Hierarchical eco-driving control for plug-in hybrid electric vehicles under multiple signalized intersection scenarios

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Hierarchical Eco-Driving Control for Plug-in Hybrid
Electric Vehicles under Multiple Signalized Intersection
Scenarios
Zhenzhen Lei1, Jianjun Cai2, Jie Li2, Dekun Gao2, Yuanjian Zhang3, Zheng Chen4* and Yonggang Liu2*
1School of Mechanical and Power Engineering, Chongqing University of Science & Technology, 401331, Chongqing, China
2State Key Laboratory of Mechanical Transmissions, Chongqing University 400044, Chongqing China
3Department of Aeronautical and Automotive Engineering, Loughborough University, Loughborough LE11 3TU,
United Kingdom
4Faculty of Transportation Engineering, Kunming University of Science and Technology 650500, Kunming China
Email: 2010048@cqust.edu.cn, 202132021008@cqu.edu.cn, jieli593@cqu.edu.cn, dekun_gao@163.com,
y.y.zhang@lboro.ac.uk, chen@kust.edu.cn, andyliuyg@cqu.edu.cn
*Corresponding author: Zheng Chen (chen@kust.edu.cn) and Yonggang Liu (andyliuyg@cqu.edu.cn)
Abstract: With the development of vehicle-to-everything (V2X) and autonomous driving technologies, plug-in
hybrid electric vehicles (PHEVs) enable to absorb surrounding information to enhance economic driving. This study
proposes a dynamic inverse hierarchical optimization method, which incorporates traffic-signal phase and timing
as well as road data, to plan economic velocity and improve PHEV energy consumption. The hierarchical control
framework determines the desired speed and arrival time in the upper layer using the shortest path faster algorithm.
The lower level accounts for multi-objective velocity planning based on particle swarm optimization and Pareto
theory. The inverse layering method solves the economic velocity optimization problem. With the support of V2X
and autonomous driving technologies, the method enhances energy efficiency and computational efficiency in
PHEVs through dynamic inverse hierarchical optimization. Simulation results highlight that the proposed algorithm
leads to 7.43% improvement in energy consumption economy and the reduced calculation time, compared to the
existing solutions. The hardware-in-the-loop experiments validate the real-time applicability of the proposed
algorithm.
Key words: Eco-driving, economic velocity planning, plug-in hybrid electric vehicle, Pareto theory, Backbone
multi-objective particle swarm optimization.
I. INTRODUCTION
Energy conservation and emission reduction are the mainstream development direction in automotive industry.
Clean energy vehicles have been flourishing in recent one decade due to its low emission, environmental friendliness
and high operation efficiency. One of the prevailing solutions in clean energy vehicles is plug-in hybrid electric
vehicle (PHEV) [1]. Compared with classical hybrid electric vehicles (HEVs), PHEVs can supply a certain all-

electric range (AER), thanks to the deployed large-capacity battery. In particular, by means of advanced energy
management and optimization of the engine’s working range, PHEV can bring a better fuel economy without
sacrificing the driving performance [2]. On the other hand, the wide development of wireless communication
technology facilitates the interaction between vehicles and infrastructure [3]. As such, vehicles can acquire abundant
surrounding environment information through vehicle to everything (V2X) communication, such as road status
information (road gradient, velocity limit and curvature), signal light timing information, and traffic status
information [4]. In this context, exploring the abundant driving environment information can not only improve the
travel efficiency, but also significantly reduce the vehicles’ energy consumption via reasonable optimization of
operation state of vehicles (in particular HEVs and PHEVs) [5]. This is also referred to as eco-driving control.
Currently, eco-driving research predominantly focuses on optimizing suggested driving actions and future
speed profiles using driving route and time information obtained through V2X technology [6]. This valuable driving
environment information typically includes road information, traffic-signal phase and timing (SPaT) information,
and traffic status information [7, 8]. Road information encompasses factors such as road gradient, curvature, and
velocity limits [9]. For instance, Xu et al. [10] propose a speed planning method based on model predictive control
(MPC) that takes into account road slope information in highway driving. Feng et al. [11] calculate optimal speed
and transmission gears by incorporating road curvature information into the vehicle fuel consumption model.
