles as an alternative to traditional fuel vehicles, academic research on electric vehicle projects is increasing (Kucukoglu et al. 2021). The electric vehicle routing problem (E-VRP) is an extension of the traditional vehicle routing problem (VRP), taking into account the battery restraint and charging operation, finding optimized routes specifically for electric vehicles.
Team orienteering problem (TOP) is a special class of logistics distribution vehicle routing problem. In this problem, a limited number of vehicles provide services for a group of customers with a certain reward under certain constraints. Due to time or travel cost constraints, each location can be visited at most once, and the distribution path of these vehicles needs to be optimized to maximize the total profit of the fleet. It is often used in tourist attraction planning, postdisaster rescue and other scenarios.
This paper will sort out and analyze the existing research results at home and abroad on the two major variants of the vehicle routing problem, electric vehicle routing problem and team orienteering problem, find out the innovation points, propose that electric vehicle replace the fuel vehicle used in the team orientation problem as the goal of future research work, establish the corresponding mathematical model, and briefly describe the solution algorithm planned to use.

Related Research on Electric Vehicle
Routing Problem (1) Electric vehicle routing problem with full recharge Conrad and Ryan (2011) replaced the fuel vehicle used in the VRP problem with a charging vehicle and proposed the Recharging VRP (R-VRP) problem, which only allows the vehicle to be charged at the customer node. The green vehicle routing problem (G-VRP) proposed by Erdogan and Miller-Hooks (2012) is considered to be the origin of the electric vehicle logistics routing problem (E-VRP). They built a mixed integer linear programming model considering charging stations and used the improved Clarke and Wright saving algorithm and density-based clustering algorithm. On this basis, Schneiders et al. (2014) added vehicle load and customer time window as model constraints, namely, E-VRP with time windows and recharging stations (E-VRPTW) for electric vehicle routing problem considering customer time window. Each customer node is given a time window, and the vehicle can only serve the customer within the time window. If the vehicle arrives early, it needs to wait; otherwise, it cannot be served. A hybrid meta-heuristic algorithm combining variable neighborhood search algorithm and tabu search algorithm is used to obtain an approximate solution. (2) Electric vehicle routing problem with partial recharge Felipe et al. (2014) proposed the problem of green vehicle routing problem with partial recharge (G-VRP with Partial Recharges (G-VRP-PR), that is, it is necessary to consider not only the charging time and location of the vehicle, but also the charging amount, and solve the problem by using the local search algorithm within the framework of non-uncertain simulated annealing. Catay (2016, 2018) proposed the electric vehicle routing problem with partial recharge (E-VRPTW-PR), and used three charging stations with different charging rates, namely slow normal and fast charging; The higher the charging rate, the vehicle gets the same amount of power for less time, but at a higher cost. In addition, using an adaptive large neighborhood algorithm that introduces new insertion and removal operators, they demonstrate that the solution using a partial recharge strategy is superior to full charging. Desaulnier et al. (2016) consider four different scenarios (single/multiple charging stations and partial/full charging on each path) for an EV routing problem with time window (E-VRPTW); For each case, a precise branch, price and cut algorithm relying on customized oneway and two-way labeling algorithms was used to generate viable vehicle routes. Experimental results show that multifacility partial charging is more helpful to reduce route cost and number of vehicles than full charging at a single charging station. Montoya et al. (2017) divided the charging process of electric vehicles into two stages. In the first stage, the charging rate is the same, and the charge increases linearly with time until the terminal voltage of the battery increases to a specific maximum value. In the second stage, the current drops exponentially, the terminal voltage remains the same, and the battery charge increases in a concave shape over time.

Related Research on Team Orienteering Problem
(1) Orienteering problem The orienteering problem (OP) is a variant of the vehicle routing problem that aims to maximize profit for a single vehicle by choosing to visit customer nodes, within a specific time and/or distance limit. The single vehicle orienteering problem can be thought of as a combination of the backpack problem and the traveling sales problem.
(2) Team orienteering problem The team orienteering problem (TOP) using multiple vehicles is an important variant of the orientation problem, first proposed by Chao et al. (1996). The difference between TOP and VRP is that (1) not every given customer node needs to be accessed, (2) the vehicle load does not need to be considered, and (3) the optimization goal is to maximize profit rather than minimize cost. The solution of this problem by Chao et [20] al is regarded as the benchmark example of the team orientation problem. In order to solve this problem accurately, the authors propose a Benders branch and cut algorithm, which is able to deal with non-concave parts efficiently. In addition, the authors propose an efficient hybrid heuristic algorithm that integrates the improved coordinate search into the iterative local search, which can quickly produce high-quality solutions to this complex problem.

