# SVD Enhanced Metaheuristic for Plug-In Hybrid Electric Vehicle Routing Problem
## 1 Introduction
The difference between PHEV and ordinary HEVs is that the battery capacity of ordinary HEVs is very limited and its battery cannot be charged externally. The HEV's driving distance in pure electric mode is very short; on the contrary, a PHEV can be charged at any available electric power stations. It can operate in pure electric mode (zero-emission). After battery power is exhausted, it can automatically shift into hybrid mode (mainly fuel power). Therefore, PHEVs combine the advantages of fuel powered vehicles and pure electric vehicles. [PERSON] et al. [9] studied an electric vehicle routing problem combining conventional, plug-in hybrid, and electric vehicles. To solve this problem, they have designed a sophisticated metaheuristic which combines a genetic algorithm with local and large neighborhood search. [PERSON] and [PERSON] [10] gave detailed explanations of the advantage of PHEV and BEV under different scenarios. [PERSON] et al. [11] evaluated energy consumption, emissions and costs of PHEV. Path planning for a plug-in hybrid vehicle is a typical Hybrid Vehicle Routing Problem (HVRP). [PERSON] et al. [4] classified HVRP as a special case of GVRP. The traditional vehicle routing problem does not consider the access to the fuel stations, while the electric vehicle routing problem (EVRP) considers the access to the electric stations. The HVRP should further consider the access to both electric stations and fuel stations. In addition, HVRP takes into account the environmental impacts. The method and model in this paper are based on some assumptions--Firstly, the vehicle's speed keeps constant in the course of route driving. Secondly, PHEV has two energy sources, fuel and electricity, electricity has a high priority, and when the maximum driving capacity of the battery is exhausted, the vehicle will switch to the fuel mode. In this work, time limits, battery capacitance and fuel capacity are also the major considered constraints. The purpose is to consider the use of electricity and fuel reasonably according to the availability of electric or fuel stations while minimizing the total travel cost. A good PHEV routing solution can help enterprises or organizations reducing the overall travel cost by providing the optimal/near-optimal path planning within a certain time limit. Contribution and innovation of this study are highlighted as follows:  
* Compared with the existing HVRP studies on PHEV routing problem ([PERSON] et al. [8]), this work deals with a complicated PHEV routing problem in which the types of charging power stations (fuel station or electric station) are provided to the vehicle. The vehicle can be refueled or charged during its delivery. * The PHEV routing problem is formulated as a Mixed Integer Linear Programming model, different from previous research, various hybrid vehicles are considered. * This study proposes a new hybrid metaheuristic which combines the memetic algorithm with a powerful local search technique SVND; the experimental results show that our algorithm obtains better results than previous ones. The rest of this article is organized as follows. Section 2 reviews the relevant literature. Section 3 defines the problem. Section 4 describes the proposed memetic algorithm and SVND neighborhood search method. Section 5 reports the experimental results and the conclusion is given.