Furthermore, when determining optimal velocity trajectories, considerations are given to traffic efficiency and ride
comfort [12]. By utilizing SPaT information, vehicles improve energy consumption economy and travel efficiency
by avoiding unnecessary idling and waiting actions, as demonstrated in [13, 14]. For instance, Hao et al. [15]
optimize the speed trajectory based on SPaT information of traffic lights to help the host vehicle avoid queuing and
reduce fuel consumption. In terms of intersections, planning a reasonable vehicle speed is a common practice to
conserve energy by avoiding idling at traffic signals and sudden acceleration or deceleration [16]. Guo et al. [17]
determine optimal speed trajectories for trucks to reduce queuing delays for passenger vehicles at intersections and
minimize stops and idling. Nie et al. [18] propose a real-time dynamic predictive cruise control (PCC) algorithm to
minimize energy consumption for EVs when passing through intersections. Additionally, Bakibillah et al. [19]
design a Gaussian process model based on the Bayesian network to estimate the probability of a vehicle crossing
the intersection within a signal. While considerable research has emerged in terms of eco-driving speed planning

under simple or single intersection scenarios, the focus on long-distance and complex driving scenarios is often
lacked, which usually involves more information, more nonlinear constraints and the establishment of multi-
objective optimization functions. Therefore, further research is entailed to address these challenges and develop
comprehensive eco-driving strategies for such complex scenarios.
Typically, in multi-objective optimization, the factors such as energy consumption economy, traffic efficiency,
and ride comfort are combined into a single objective by applying different optimization coefficients [20, 21].
Va r io u s o pt i m i za t i o n m e t h od s a r e e m p l oy e d i n t h i s process, including Pontryagin’s minimal principle (PMP) [22],
dynamic programming (DP) [23], the pseudo-spectral method [24, 25], etc. For instance, Sun et al. [26] employ the
DP to address the speed planning optimization for connected and automated vehicles (CAVs) communicating with
traffic lights, accounting for the uncertainty of traffic signal timing at signalized intersections. Lin et al. [27] propose
a numerical solution for eco-driving when passing multiple intersections, combining the two- or three-stage driving
rule with the Dijkstra algorithm. Moreover, Hu et al. [28] leverage the PMP to maximize the fuel efficiency of
HEVs traveling on rolling terrain. Although abundant driving environment information can contribute to energy
saving, the application of these methods requires to consider more nonlinear constraints, thereby complicating the
solving process [29, 30]. Distinctly, addressing these nonlinear constraints with an efficient manner becomes crucial
in ensuring the solving efficiency and optimality in the optimization process.
When dealing with PHEVs, the energy management of different power sources complicates the eco-driving
control process. As a result, the control algorithm designed for PHEVs needs to be with high computational
efficiency. To lessen the computational intensity during speed planning and energy management, hierarchical
optimization is often preferred, which divides the optimization process into different layers. J. Han et al. [31]
propose a two-layer hierarchical eco-driving control framework, wherein the upper layer focuses on task planning
and the lower layer accounts for velocity planning. This decoupling control approach improves computation
efficiency, but may sacrifice the optimization performance. Similarly, Galpin et al. [32] adopt different methods in
two layers, aiming to achieve optimal or suboptimal energy economy. Kamal et al. [33] prioritize the output power
of the vehicle as the objective function to evaluate energy consumption economy, while disregarding the efficiency
of the transmission and powertrain system. By this manner, the speed planning is accelerated with the enhanced
calculation efficiency. Li et al. [34] employ a pseudo-spectral method to transform the eco-driving speed planning

problem of the nonlinear mixed-integer problem into a multi-level interconnected nonlinear programming problem,
improving computing efficiency. While the literature partially addresses the computation intensity, it is necessary
to mention that most of the optimization work focuses on segments with short durations, potentially overlooking
overall optimization performance. More in-depth exploration of optimization strategies become a necessity to
consider longer durations and achieve improved overall performance.
