Intelligent charge scheduling and eco-routing mechanism for electric vehicles: A multi-objective heuristic approach

https://doi.org/10.1016/j.scs.2021.102820Get rights and content

Highlights

  • A detailed mathematical study on the problem of Eco-routing and Charge scheduling for electric vehicles is conducted.

  • A directed weighted graph based modeling approach is adopted.

  • A multi-objective heuristic mechanism is proposed to obtain the solutions efficiently.

  • Experimental evaluation is carried out on real-life data sets.

Abstract

Due to the rising pollution and greenhouse gas emissions resulting from fossil fuel-based transportation systems, researchers and policymakers are pushing for Electric Vehicle (EV) that is envisaged as an efficient, eco-friendly alternative. However, due to their limited range and battery capacity, EVs need frequent charging, which is time-consuming and available at specific locations. Therefore, proper charge scheduling and route management of EVs is essential and significant. This paper addresses this problem by proposing an intelligent heuristic mechanism that ensures that the EVs are always routed through a path that minimizes the energy consumption and the total time to travel. We formulate it as a multi-objective optimization problem considering real-world specifications and constraints and propose a graph-based multi-objective heuristic algorithm (MoHA) to obtain the desired solutions quickly. Further, multiple variants of the proposed algorithm are proposed, and comparative analysis is performed on practical datasets. The proposed algorithm is evaluated based on some of the well-known performance metrics for multi-objective approaches. The results obtained show that the energy-aware-MoHA variant produced 32.39% better results in minimizing energy consumption, and time-aware-MoHA performed better in optimizing average time requirements by 24.32%. Moreover, the initial ordering of the EVs has significant importance on the proposed algorithm's overall performance.

Introduction

The automobile industry is one of the fastest-growing industries in today's manufacturing sector, which is predominantly driven by consumer preference-oriented intense global competition and innovation. However, the growing demand for and continuous increase in the number of vehicles has resulted in depleting non-renewable resources and the deterioration of the earth's atmosphere. Along with global population and urbanization, the current transportation system has been one of the significant contributors to the number of Greenhouse Gases (GHG) emitted that has brought severe environmental concerns and alarming pollution levels (Ramachandra, Aithal, & Sreejith, 2015). According to the Annual Energy Outlook 2018, published by the U.S. Energy Information Administration, approximately 28% of energy consumption in the U.S. has been due to transportation in 2017 (Annual Energy Outlook, 2020). Similar statistics have also been obtained by the European Environment Agency that reported the transportation sector to result in 25.8% of total EU-28 GHG emissions (EEA, 2017).

This has consequently led governments, environmental agencies, and automobile manufacturers to develop alternative modes of transportation. Electric vehicle (EV) is considered to be a promising and desirable alternative to the fossil fuel-based transportation system that has been envisioned as an efficient mechanism to address the global concern of GHG emissions and reduce the heavy reliance on fossil fuels for the current transportation systems (Wang, Liu, Du, & Kong, 2016). Compared to conventional vehicles, EVs introduce numerous benefits such as low noise, low carbon, ozone-precursor emissions, high energy efficiency, etc. However, despite the various advantages, widespread adoption of EVs is still obscured due to the factors such as battery life, charging time, availability of charging stations, the cost for charging, and safety (Lokesh & Min, 2017). EVs suffer from low engine capacity that makes the journey comparatively slower than traditional vehicles. The batteries have limited charge storage capacities, which reduce the range of distance covered in one go and require frequent charging that takes a significantly longer period of time than the traditional fuel refilling process, possessing significant challenge given the current charging infrastructure (Moghaddam, Ahmad, Habibi, & Phung, 2018).

