Solving hybrid charging strategy electric vehicle based dynamic routing problem via evolutionary multi-objective optimization

doi:10.1016/j.swevo.2021.100975

Swarm and Evolutionary Computation

Volume 68, February 2022, 100975

https://doi.org/10.1016/j.swevo.2021.100975 Get rights and content

Abstract

With the development of Electric Vehicle (EV) technology, the new generation of EVs combines the advantages of both Wireless Charging Technology (WCT) and Plug-in Charging Technology (PCT) to extend their transport distance. However, some difficulties emerge in this hybrid charging strategy based EVs for Vehicle Routing Problem (VRP). First, the availability of devices for PCT and WCT varies with time. EVs not only need to find the optimal routes but also to determine charging strategies according to the environment. Second, in such a dynamic environment, the Pareto-optimal Solutions (POS) should be rapidly tracked and Decision Makers (DMs) should pick desired solutions quickly for implementation. To address these issues, in this work, we propose a framework to reuse knee points into the newly generated environment. Reusing knee points can provide high-quality knowledge to generate a better initial population and the knee points also bring convenience to DMs. In this work, we also introduce a benchmark of Hybrid Charging Strategy based Dynamic Vehicle Routing Problem (HCS-DVRP). The obtained experimental results on this benchmark validate that our proposed design can achieve a promising optimization performance via reusing knee points.

Introduction

The Vehicle Routing Problem (VRP) has been intensively investigated in supply chain management, city logistics, and other real-world applications [1], [2]. The objective of VRP is to optimize routes of vehicles so as to minimize total routing cost (e.g., cost of energy, travel distance, etc.) and satisfy constraints at the same time. In the last decade, many studies for solving VRP have been proposed. Among these designs, computational intelligence approaches have attracted more attention and interests lately. Yan et al.[3] incorporated a graph-based fuzzy assignment scheme into the evolutionary search to minimize the total travel cost. Zhang et al.[4] designed an evolutionary scatter search particle swarm optimization algorithm to solve the VRP with time windows. Wang et al.[5] developed a two-stage multiobjective evolutionary optimization algorithm to balance convergence and diversity of the population for solving VRP. Mavrovouniotis et al. [6] suggested an improved ant colony optimization (ACO) algorithm to solve combinatorial dynamic optimization problems. The ant immigrant mechanism can replace a portion of the population with some elite solutions from previous environments.

Nowadays, Electric Vehicles (EVs) have been slowly mature and applied intensively due to their environmentally friendly characteristics[7]. Traditional EVs need to charge at the fixed sites like homes or charging stations. This constraint has made EVs inconvenient and has limited their adoption due to insufficient or limited charging facilities. Recently, Wireless Charging Technology (WCT) has been steadily developed[8]. Combined with the WCT, EVs could not only save the transport time without stopping to recharge, but also extend their transport distance. However, the cost of WCT is significantly higher than that of traditional Plug-in Charging Technology (PCT). To be specific, the PCT scheme is money-saving but time-consuming [9], while the WCT scheme can save travel time but is not economical. Hence, it is expected to properly combine these two charging strategies during transportation. Therefore, the VRP of this hybrid charging strategy involves the trade-off between charging cost and travel time and can be viewed as a multiobjective problem.

Two difficulties are brought in the hybrid charging strategy based EVs. First, the availability of PCT and WCT may vary over time due to the allocation or repair of charging devices. In such a changing environment, EVs not only need to find the optimal routes to minimize travel cost but also determine charging strategies with efficiency. Second, existing evolutionary multiobjective optimization algorithms for VRP often find a large number of solutions. However, only few solutions can be implemented for real-world applications, so picking solutions for implementation among a massive number of candidates is a mentally challenging burden to Decision Makers (DMs). Especially, DMs should make decisions as quickly as possible in the dynamic changing environment.

To track the Pareto-optimal Solutions (POS) rapidly under the dynamic environment, a promising way is to reuse the archive memory[10], [11], [12], [13], [14], [15] to share the past search experiences which provide useful knowledge for enhancing the problem-solving performance in the newly changed environment. For example, a prediction technique was employed to generate the POS in the new environment and these predicted solutions can be treated as an initial population for guiding the search direction[16]. However, existing methods often reuse the whole population pool and do not carefully select solutions, which results in many computing resources being wasted on low-quality solutions. In fact, we believe that reusing only a few high-quality solutions not only can improve the performance of the predicted population but also save computing resources. Moreover, it is unnecessary to reuse the whole population, because DMs often pick only few solutions for evaluation and implementation.