Based on the thorough analysis conducted, it becomes evident that a body of the research in this field has
primarily focused on economic velocity planning within simple or single intersection scenarios. However, there
appears to be a significant research gap concerning continuous and dynamic complex scenes, such as consecutive
multi-intersection scenarios [35]. In these multi-intersection scenarios, a multitude of nonlinear constraints arise,
thereby amplifying the computational burden associated with calculating globally optimal speed trajectories.
Moreover, the complexity of these scenarios results in increased computation time, prompting certain studies to
resort to simplified speed planning approaches. Unfortunately, this trade-off between computational efficiency and
accuracy often leads to suboptimal energy consumption economy and diminished comfort in speed tracking.
Furthermore, while the introduction of vehicle wheel energy models has been a common practice to characterize
energy consumption for real-time applications [36], it is worth noting that these models often lack the required
precision for the PHEV, consequently raising concerns about the overall optimization performance. Given the
aforementioned research gaps and challenges, it is imperative to undertake an alternative investigation into
optimizing the economic speed trajectories of PHEV when navigating through multiple consecutive intersections.
Such an endeavor should prioritize both high computational efficiency and effective utilization of energy resources.
To tackle the mentioned problems, a real-time hierarchical eco-driving approach is proposed, which is divided
into two layers accounting for different tasks. That is, the upper layer is responsible for task planning, and the lower
layer takes charge of velocity planning. To attai n it , th e route fr om the st arting point to the destination is fi rstly
divided into multiple segments by intersections, as shown in Fig. 1. In the upper layer, by comprehensively
considering the energy consumption economy, comfort and traffic efficiency, a shortest path faster algorithm (SPFA)
is adopted to determine the desired speed and time of vehicles to the end points of each segment. In the lower layer,
the speed profiles of each segment are designed combining the Backbone multi-objective particle swarm
optimization (BBMOPSO) algorithm and a fast energy consumption model, and then the speed profiles of each

section are integrated into the speed track of the whole scenario. BBMOPSO, as an improved particle swarm
optimization algorithm (PSO), abandons the particle velocity update of traditional PSO, and replaces it with the
Gaussian sampling of global optimal position and individual optimal position, thus significantly promoting the
optimization speed. The simulation results manifest that the proposed eco-driving method can adapt to complex
working conditions and conform to the requirement of real-time eco-driving control, greatly promoting the energy
consumption economy of PHEVs with high computational efficiency. The main contributions of this paper can be
attributed to the following three aspects: 1) Building upon the existing research in eco-driving, we systematically
propose a real-time multi-intersection eco-driving strategy that properly plans vehicle velocities and brings
significant reductions in vehicle energy consumption. 2) In comparison to conventional methods, an innovative
inverse hierarchical method is introduced to couple the task planning layer and velocity planning layer, leading to
enhanced overall energy consumption economy. 3) A dynamic output method is adopted to achieve the preferable
trade-off between real-time adaptability and energy-saving capabilities.
Fig. 1. Schematic diagram of vehicle driving route after segmenting.
The remainder of this paper is structured as follows. Section Ⅱ establishes the fast energy consumption model
of the studied PHEV. Section Ⅲ illustrates the real-time eco-driving problem under multi-intersection scenarios and
designs the corresponding control algorithm. Section Ⅳ provides the detailed simulation and experimental based
on the proposed method. Finally, the main conclusions and future work are given in Section Ⅴ.
II. SYSTEM MODELING
In this section, the vehicle powertrain is modeled, followed by the energy consumption model of the vehicle.
A. Vehicle Powertrain Modeling
The powertrain configuration of the target PHEV in this study is with an intelligent multi-mode drive (i-MMD)
topology, as shown in Fig. 2. This vehicle can provide a number of working modes: electric vehicle (EV) drive
mode, hybrid drive mode, pure engine mode, regenerative braking mode and mechanical braking mode. In this
specially designed topology, there exist a fixed transmission ratio between the engine and the generator, between
the engine and the wheels, and between the drive motor and the wheels. The vehicle control unit (VCU) can control
0m 300m 700m 1200m

the switch of operation modes by regulating the working state of the engine, generator, drive motor and clutch.