A significant amount of existing literature tried to address the aforementioned challenges, particularly the charging issue of EVs. Researchers have proposed energy-efficient routes and various charging profiles for the vehicles considering real-world challenges (Battarra, Gargiulo, Tremiterra, & Zucaro, 2018; Kin, Verlinde, & Macharis, 2017). Sayarshad, Mahmoodian, and Gao (2020) a Markov Decision Process-based approach to obtain the best routes for electric taxis that are assigned to consumers with elastic demands. An energy-efficient route is defined to be a path for an EV from the source to the destination that consumes the least amount of energy, also known as ‘eco-routing’ (Boriboonsomsin, Barth, Zhu, & Vu, 2012; Cela et al., 2014; Nie & Li, 2013). Boriboonsomsin et al. presented one such early work in Boriboonsomsin et al. (2012) where they proposed an eco-routing navigation system. Authors in Cela et al. (2014) proposed a real-time eco-routing framework that captures not only energy consumption but also on-board power splitting between batteries and super-capacitors. Le Rhun, Bonnans, De Nunzio, Leroy, and Martinon (2020) proposed an eco-routing mechanism considering the traffic conditions on the road. They utilized the A* algorithm to solve the optimal pathfinding problem. Authors in Yang et al. (2017) presented an EV routing mechanism based on crowdsensing. Han, Han, and Sezaki (2010) used dynamic programming for optimal charge controlling of EVs along with vehicle-to-grid frequency regulation services. Authors in Gan, Topcu, and Low (2013) proposed a distributed optimal charge scheduling algorithm for EVs; however, their focus was to flatten out the grid load profile. A similar valley filling objective by EV scheduling was also targeted by Rivera, Goebel, and Jacobsen (2017). A distributed charging algorithm was also proposed by Floch, Belletti, and Moura (2016) where they explored the principle of duality, considering the perspective of both the EVs and the utility grid. Yi and Bauer (2018) presented a stochastic optimization model for routing EVs that incorporates uncertainties related to future charging demands.

Apart from eco-routing, a significant amount of research has been carried out on scheduling EVs’ charging process at charging stations. Brady and O’Mahony (2016) proposed probabilistic modeling of daily travel and charging profiles for a set of EVs, which are then used to model the power demands. The overall objective of their study is to determine the schedules and charging patterns to have a better decision-making system for the EVs. Authors in Minett, Salomons, Daamen, van Arem, and Kuijpers (2011) proposed graph-based modeling of the EV charge scheduling problem and proposed a routing method based on Dijkstra's shortest path algorithm. However, the proposed routing method is more suited for the traditional source-to-destination routing problems. Pourazarm, Cassandras, and Malikopoulos (2014) suggested a pathfinding algorithm based on dynamic programming by considering graph-based modeling of the problem. Their overall objective has been to reduce the total time elapsed for a tour that includes charging time as well as traveling time. Similarly, Qin and Zhang (2011) targeted minimizing waiting time with the help of a distributed charge scheduling scheme. Authors in Tong (2019) developed a mechanism to obtain the driving cycle for public electric buses in a city network, specifically for the Supercapacitor bus deployed in Hong Kong. Yao, Liu, Lu, and Yang (2020) also addressed a similar scheduling problem of electric buses to minimize annual total scheduling costs, including the purchase costs of the vehicles and chargers, the operating expenses of deadheading and timetabled trips, etc. Mukherjee and Gupta have presented a comprehensive summary of EV charge scheduling in Mukherjee and Gupta (2015).

Most of the aforementioned existing literature has used either energy-optimized routing or time-efficient routing to address the limited battery capacity and charge scheduling problem. However, only energy-efficient routes or time-efficient routes may not always be desirable, particularly for real-world scenarios. For example, two separate paths may exist from a particular source to a destination where one of them is energy efficient with higher time requirements due to traffic congestion. The other one is time efficient due to less congestion but consumes more energy because of the road conditions. Thus, in practice, there exists a trade-off between energy-efficient and time-efficient routes. In this work, our objective is to address this multi-objective optimization problem and obtain trade-off solutions efficiently. Some previous works towards the same research direction were carried out in Houshmand and Cassandras (2018), Nunzio, Thibault, and Sciarretta (2017), Sun and Zhou (2016). Houshmand and Cassandras (2018) presented a combined vehicle routing and Power-train Control mechanism with the target to calculate the optimal energy route as well as the optimal power-train control strategy. Sun and Zhou (2016) addressed this problem by proposing an optimal cost algorithm to obtain a trade-off between traveling cost and time consumed, focusing on plug-in EVs. Nunzio et al. (2017) presented a graph-based bi-objective solution of eco-routing that minimizes both energy consumption and time. However, they mostly solved the problem by reducing the two objectives into a single objective problem using the weighted sum method. However, such a solution lacks clarity as obtaining proper weights for objectives is challenging. Moreover, the models presented in the majority of the existing literature assume that the EVs always travel on flat surfaces, which is not practical. For example, the energy consumption and time requirement will be different while traveling up a hill than getting down to a lower altitude point. Therefore, the applicability of the existing works on uneven surfaces, such as hill stations, is questionable.

