# SVD Enhanced Metaheuristic for Plug-In Hybrid Electric Vehicle Routing Problem
## 1 Introduction  
Transportation plays an important role in the logistics system. Actually, transportation for logistic mainly contained two phases: sending raw materials from suppliers to manufacturers and the delivery of finished products from manufacturers to customers [1]. However, current transportation mostly employs fuel powered vehicles, which emit a lot of greenhouse gases (GHG) and harmful substances, such as carbon dioxide and sulfide, causing various environmental problems. Therefore, energy saving and emission reduction are more than necessary for logistic transportation. Recently, the conception of green logistics has been proposed. Green logistics is more environment-friendly. It has quickly become a hot research subject. By optimizing the usage of logistic resources, it focuses on restraining the environmental harm while reducing the whole logistic cost. In order to build green logistics, the first objective is to make a reasonable layout and path planning. This is usually regarded as a Vehicle Routing Problem (VRP). The VRP is a well-known NP-hard combinatorial optimization problem. It was first introduced in 1959 [2]. The VRP problem is different from traditional routing problems such as Traveling Salesman Problem (TSP), it can be more complicated by taking consideration of multiple vehicles and various constraints. The classical VRP problem can be summarized as follows [3]--there is a certain number of customers with different cargo needs. Distribution centers provide cargo to customers. A fleet is responsible for distributing cargo and organizing appropriate driving routes. The aim is to satisfy the customer's needs and to achieve goals like minimizing the travel distance, reducing costs or optimizing travel time under certain constraints. [PERSON] et al. [4] provided a review study on VRP and classified them into two categories--traditional VRP and Green Vehicle Routing Problem (GVRP) which is firstly proposed by [PERSON] and [PERSON] [5]. Compared to VRP, GVRP considers environmental factors in the whole route planning. GVRP aims to achieve the balance of economic and environmental interests. The abbreviation of HVRP used in this work is derived from [PERSON]'s [6] article, in which the Hybrid Vehicle Routing Problem is defined as an extension of the classical VRP where vehicles can work both electrically and with traditional fuel. [PERSON] et al. [4] classified HVRP as a special case of GVRP. Green vehicles or environment-friendly vehicles are also known as new energy vehicles (NEVs), of which, Battery Electric Vehicle (BEVs) is considered one of the most promising solutions to zero-emission transportation. Compared to traditional fuel powered vehicles, BEVs use renewable sources, they are not only much more environment-friendly, but also more energy efficient [6]. However, due to the limitation of the battery capacity, they require frequent visits to recharging stations along the route. At present, the major issue for BEV is that the number of charging stations in urban areas is quite limited globally. In addition, due to the physical characteristics of electric batteries, pure electric vehicles now have shorter transport distances in cold regions. Therefore, BEVs are ideal for last mile deliveries rather than long distance transportation. Hybrid electric vehicles (HEVs), on the contrary, are powered by both fuel and electricity [7]. It can be more practical for long distance logistics. A Plug-in Hybrid Electric Vehicle (PHEV) is the latest generation of HEVs. The PHEV used in this paper is not for inter-city logistics distribution, but for intra-city logistics distribution. PHEVs have been gradually applied in intra-city logistics in many countries. In terms of logistics, PHEVs can be more economical and environment-friendly than traditional fuel powered vehicles [8]. Furthermore, it can serve a much longer distance compared to pure electronic logistic vehicles.