From the above discussions, an advisable approach is to reuse few high-quality solutions when the environment has changed so that computational resources and the cognitive burden to DMs are relieved. In the evolutionary multi-objective optimization domain, knee points refer to a subset of non-dominated solutions with higher HyperVolume (HV) values [17] and contain valuable information for guiding the search direction towards the optimal solutions[18], [19]. Besides, knee solutions are often preferred by DMs since they don’t require any subjective preferences from DMs [20], and knee point-based Multi-Criteria Decision Making (MCDM) approaches have sufficient interpretations of the geometry[20]. An illustration of the benefits of the knee point is presented in Fig. 1. Hence, providing knee solutions can bring convenience to DMs, and reusing these high-quality knee solutions as knowledge can be effective in generating a better initial population to enhance evolutionary performance when the environment changes.

In this paper, we propose an innovative framework combining both historical archive and knee-based MCDM strategy to handle the Hybrid Charging Strategy based Dynamic Vehicle Routing Problem (HCS-DVRP). The backbone of the proposed Transfer Knee points based MCDM algorithm (TK-MCDM) consists of three critical components, namely, knee selection, training solutions collection, and reuse function learning. First, the objective space is divided and a knee pointis identified in each division. Second, we collect training samples for training the reuse function by considering the imbalanced problem. Subsequently, a reuse function is learned to predict initial knee points in the changing environment by exploiting the collected training solutions.

The contributions of our work are as follows:

1.
The proposed work utilizes knee points not only for accelerating the convergence and maintaining the diversity of the population, but also relieving DMs’ burden of picking solutions. Therefore, DMs can adopt knee solutions easily for implementation, which is of great importance to those real-world dynamic applications, such as the one studied here.
2.
We design an adaptive learning mechanism to reuse a small number of knee points instead of a large number of common individuals, which can significantly save computing resources and improve performance.
3.
Since the number of knee points is far less than that of other types of solutions, which leads to the imbalanced problem[21]. To address the issue, we generate some artificial knee points to balance the minority for better training the reuse function.

The rest of this paper is organized as follows. Section II presents some existing research works about Dynamic Vehicle Routing Problem (DVRP) briefly. In Section III, we give the mathematical definition for the proposed problem, HCS-DVRP. The proposed algorithm TK-MCDM for HE-DVRP is then detailed in Section IV. Furthermore, Section V introduces a benchmark of HCS-DVRP and discusses the empirical studies conducted to verify our proposed algorithm. Finally, the conclusions are drawn in Section VI.

Section snippets

Related work

In this section, we give a brief review of the recent literatures about Dynamic Vehicle Routing Problem (DVRP). The DVRP and its variants have been widely studied in recent years. Generally, solvers for DVRP aim to meet requests from several destinations or customers and minimize the travel cost and time simultaneously.

DVRP often involves large-scale decision variables, and some works focus on dealing with high-dimensional decision variables efficiently. Kim et al. [22] proposed a Markov

System model and definitions

The formal definition of HCS-DVRP can be expressed as follows: The weighted undirected graph $G (V, E)$ stands for the traffic network, where $V$ and $E$ represent the set of vertices/nodes and edges, respectively. Let $x_{i j} \in {0, 1}$ be a binary variable. $x_{i j} = 1$ implies that the optimal route includes the edges ${(i, j) | (i, j) \in E, i, j \in V)}$ , while $x_{i j} = 0$ denotes $x_{i j}$ does not belong to the found optimal route. When an EV travels from node $i$ to node $j$ , the State of Batteries (SoB) of the EV is presented as $s_{j} = s_{i} + s_{i}^{p l} + s_{i}$

Representation and operator

The chromosome used for encoding HCS-DVRP consists of three segments, as shown in Fig. 2. The first segment represents the order of routing in which each component is the identification of the node, while the second and third segments represent the PCT charging time $t_{i}^{p l}$ at node $i$ and the WCT charging time $t_{i j}^{w i}$ via edge $(i, j)$ , respectively. The second and third segments are encoded with real numbers.