Motivated by the above findings and the research gap in the literature, in this paper, we propose a multi-objective optimization framework for charge scheduling and eco-routing of EVs that minimizes both the average touring time and the average energy consumption. The touring time includes time to travel on roads, waiting time at the Charging Station (CS), and charging time at the CSs. Although there have been several works that tried to solve similar problems (Le Rhun et al., 2020; Nunzio et al., 2017; Zhang, Luo, & Li, 2016), a limited number of works exist that focus on the multi-objective optimization problem discussed in this work. Moreover, the existing solutions’ poor efficiency makes these algorithms difficult to scale up in real life. Compared to the current literature, the novelty and unique contributions of this work can be listed as follows:

  • 1

    We discuss the multi-objective optimization problem of eco-routing and charge scheduling of EVs. We present a detailed mathematical formulation for the problem whereby the traffic network is modeled as a graph. The nodes in the graph represent junctions in the city and charging stations, which can be at various altitudes, represented by their respective elevation parameters. The graph's edges indicate possible paths in the network with weights corresponding to the distance between the two connecting nodes.

  • 2

    We propose an intelligent Multi Objective Heuristic Algorithm (MoHA), which is essentially a graph-based scheduling approach that utilizes the multi-objective A* search algorithm to obtain the desired solutions efficiently. We present four variants of the MoHA, viz., energy-aware, time-aware, random, weighted, each of which follows different strategies to break ties among multiple potential non-dominated solutions.

  • 3

    Unlike the existing similar multi-objective optimization solutions that produce results after transforming the problem into a single objective, the proposed heuristic algorithm produces an approximated Pareto front. We evaluate the quality of the solutions produced by the proposed MoHA and its variants in comparison to the Pareto optimal solutions for up to 20 devices using the well-known performance metrics for multi-objective heuristic solutions. In particular, the tools used are Error Ratio (ER), Generational Distance (GD), Schott's Spacing Metric (SS), and Hyper-volume Ratio (HVR). These metrics measure the quality of the Pareto front obtained using MoHA with respect to the relative distance from the optimal Pareto front.

  • 4

    The proposed MoHA is also evaluated using practical datasets consisting of graphs generated from the real-world scenario. Comparative performance analysis has been performed among the four variants of MoHA for up to 10000 EVs. The results obtained show that the variants produce trade-off solutions to the multi-objective optimization problem quite efficiently. Through simulation studies, we also analyze the effect of the elevation parameter on the overall quality of the results obtained by MoHA.

The rest of the paper is structured as follows. Section 2 presents the system model and introduces the multi-objective optimization problem formally. In Section 3, we propose the multi-objective heuristic algorithm. Simulation results are presented and discussed in Section 4. Finally, some concluding remarks and future works are presented in Section 5.

Section snippets

System model and problem description

Consider a traffic network represented as a graph G(V, E). The nodes in the graph G mainly represent the CSs (a total of m CSs), and the sources and destinations of the EVs. Connecting the nodes are the edges that represent possible paths among them. Each node vpV is characterized by an elevation parameter (Ep), which is a measurement of their physical altitude. Each edge epq ∈ E represents a direct path from vp to vq, and is assigned the weight Dpq, which represents the actual ground distance

Proposed multi-objective heuristic algorithm

In this section, we propose a multi-objective heuristic algorithm (MoHA) to schedule the given set of EVs on a city network to minimize average touring time and average energy consumption for the complete set. The proposed algorithm is a graph-based centralized scheduling strategy for the EVs; the pseudo-code of the same is presented in Algorithm 1. The inputs to the algorithm are specifications regarding the city network (such as the number of CSs, the elevation parameters, the types of

Experimental results and discussions

We have implemented the proposed MoHA in Java on a computer having Intel Xeon processor E5-2609 v3 (15 MB Cache, 1.90 GHz, 6 cores) with 132 GB of RAM. We tested the proposed algorithm in a simulated environment on randomly generated synthetic data as well as on a real-life transportation network. To depict a real-life scenario for the experiments, we consider four of the most widely available commercial EVs (Kisacikoglu, Erden, & Erdogan, 2018): Tesla Model S, BMW i3, Chevrolet Volt, and

Conclusions and future work

In this paper, we discuss the multi-objective optimization problem of scheduling and routing of EVs to minimize both time and energy consumption. The problem is composed of two sub-problems, which are themselves intractable, making the whole problem hard to solve optimally in polynomial time. We presented a detailed MILP formulation of the problem and proposed an efficient multi-objective heuristic algorithm (MoHA) and its variants to obtain desirable solutions efficiently. We discussed the

Acknowledgement

This work was supported in part by the IMPRINT-2 initiative undertaken by MHRD and DST through SERB, Govt. of India with sanction order no: IMP/2018/000323.

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