Fig. 2. Powertrain of the studied PHEV.
a. Engine Model
Based on the massive data obtained from the bench experiment, the fuel consumption rate of the engine under
different working conditions can be obtained using a two-dimensional interpolation method. The efficiency of the
engine, engine efficiency can be calculated by
(1)
where denotes the engine efficiency, stands for vehicle fuel consumption rate, measured in g/kWh and
obtained from the bench experiment, and q represents the gasoline calorific value, which is equal to 4.6×104J/g.
b. Motor Model
In this research, the studied PHEV is equipped with two motors: one is the drive motor and the other one is the
generator. The drive motor accounts for converting electrical energy into mechanical energy, or converting the
kinetic energy of the vehicle into electrical energy in the regenerative braking mode; and the generator takes charge
of converting the mechanical energy output by the engine into electrical energy. The efficiency data of the motor
and motor controller at different velocities and torques can be obtained through the bench experiments. The
efficiency of motors is shown in Fig. 3, which shows the optimal efficiency at moderate torque and speed.
c. Battery Model
The battery of PHEV in this study is a ternary lithium-ion battery with the rated capacity of 70 Ampere hour
(Ah). In this study, an equivalent model of the battery is established using an internal resistance model, which
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consists of an ideal voltage source and a series resistor. Taking the battery discharge process as an example, besides
providing energy to drive the motor, a portion of the ideal voltage source's energy is converted into heat through the
internal resistance. The values of the battery open circuit voltage and internal resistance are mainly influenced by
temperature and State of Charge (SOC) of the battery. However, this study does not consider the influence of
ambient temperature and thus neglects the impact of temperature on the open circuit voltage and internal resistance.
SOC represents the ratio of the remaining capacity of the battery to its fully charged capacity, and is formulated as,
(2)
where SOC0 represents the initial SOC value of the battery, expresses the rated capacity of battery, equaled to
70 Ah, and denotes the battery current at time t, which is calculated by the ratio of power to voltage.
Fig. 3. Numerical model of generator system efficiency. (a) Efficiency of motor, (b) Efficiency of generator.
B. Energy Consumption Model of PHEV
The VCU regulates the engine operating point to high-efficiency area by reasonably distributing the torques of
motor and engine, so as to bring better energy consumption economy. In this paper, a rule-based energy management
strategy is initially adopted, and the VCU determines the working mode of powertrain according to the battery SOC,
the required driving force and vehicle velocity. The energy consumption cost is used as the evaluation index of the
vehicle energy economy. Based on the built PHEV component model and energy management strategy, the vehicle
energy consumption under different working conditions can be obtained via interpolation. In order to reduce the
computation burden of the interpolation method, a fast energy consumption model is proposed based on the
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polynomial fitting principle. In this study, the power consumption and fuel consumption are converted into the total
cost by a weighted manner, as:
(3)
where , and represent the energy consumption cost per unit time, the power of the power battery and
the gasoline consumed per unit time, respectively. Besides, and denote the price of electricity and the price
of gasoline, respectively. The energy consumption cost rate when the road gradient is 0 and the vehicle SOC is 0.7
and 0.4 is shown in Fig. 4.
Fig. 4. Ve h ic l e e ne r g y c o s t r at e u n de r d i ff e r e nt S O C .
The polynomial fitting method is leveraged to fit the efficiency model of each component of the PHEV. The
modelling accuracy is verified under two typical operating conditions (including NEDC and WLTC), as shown in
Fig. 5, and the specific energy costs and errors are shown in Table 1, from which we can find that the designed
method can closely track the variation rate with a difference of less than 0.5% and the coefficient of determination
R2 is very close to 1, justifying the fidelity of the model.
Fig. 5. Comparison of interpolation model and fitting model under NEDC and WLTC working conditions.
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Table 1 Cost comparison between interpolation model and fitting model under typical working conditions
Wo rk in g
condition
Energy consumption cost of
interpolation model (CNY)
Energy consumption
cost of fit model (CNY)
Deviation
R2
NEDC
2.3663
2.3778
0.4869%
0.9992
WLTC
7.3179
7.3051
0.1747%
0.9999
Since the numerical value of the vehicle velocity imposes neglected effect on the calculation time of the energy
consumption model, a uniform velocity condition with a length of 1 km is constructed to compare the calculation
time of two energy consumption models. The configuration of the computing platform includes CPU with Intel i7-
11700 processor and 16 giga-byte RAM. The simulation calculation shows that the calculation time of the
interpolation energy consumption model is 58.97 s, and the calculation time of the fitted energy consumption model
is 1.12 s. To sum up, compared with the interpolation energy consumption model, the vehicle energy consumption
model based on the polynomial fitting method can significantly reduce the calculation time and improve the
calculation efficiency without discounting the modeling accuracy.