For each segment, different operators are carried out. The order crossover (OC) and swap

The proposed benchmark HCS‐DVRP

The proposed HCS-DVRP benchmark contains 24 test instances modified by commonly used VRP benchmark[49]. These test instances have three categories: “C” (C1 and C2), “R” (R1 and R2) and “RC” (RC1 and RC2). “C” and “R” represent nodes located in clusters or the random distribution, respectively. “RC” means a mixture of “R” and “C”. Each category has two different scales: 25 and 50 nodes. The structure of the HCS-DVRP benchmark instance can be viewed in Fig. 6, where the red square represents the

Conclusion and future work

In this work, a framework combining both historical archive and knee-based MCDM strategy in solving HCS-DVRP is proposed by optimizing routes and determining charging strategies according to the changing environment. Firstly, reusing knee points can better accelerate the convergence. Secondly, it can relieve the burden for implementation. In addition, we design an adaptive reuse mechanism and address the induced imbalanced problem during reusing the knee points by generating artificial knee

CRediT authorship contribution statement

Zhenzhong Wang: Conceptualization, Methodology, Software, Writing – original draft. Kai Ye: Software. Min Jiang: Supervision, Conceptualization, Methodology, Writing – review & editing. Junfeng Yao: Supervision. Neal N. Xiong: Writing – review & editing. Gary G. Yen: Conceptualization, Methodology.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgment

This work was supported by the National Natural Science Foundation of China (No. 61673328).

References (54)

M. Mavrovouniotis et al.
Ant algorithms with immigrants schemes for the dynamic vehicle routing problem
Inf Sci (Ny)
(2015)
E. Fatnassi et al.
Discrete honeybee mating optimization algorithm for the routing of battery-operated automated guidance electric vehicles in personal rapid transit systems
Swarm Evol Comput
(2016)
M. Mavrovouniotis et al.
A survey of swarm intelligence for dynamic optimization: algorithms and applications
Swarm Evol Comput
(2017)
S. Li et al.
A modular neural network-based population prediction strategy for evolutionary dynamic multi-objective optimization
Swarm Evol Comput
(2021)
Y. Guo et al.
Ensemble prediction-based dynamic robust multi-objective optimization methods
Swarm Evol Comput
(2019)
C. Wang et al.
A grey prediction-based evolutionary algorithm for dynamic multiobjective optimization
Swarm Evol Comput
(2020)
X. Li et al.
Flexible time-of-use tariff with dynamic demand using artificial bee colony with transferred memory scheme
Swarm Evol Comput
(2019)
F. Zou et al.
A reinforcement learning approach for dynamic multi-objective optimization
Inf Sci (Ny)
(2021)
F. Zou et al.
A knee-guided prediction approach for dynamic multi-objective optimization
Inf Sci (Ny)
(2020)
C. Wang et al.
A multi-objective genetic algorithm based approach for dynamical bus vehicles scheduling under traffic congestion
Swarm Evol Comput
(2020)

M. Jiang et al.

Transfer learning-based dynamic multiobjective optimization algorithms

IEEE Trans. Evol. Comput.

(2018)

X. Zhang et al.

A knee point-driven evolutionary algorithm for many-objective optimization

IEEE Trans. Evol. Comput.

(2015)

Cited by (22)

