# SVD Enhanced Metaheuristic for Plug-In Hybrid Electric Vehicle Routing Problem
## 4 Methodology
### Memetic Algorithm
The data of these instances are derived from Capacitated Vehicle Routing Problem (CVRP). This instances consists of datasets

Figure 3: Flowchart: Hybrid Memetic Algorithm. for CVRP proposed by [PERSON] et al. (datasets A, B, and P), by [PERSON] and [PERSON] (for dataset E), by [PERSON](for dataset F). All instances are available in [[http://neo.lcc.uma.es/vrp/vrp-instances/](http://neo.lcc.uma.es/vrp/vrp-instances/)]([http://neo.lcc.uma.es/vrp/vrp-instances/](http://neo.lcc.uma.es/vrp/vrp-instances/)). In order to better study the impact of electric stations and fuel stations on PHEV routing problem research, we divided the test into three situations, taking different number of electric stations and fuel stations for testing. The first case consists of 0 electric station and 0 fuel station (E0F0). The second scenario considers 2 electric stations and 2 fuel stations (E2F2) and the third case has 4 electric stations and 4 fuel stations (E4F4). In order to facilitate the comparison with existing methods, we use the same station locations as in the work of [PERSON] et al. [8]. Running tests were conducted on 14 kinds of test data under these three conditions, and their costs and distances were recorded. Specifically, for CVRP, it can be understood as a specific case of our E0F0 situation in this work where the fuel and electric stations are not considered. By replacing the time constraint with load constraint, some modifications to the proposed algorithm can be used to solve CVRP. Compared with HVRP defined by [PERSON], our optimization goal is to minimize the total cost and our article covers all the constraints of their articles and adds a few additional constraints. It is shown that the proposed algorithm can solve the problems with energy stations and general vehicle routing problems without energy stations. Parameter sensitivity analysis has been done in the work of [PERSON] and [PERSON], [PERSON] and [PERSON]. Therefore, in this work, our parameter settings are consistent with theirs which are \(P_{c}=0.5\), \(P_{better}=0.8\), \(P_{mincopy}=0.15\), \(P_{maxcopy}=0.9\), \(iter_{max}=1000\). When E2F2 and E4F4 are used, \(l_{max}\) is set to 5 and has five neighborhood structures. When E0F0 is used, \(l_{max}\) is set to 3. At this time, insert and delete station are not performed. For the layout of the fuel station and electric station, the methods we used are as follows--E2F2, 1 and 2 for charging stations, 3 and 4 for gas stations, then the customer sequence will start from 5, and \(-1\) for depot. Similarly, we can get the distribution of E4F4. [PERSON] et al. [8] compared Plug-in Hybrid Electric Vehicle (PHEV) with Mild Hybrid Vehicles and Conventional Vehicles. The results suggested that PHEV has more advantages than the others. Thus, we considered the PHEV in our work. This paper focuses on the PHEV routing problem, which considers a series of constraints in the VRP problem such as time limits, fuel capacity, electric capacity, fuel station and electric station. Table 2 presents the experimental results of the proposed algorithm for this problem with different power station arrangement (e.g., E0F0, E2F2 and E4F4). We have 14 instances tested under these cases, and each configuration is tested 10 times. The size of the population is 1000, the number of iterations is set to 100. With the increasing number of customers in test cases, the average CPU time of these instances are between 3 and 30 s. The best value of cost, the mean value of cost, the related mile value of the best obtained solution and the mean value of mile for each configuration are presented in Table 2. Since the objective of this paper is to minimize the total cost, the related mile in the table refer to the distances corresponding to the solution with best cost value, instead of the shortest distance in the 10 runs. In most cases, the related mile is less than the average mile in Table 2, but there are