III. REAL-TIME ECO-DRIVING CONTROL AT MULTI-INTERSECTIONS
The real-time eco-driving at multi-intersections can be treated as a dynamic inverse optimization problem. In
this paper, we address this problem by optimizing the economic vehicle velocity trajectory using a two-part
approach: the trajectory from the starting point to the first intersection, and the trajectory from the first intersection
to the destination. By considering factors such as energy consumption economy, comfort, and traffic efficiency, the
proposed method enables the rapid generation of a velocity trajectory, given the vehicle's driving route and expected
travel time. The structure of the proposed eco-driving approach is illustrated in Fig. 6, and the calculation procedure
for obtaining the multi-intersection vehicle velocity trajectory is divided into six distinct steps.
1). Upon obtaining the whole trip, the vehicle route is segmented into multiple sections based on the V2I-
acquired driving environment information.
2). The expected average velocity for the entire trip is determined by considering the expected travel time and
route length. By comparing this with the road velocity limit, the expected vehicle velocity at the end of each road
segment can be derived.
3). The velocity trajectory at multi-intersections is initialized, consisting of uniform acceleration, uniform
velocity and uniform deceleration. By combining with the initial vehicle state and the fast energy consumption
model, the SOC trajectory for the entire trip is generated.

4). With the road information, initial battery SOC and velocity at the start and end of each road segment, a set
of velocity trajectories is generated using the lower-level multi-objective vehicle velocity planning method based
on the BBMOPSO algorithm. These trajectories are approximately evenly distributed in terms of travel time.
5). Feasible travel time at the end of each road segment is calculated, and the SPFA algorithm is employed to
optimize the travel time for each segment, thereby addressing problems with negative edges and reducing
computational complexity. On this basis, the vehicle speed trajectories for each road segment are integrated.
6). The current vehicle state is utilized as the initial state for the next optimization, replacing the initial full
speed trajectory. The number of iterations in the velocity planning layer's heuristic algorithm is increased, and steps
3) to 5) are repeated iteratively until the end of the trip.
The final optimized speed track consists of two parts: a rapid speed profile planning within a certain duration
after the start of the trip and an accurate speed profile for the rest of the trip.
Fig. 6. The framework of the real-time eco-driving of multi-intersection.
A. Multi-Objective Velocity Planning
To guarantee the overall optimization of multiple targets (energy economy, traffic efficiency, and comfort), it
is imperative to set up a weighted manner according to the optimization importance. Note that in the real-time eco-
Segment The Route in The Spatial Domain
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Eco-Driving Velocity trajectory for PHEV in
Multi-intersections
Multi-objective Vehicle Velocity Planning Method
Task Planning Based on SPFA

driving solving process, the multi-objective vehicle velocity planning method runs twice. The biggest difference
between the two optimizations is the number of iterations of the BBMOPSO algorithm. After iterative optimizations,
the number of iterations for the first optimization is 50, aiming to prioritize computational efficiency and quickly
converge to a satisfactory solution, and the number of iterations for the second optimization is 300, and the main
target of second optimization accounts for prioritizing the attainment of the optimal solution.
