A hybrid variable neighborhood search approach for the multi-depot green vehicle routing problem
Introduction
Transportation activities are the largest source of greenhouse gas (GHG) emissions in the US and fourth largest globally (www.epa.gov). They were responsible for 27% of total (GHG) in the EU in 2017. GHG emissions had increased by 2.2% in 2017 compared to 2016, mainly because of higher emissions from road transport. Almost 72% of the total transport-related GHG emissions were caused by road transport, of which 9% were from light commercial vehicles and 19% from heavy-duty vehicles (www.eea.europa.eu). In comparison to its 1990 levels, GHG emissions should fall by around two thirds by 2050 in order to meet 60% emission reduction target of European Commission (EC Transport White Paper, 2011). So, the shift to cleaner vehicles in public and freight transport is a must in order to meet the targets and achieve the desired reductions in GHG emissions to avoid dangerous levels of global warming.
Nowadays, many logistic companies add their fleets with green vehicles that run with alternative fuel (such as ethanol, natural gas, electricity) instead of fossil fuel in order to lessen the adverse effects of their operations on the environment. Consequently, route planning of these alternative fuel vehicles (AFVs) has received increasing attention in the Vehicle Routing Problem (VRP) literature over the last decade. In the classical VRP, the fuel tank capacity of the vehicles is assumed unlimited since the vehicles can refuel easily and fast at any public gas station. However, green vehicles need alternative fuel stations (AFSs) for refueling, which are scarce (Koç and Karaoglan, 2016). The range anxiety of the AFVs and the scarcity of the AFSs make the resulting VRP more complex to model and solve.
The Green Vehicle Routing Problem (GVRP) was proposed by Erdoğan and Miller-Hooks (2012) as an extension of the Capacitated VRP (CVRP) where a fleet of AFVs was used to serve the customers instead of internal combustion engine vehicles (ICEVs). In this study, we address the Multi-Depot GVRP (MDGVRP), which is a relevant problem for many logistics companies that operate multiple regional depots for their last-mile delivery operations and employ AFVs to cut down their emissions and reduce fuel costs. In MDGVRP, the AFVs depart from the depot, serve a set of customers, and complete their tours at the depot without exceeding their driving range and the maximum tour duration. All customers must be served by exactly one AFV and AFVs may refuel at depots and public refueling stations when they run out of fuel. The objective is to minimize the total distance travelled. Note that the existence of multiple depots increases the difficulty of the problem significantly as each subset of customers assigned to a depot requires solving a separate GVRP. Since the utilization AFVs with limited autonomy makes the GVRP a challenging problem, its extension to MDGVRP brings even more complexity to the problem.
To solve this problem, we develop a hybrid algorithm that combines Variable Neighborhood Search (VNS) with Tabu Search (TS). The proposed algorithm applies TS with multiple, problem specific neighborhood structures as the local search mechanism within the general VNS (GVNS) scheme and is referred to as GVNS/TS. We perform an extensive experimental study to investigate the performance of the proposed method and provide insights for both researchers and practitioners. Various metaheuristic algorithms have been successfully employed for solving different VRP variants; however, VNS stands out with its simple algorithmic structure, ease of implementation, and good performance despite the use of very few parameters. Furthermore, allowing non-improving moves in a multiple neighborhood framework offers more potential for achieving high quality solutions compared to other simple local search methods such as Variable Neighborhood Descent (VND). These factors constitute the main motivation behind our methodology selection.
Our contributions may be summarized as follows: (i) we introduce MDGVRP and formulate its MILP model; (ii) we propose an efficient hybrid GVNS/TS method to solve it by implementing new problem specific neighborhood structures; (iii) we present an extensive computational study to evaluate the performance of the proposed method and provide managerial insights, (iv) we present new benchmark results to the literature. The remainder of this paper is organized as follows: Section 2 provides a review of related literature. Section 3 presents the mathematical formulation of the problem. Section 4 details the proposed GVNS/TS solution methodology. Section 5 presents the computational study and discusses the numerical results. Finally, conclusion remarks are provided in the last section.
Section snippets
Literature review
In the GVRP introduced by Erdoğan and Miller-Hooks (2012) the AFVs were allowed to refuel en-route in public refueling stations and the tank was assumed to be fully filled in constant time. The authors modelled the mixed integer linear programming (MILP) formulation of the problem where the objective is to minimize the total distance travelled and proposed two construction heuristics to solve it. Schneider et al. (2014) investigated the utilization of an electric vehicle (EV) fleet within the
Problem formulation
Our model extends the GVRP formulation of Erdoğan and Miller-Hooks (2012) to the multiple-depot setting. For ease of understanding, we follow the same mathematical formulation and notation convention. Let denote a complete directed graph where and represent the set of vertices and set of arcs, respectively. consists of three subsets: set of depots , set of customers , and set of refueling stations . is the service time
Solution methodology
We present a hybrid GVNS/TS algorithm for solving MDGVRP. The basic component of the algorithm is General Variable Neighborhood Search (GVNS) developed by Mladenović and Hansen (1997). The neighborhood structures in GVNS/TS are changed systematically through the VNS approach and the local search is applied by implementing TS, which was originally developed by Glover (1986). VNS has a simple algorithmic structure and involves very few parameters; however, it is one of the most successful
Experimental study
In this section, we first tune the parameters of GVNS/TS by performing initial experiments using a subset of the GVRP instances generated by Erdoğan and Miller-Hooks (2012). Next, we evaluate the performance of GVNS/TS using the whole set of GVRP instances by comparing its results with those from the literature. Then, we modify the GVRP instances to create MDGVRP instances and solve them with GVNS/TS. For small-size data set, we use CPLEX to evaluate its performance. For large-size data set, we
Concluding remarks
In this paper, we introduced a variant of the well-known Green Vehicle Routing Problem, namely Multi-Depot Green Vehicle Routing Problem where the customers are served from a set of depots using a fleet of AFVs. To solve the problem, we developed a hybrid GVNS/TS approach that combines the General Variable Neighborhood Search method (GVNS) with Tabu Search (TS). In our GVNS/TS, the neighborhood structures are systematically changing through the VNS approach and a TS-based local search procedure
CRediT authorship contribution statement
Mir Ehsan Hesam Sadati: Conceptualization, Methodology, Software, Validation, Formal analysis, Writing - original draft, Visualization, Investigation, Data curation. Bülent Çatay: Conceptualization, Methodology, Validation, Formal analysis, Resources, Writing - original draft, Writing - review & editing, Data curation.
Acknowledgments
The authors wish to thank the three anonymous reviewers for providing valuable comments and suggestions throughout the review process of the paper.
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