Electric Vehicle Team Orienteering Problem
There are few researches on the electric vehicle team orientation problem, and most of the existing literatures focus on the team orienteering of unmanned aerial vehicles (UAVs) and electric vehicle tourism problem.
Rubiano et al. (2018) studied a random team orientation problem, in which a group of UAVs need to visit a series of customers, the reward obtained by visiting customers is a random variable, and the service time of each customer depends on the reward obtained. The goal is to find the optimal set of customers that each UAVs must visit without violating the driving range constraints. Saeedvand et al. (2020) consider the application of TOPTW problem in the humanoid robot disaster relief scenario, where each robot has a limited amount of power, and it can obtain profits by visiting the task within the time window. The problem aims to optimize five different objectives: task profit, task finish time, total energy, maximum energy consumption of a single robot, and penalty for missing the time window.
Wang et al. (2018) combined the orienteering problem considering the time window with range limited electric vehicles to propose the electric vehicle tourist trip design problem with time windows (ETTDPTW). In addition, the authors introduce a model that can simulate the change of battery power state at various points along the route to check whether the next arc of the trip is feasible. Chen et al. (2020) studied the problem of electric vehicle travel planning, aiming to maximize profitability and minimize energy anxiety within prescribed limits; In addition, two scenarios of full charging and partial charging are considered. In order to solve this problem, the authors establish a bi-objective mixed integer model and use an interactive branch-and-bound algorithm based on non-dominated sets to solve it, so as to obtain the optimal solution under different charging strategies. Karbowska-Chilinska and Chociej (2020) investigate the multistage travel design problem, considering an itinerary composed of multiple connected trips, i.e., the multistage strategy. Therefore, this set of connected trips can be viewed as a "team" trip, i.e., a team orienteering problem.

Summary of Research Status and Innovation Points
Through the review and analysis of the existing literature, it can be seen that at present, domestic and foreign scholars have relatively rich research results on the electric vehicle routing problem and team orienteering problem. In terms of solving algorithms, no matter it is exact algorithm or heuristic algorithm, there are also rich theoretical results. However, in terms of electric vehicle routing problem, most domestic and foreign researches focus on minimizing driving distance, distribution time or operating cost, but seldom consider the team orienteering problem aiming at maximizing profit.
Therefore, the future research work will be based on the mathematical model and optimization algorithm theory and research results of the existing electric vehicle routing problem and team orienteering problem, combined with constraints such as charging time and customer time window that need to be considered in the actual distribution situation. After constructing a 0-1 mixed integer linear programming mathematical model for the team orienteering logistics distribution problem of electric vehicles with a time window, it is planned to design an adaptive large neighborhood search algorithm or deep reinforcement learning to solve the problems in this paper.
The core of the next research work is to set the maximization of collection profit as the objective function, consider the profits obtained by serving each customer point, and take the nonlinear charging process, charging time and customer time window of the distribution vehicle as the constraint conditions to ensure that the model is more practical. For the established mathematical model, it is planned to use an improved adaptive large neighborhood search algorithm to solve it, and verify the feasibility of the algorithm for the model.
All in all, the innovation points of future research are as follows: (1) A new problem of electric vehicle routing problem, that is, electric vehicle team orientation problem, is essentially a combination of electric vehicle routing problem and team orienteering problem. (2) The more practical partial nonlinear EV charging process is considered, thus saving charging time and power. (3) An adaptive large neighborhood search algorithm suitable for solving the problem model is designed and developed.

Conclusion
Under the influence of national policy incentives and environmental awareness, the use of electric vehicles has become an inevitable trend of future social development. By combing the existing research results of E-VRP, this paper finds that the application trend of electrification of urban delivery vehicles has been widely recognized in the academic fields at home and abroad. However, team orienteering problem, as a variant of vehicle routing problem, is rarely considered to be combined with electric vehicles. Therefore, based on the analysis of the domestic and foreign research status of E-VRP and TOP, the future research work will consider combining E-VRP and TOP to form an E-TOP problem and establish the corresponding mathematical model.