a) Velocity Planning
In this paper, the road segment is divided into a number of sub-segments equidistantly, and the endpoints of
the sub-segments are called nodes, and the velocity at the node position is considered as the decision variable, i.e.,
(4)
(5)
where stands for the decision variable of the mth road segment; represents the vehicle velocity at the nth
node on the mth road segment, and ; k is the number of sub-road segments of the mth road segment;
denotes the length of the mth road segment, represents the distance between nodes, and is set to 10 m to
optimize the velocity planning strategy more effectively; and express the initial velocity of the vehicle
and the expected velocity of the vehicle when it reaches the end of the kth road segment, respectively. The state
variable u characterizing vehicle states includes the vehicle position p and the battery SOC, as:
(6)
Common comfort evaluation indicators include the weighted root mean square value of acceleration [37],
acceleration disturbance [38], and the integral of impact, among others. It is important to note that the degree of
shock refers to the derivative of acceleration with respect to time, also known as jerk. By using a weighted impact
degree as a comfort evaluation index, sudden accelerations can be minimized, ensuring passengers do not
experience drastic changes in acceleration. This approach also helps reduce the maximum impact value, thereby
improving ride comfort. In this study, we consider the weighted impact degree as the evaluation index of comfort,
which is calculated as the sum of the integral of the impact degree and the maximum impact degree, as:
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velocity trajectory. The evaluation indicators of vehicle energy economy and traffic efficiency are energy
consumption cost and travel time, respectively. The evaluation indicators of the vehicle velocity trajectory in spatial
domain can be formulated, as:
(8)
(9)
where and represent the travel time of the kth road segment and the travel time of the nth road segment,
respectively; expresses the energy consumption cost rate of the vehicle at time t; denotes the average
velocity of the vehicle in the nth segment.
The overall objective function and constraints in terms of motion dynamics and powertrain limits should be
satisfied, as follows:
(10)
(11)
where , and are the weight coefficient of energy consumption cost, ride comfort and travel time,
respectively. The three weighting factors are set to 1, (0.9/2)² and 0.1, respectively.
b) Particle Update of the BBMOPSO Algorithm
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velocity planning problem, we propose an innovative solution, that is, a lower-level multi-objective velocity
planning method that leverages the BBMOPSO algorithm and incorporates the principles of the Pareto optimal
theory. The primary objective of this method is to achieve a well-balanced and efficient solution that adequately
considers all the objectives without being overly influenced by specific weight values. By integrating Backbone
PSO with the Pareto optimal theory within the BBMOPSO framework, the proposed approach not only enables the
resolution of multi-objective optimization problems but also enhances the balance between the algorithm's
exploration and exploitation functions [39]. This integration ensures a more comprehensive and robust optimization
process, allowing for more effective and reliable velocity planning in complex scenarios. The detailed operation
mechanism of particle position update of BBMOPSO is formulated, as:
(12)
(13)
(14)
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where r is a random number subject to uniform distribution in the range of [0,1]; and represents the
probability of searching around and , respectively; R denotes the search radius adjustment factor, j
stands for the number of current iterations; and expresses the inflection point of the "exploration" and
"development" modes, and is equal to . aa is the rate of change, , where is the
maximum number of algorithm iterations.
c) External Memory Update Strategy
In order to make the Pareto solution set in the external memory as evenly distributed as possible, a clustering
algorithm based on travel time difference is leveraged to divide the particles into several categories. The specific
steps include: 1) sorting the particles in the external memory according to the length of time, 2) calculating the
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difference between all two adjacent particles, and setting the maximum value to be less than or equal to ,
and 3) combining all the individuals whose difference is less than into one class. Note that larger
imposes a greater impact on clustering. When decreases, the number of classes increases, and even some classes
are with only one or no particles. In this paper, is set to 0.3 after iterative optimization. When the number of
optimal particles in the external memory exceeds the maximum threshold, the particles of the memory need to be
trimmed. The specific steps involve: 1) leveraging the clustering algorithm to divide the Pareto solution set into
several classes; 2) discarding the least comfortable particle from the class with the largest number of particles; and
3) determining whether the number of non-dominated solutions in the memory exceeds the capacity threshold and
conducting the clipping operation if necessary.
d) Global Optimal Particle Selection
All the feasible solutions in the external memory are with non-dominated property. According to the Pareto
optimality theory, it is impossible to find the optimal particles for three optimization objectives in the solution set.
In addition, selecting the global optimal particle is critical in the execution of the PSO algorithm and delivers a
significant impact on the diversity of the Pareto solution set. To expand the distribution range of the Pareto solution
set as much as possible, it is imperative to scatter the particle swarm to the sparse area of the non-dominated solution
set. There exists a strong correlation between the position of the global optimal particle and the update of the particle
position, therefore the roulette method is adopted to realize the selection of the global optimal particle. The detailed
steps are as follows.