Dynamic constrained multi-objective optimization based on adaptive combinatorial response mechanism [Formula presented]
2024, Applied Soft Computing
In dynamic multi-objective optimization problems (DMOPs), objective functions, problem parameters, and constraints may change over time. Mainly, DMOPs use response mechanisms to generate the initial population after the environment changes. In this research, we develop an adaptive version of the combinational response mechanism (ACRM). ACRM uses three response mechanisms based on diversity, prediction, and memory to form the initial population. In ACRM, the number of solutions generated by a response mechanism is determined by reinforcement learning according to the severity of environmental changes. The background knowledge is transferred to reinforcement learning using the Q-value initialization method. Thus, in the early stages of optimization, when the experience gained from the environment is low, the proposed algorithm improves its performance using background knowledge. Also, we develop a new combinational constraint handling technique (CCHT). This method uses the dynamic information of the environment (i.e. the ratio of feasible solutions) to choose the appropriate constraint handling technique. The results of the tests on 23 dynamic test functions and seven dynamic constrained test functions indicate that the performance of the proposed algorithm can compete with advanced evolutionary algorithms in terms of the degree of convergence and variety of solutions.
Permanent link to reproducible Capsule: <https://doi.org/10.24433/CO.1949267.v1>.
MOEA/D with customized replacement neighborhood and dynamic resource allocation for solving 3L-SDHVRP
2024, Swarm and Evolutionary Computation
Split delivery heterogeneous vehicle routing problem with three-dimensional loading (3L-SDHVRP) is a critical issue in manufacturing logistics. Current mainstream research formulates this problem as a single objective optimization problem, which fails to reveal the relationship among multiple conflicting objectives and cannot provide various trade-off solutions for decision-makers in real-world logistics scenarios. This paper concentrates on a multi-objective 3L-SDHVRP and proposes a multi-objective evolutionary algorithm based on decomposition with customized replacement neighborhood and dynamic resource allocation (called MOEA/D-RD) to deal with it. The numerical experiments on the dataset from the 11th International Conference on Evolutionary Multi-Criterion Optimization (EMO 2021) show the superior performance of the proposed method over some state-of-the-art ones. The source code of MOEA/D-RD is available at https://github.com/CIAM-Group/EvolutionaryAlgorithm_Codes/tree/main/MOEAD-RD.
A novel combinational response mechanism for dynamic multi-objective optimization
2023, Expert Systems with Applications
Many real-world multi-objective optimization problems are dynamic. These problems require an optimization algorithm to quickly track optimal solutions after changing the environment. In most dynamic multi-objective optimization algorithms, response mechanisms are used to generate the initial population after the environment changes. In the present study, a novel Combinational Response Mechanism (CRM) is proposed, which consists of three parts. After detecting the environmental change, in the first part, RM-rand, a subpopulation of random solutions is generated using DE/rand/1 operator and Cauchy mutation. The second part, RM-Tr&SP, predicts a subpopulation of solutions using transfer learning (TL) and special points. The third part, RM-M, uses the best solutions of the previous environment with a propagation method based on crowding distance to generate the third subpopulation. A combination of the solutions of these three subpopulations is considered the initial population of the new environment. The proposed response mechanism can converge the set of solutions while maintaining their diversity. Thus, generating solutions with good convergence and diversity makes the initial population more adaptable to the new environment. The examinations were done on 24 common test functions. The experimental results indicate that the performance of the proposed response mechanism in dynamic multi-objective optimization is competitive with five advanced evolutionary algorithms.
Multi-regularization sparse reconstruction based on multifactorial multiobjective optimization
2023, Applied Soft Computing
In recent sparse reconstruction, the sparsity and reconstruction error can be considered as two objectives and tackled by multiobjective optimization methods. Since the sparse reconstruction problem can be modeled in multiple regularization forms, it can be addressed in a multifactorial multiobjective optimization paradigm by the evolutionary multitasking approach to transfer useful information across multiple regularization forms to help solve the problem. In this paper, a multi-regularization based on multifactorial multiobjective optimization is proposed to solve the sparse reconstruction problem. First, the sparse reconstruction problem is constructed as a multi-regularization model. Then, this model is optimized by a multifactorial multiobjective optimization method. In the evolutionary process, considering the priority of different regularization in the multi-regularization model, a preference-based selection method is designed. In addition, to accommodate the sparsity characteristic of the sparse reconstruction problem, a sparsity-oriented crossover operator is performed. Finally, an iterative-thresholding-based local search is incorporated into the algorithm to improve the convergence performance. Experiments on multiple datasets and image reconstruction tasks demonstrate the effectiveness and practicality of the proposed algorithm.
Real-time collaborative feeder vehicle routing problem with flexible time windows
2022, Swarm and Evolutionary Computation
Citation Excerpt :
Zhu et al. [56] studied a multi-objective optimization problem with three conflicting objectives (i.e., route length, response time, and workload) for the dynamic pickup-and-delivery problem (DPDP). Furthermore, Wang et al. [43] offered a hybrid charging strategy to solve the DVRP. The proposed model aimed to minimize the total time of travel and the total cost of charging.
Today, transportation has become a vital service due to increased competition among businesses. In this regard, customer service is one of the major challenges of logistics units. Companies can improve logistics costs, capacity utilization, service levels, and customer satisfaction by sharing new demands. The need for fast, flexible, reliable, and low-cost delivery is another challenge in urban areas for the distribution of goods. As demand increases, more vehicles are needed to deliver goods and congestion increases in urban transportation networks. A feeder vehicle routing problem (FVRP) consists of a heterogeneous fleet of vehicles, including trucks and motorcycles. In this problem, motorcycles pass easily in crowded areas, and the traffic of urban logistics is distributed easily. More importantly, it reduces the number of returns to the physical depot, lowers the costs, and leads to time savings. This study introduces the real-time collaborative feeder vehicle routing problem (RTCFVRP) with flexible time windows in which vehicles are permitted to serve customers before and after the time window. We propose the mixed-integer linear programming model with the CPLEX mathematical programming solver applying the augmented epsilon constraint. Also, multi-objective particle swarm optimization (MOPSO) and MOPSO-variable neighborhood search (MOPSO-VNS) were developed regarding the complexity of the problem. The performance of these algorithms was compared with Pareto solutions generated by the non-dominated sorting genetic algorithm-II (NSGA-II) and multi-objective evolutionary algorithm based on decomposition (MOEA/D) in both static and dynamic modes. Finally, in addition to statistical analysis, the AHP-TOPSIS method is employed to analyze and prioritize algorithms. The obtained results show the better performance of the proposed algorithm in both static and dynamic modes in small and large-size instances.
A fast sampling based evolutionary algorithm for million-dimensional multiobjective optimization
2022, Swarm and Evolutionary Computation
With their complexity and vast search space, large-scale multiobjective optimization problems (LSMOPs) challenge existing multiobjective evolutionary algorithms (MOEAs). Recently, several large-scale multiobjective evolutionary algorithms have been developed to tackle LSMOPs. Unlike conventional MOEAs that concentrate on selection operations in the objective space, large-scale MOEAs emphasize operations in the decision space, such as offspring generation, to tackle the large number of decision variables. Nevertheless, most present large-scale MOEAs experience difficulty effectively and efficiently solving LSMOPs with tens of thousands or more decision variables or exhibit poor versatility in solving different LSMOPs. We propose a fast large-scale MOEA framework with reference-guided offspring generation, named FLEA, aiming at these issues. Generally, FLEA constructs several reference vectors in the decision space to steer the sampling of promising solutions during offspring generation. A parameter is used to allocate computation resources between the convergence and diversity of the offspring population adaptively. Without computationally expensive problem reformulation or decision variable analysis techniques, the proposed method can significantly accelerate the search speed of conventional MOEAs in solving LSMOPs. FLEA is examined on various LSMOPs with up to 1.6 million decision variables, demonstrating its superior effectiveness, efficiency, and versatility in large-scale multiobjective optimization.