1) Divide all non-dominated solutions into several classes based on the above clustering method.
2) Eliminate all categories without particles, and calculate the fitness value of this category according to the
number of particles in each category, as formulated in (16).
3) Randomly select a class by means of roulette according to the fitness value of each category, randomly
4) Select a particle stochastically from the selected class as the global optimal particle.
(16)
where represents the fitness value of the z th class; denotes the number of non-dominated solutions
q
max
q
max
lq
l
l
l
()
()
1
()
Nz
v
Nz
z
e
Pz
e
b
b
-
-
=
=
éù
ëû
å
()Pz
()Nz

in the z th class; is the optimal particle selection coefficient, taken as 10, and v express the
number of classes.
B. Task Planning Based on the SPFA
In the task planning layer, based on the obtained SPaT information, the SPFA is leveraged to optimize the
travel time of each road segment, and the optimization targets include energy economy and traffic efficiency. By
preventing vehicles from parking at intersections, the vehicle energy consumption is reduced to ensure traffic
efficiency. The main purpose of SPFA is to solve the single-source shortest path problem, and similar algorithms
include the Dijkstra algorithm [40] and the Bellman-ford algorithm [41]. Comparing with them, SPFA can not only
solve problems with negative edges, but also result in higher computational efficiency. The detailed search
procedure is illustrated below. At the endpoints of each road segment, the expected travel time of full trip is divided
into multiple segments with equal intervals. The black dots in Fig. 7 represent the travel time nodes divided by equal
intervals. In this study, the interval is set to 2 s. To reduce the computational load, the travel time nodes on the red
phase are eliminated. Note that the calculation efficiency can be further improved by screening the feasible vehicle
travel time at the endpoints of each road segment again.
Fig. 7. The schematic diagram of SPFA algorithm to optimize the travel time of road segments.
After determining the feasible travel time at the endpoints of the intersections, the SPFA is harnessed to
optimize the travel time of each road segment. First, the expected travel time of all “edges” formed by feasible
travel times between the endpoints of adjacent intersections is calculated. Second, in the set of vehicle velocity
trajectories with approximately uniform distribution in travel time solved by the BBMOPSO algorithm, the velocity
trajectory is selected for each edge according to the difference between the actual travel time and the expected travel
time. Third, the weighted sum of the energy consumption and the travel time of the vehicle speed trajectory is used
as the optimization objective, as shown in (16). The selected vehicle speed trajectory is considered as the actual
b
1, 2, ,zv=
0 300 700 1200
30
60
90
120
150
180
210
Time (s)
Position (m)
Traffic path
Optimal path

vehicle speed trajectory of the road segment. Finally, the SPFA is implemented to solve the above optimization
problem, as shown in Fig. 6, from the feasible solution space composed of all black edges to find the red edge
(optimal solution). By this manner, the vehicle velocity trajectory of each road segment is integrated into the
economic vehicle velocity of multi-intersection.
(17)
where denotes the total cost of the whole journey; and represent the energy consumption and the
travel time in the m th road segment, respectively; , and M express the number of road segments in
the whole journey. is the travel time coefficient of the road segment, as:
(18)
(19)
where represents the deviation between the travel time of the road segment and the expected travel time;
denotes the expected travel time of the vehicle on the mth road segment. To reduce the calculation error, the real
travel time is used to replace the expected travel time when a phased optimal solution is found in the solution process.
IV. SIMULATION AND EXPERIMENTAL VALIDATIONS
To manifest the effectiveness of the proposed method, simulation and experiment validations are respectively
conducted. The main parameters of the vehicle are listed in Table 2. It is worth noting that the price of fuel is set as
CNY 7.05 per liter, and the price of electricity is set as CNY 1.5 per kWh. In addition, we assume that all the driving
environment information required by the host vehicle can be obtained through the V2I technology.