View all citing articles on Scopus

View full text

Survey PaperSolving hybrid charging strategy electric vehicle based dynamic routing problem via evolutionary multi-objective optimization

Abstract

Introduction

Section snippets

Related work

System model and definitions

Representation and operator

The proposed benchmark HCS‐DVRP

Conclusion and future work

CRediT authorship contribution statement

Declaration of Competing Interest

Acknowledgment

Inf Sci (Ny)

Swarm Evol Comput

Swarm Evol Comput

Swarm Evol Comput

Swarm Evol Comput

Swarm Evol Comput

Swarm Evol Comput

Inf Sci (Ny)

Inf Sci (Ny)

Swarm Evol Comput

Inf Sci (Ny)

Swarm Evol Comput

Swarm Evol Comput

Swarm Evol Comput

Swarm Evol Comput

Eng Appl Artif Intell

Drone routing in a time-dependent network: towards low cost and large range parcel delivery

IEEE Trans. Ind. Inf.

Placement and routing optimization for automated inspection with uavs: a study in offshore wind farm

IEEE Trans. Ind. Inf.

A graph-based fuzzy evolutionary algorithm for solving two-echelon vehicle routing problems

IEEE Trans. Evol. Comput.

An evolutionary scatter search particle swarm optimization algorithm for the vehicle routing problem with time windows

IEEE Access

A two-stage multiobjective evolutionary algorithm for multiobjective multidepot vehicle routing problem with time windows

IEEE Trans Cybern

A new coil structure and its optimization design with constant output voltage and constant output current for electric vehicle dynamic wireless charging

IEEE Trans. Ind. Inf.

An electric vehicle routing optimization model with hybrid plug-in and wireless charging systems

IEEE Access

A fast dynamic evolutionary multiobjective algorithm via manifold transfer learning

IEEE Trans Cybern

Transfer learning-based dynamic multiobjective optimization algorithms

IEEE Trans. Evol. Comput.

A knee point-driven evolutionary algorithm for many-objective optimization

IEEE Trans. Evol. Comput.

Survey Paper
Solving hybrid charging strategy electric vehicle based dynamic routing problem via evolutionary multi-objective optimization