Table 2 The basic parameters of objective PHEV
Characteristic
Va l u e
Mass (kg)
1885
Frontal area (m2)
2.68
Air drag coefficient
0.34
Tire rolling ra dius (m)
0.36
Rolling resistance coefficient
0.0075
Gear ratio from drive motor to wheel
11.7 34
Gear ratio from engine to wheel
3.176
Gear ratio from engine to generator
0.377
Battery capacity (Ah)
70
z seconds(s)
5
1
()
M
mm
m
QQt
k
=
=+
å
Q
m
Q
m
t
1, 2, ,mM=
k
0.01 0
0 0
ee
ke
³
ì
=í<
î
des
mm
des
m
tt
t
e
-
=
e
des
m
t

A. Simulation Validation
In this study, to substantially examine the performance of the proposed algorithm, three eco-driving
optimization methods are discussed, including 1) forward hierarchical eco-driving optimization based on DP and
SPFA, 2) forward hierarchical eco-driving optimization based on BBMOPSO and SPFA, and 3) dynamic inverse
hierarchical eco-driving optimization scheme. These three methods are simplified as FDS-opt, FBS-opt and DI-opt
hereinafter. The adopted FDS-opt and FBS-opt are detailed in [31], and for simplicity they are not detailed
introduced here. The optimization model of the task planning layer in FDS-opt and FBS-opt remains the same, and
the optimization problem can be formulated as:
(20)
where is the total cost of the vehicle for the whole trip; and denote the static and dynamic energy
consumption of the vehicle in the mth road section, respectively; means the average speed of the mth road
section; , and denote the length, the travel time and the gradient of the mth road segment, respectively;
stands for the efficiency of vehicle braking energy recovery, if , then , otherwise
; and , where express the number of road segments in the whole journey.
The simulation scene settings are shown in Table 3. The whole trip consists of three road segments, and two
traffic lights are set. A rule for transmit ting the timing inf ormat ion of tra ffic lights based on the V2I technology is
formulated, and only four parameters are required to represent the SPaT information, namely .
Thereinto, means the phase of the traffic signal at the current moment, “1” represents the green phase (the green
and yellow phases are indistinguishable in this paper), and “0” indicates the red phase; denotes the time the
traffic signal has lasted in the current phase; stands for the full duration of a green phase; and is the
duration of a complete red phase. In addition, the initial velocity of the vehicle at the starting point and the final
1
2
22
1
()
( cos sin )
1()
2
M
sta dyn
fmmm
m
sta
mmm m m
dyn
mmmrecu
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m
m
QEEt
E s cv mgf mg
Emvv
s
vt
k
aa
l
=
-
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ï
ï
ï=+ +
ï
í=-
ï
ï
ï=
ï
î
å
f
Q
sta
m
E
dyn
m
E
m
v
m
s
m
t
m
a
recu
l
22
10
mm
vv
-
-³
1
recu
l
=
0.8
recu
l
=
1, 2, ,mM=
M
[, , , ]
last G R
TTT
z
z
last
T
G
T
R
T

vehicle velocity at the end point are set to 0 km/h, the initial SOC of the vehicle is 0.8, and the expected travel time
of the whole journey is 110 s.
The simulation results of the dynamic backward hierarchical speed planning control are shown in Fig. 8. As
can be found, the BBMOPSP algorithm iteratively optimizes the cost function, and delivers the feasible velocity
trajectory with the consideration of energy economy, comfort and traffic efficiency. As shown in Fig. 8 (a) and (b),
the optimal cost is decreased rapidly, and the velocity trajectories are optimized all the time. The SPFA algorithm is
leveraged to determine different passing points, as shown in the black dots in Fig. 8 (c). Finally, it can be seen from
Fig. 8 (d) that the optimization results of each section are integrated, and the acceleration and deceleration appear
in one after another through continuous intersections. The contrastive optimization results with different methods
are shown in Fig. 9. The characteristics of the vehicle velocity trajectory (including travel time, energy consumption
cost and comfort) solved by different eco-driving optimization methods, and the calculation time of different
methods are listed in Table 4.
Table 3 The simulation scene settings
Scene settings
Value
The length of the whole journey (m)
1200
The lengths of the three raod segments (m)
[300, 400, 500]
The length of the intersection (m)
30
The upper limit of the road segment (km/h)
80
The upper limit of the intersection (km/h)
30
The SPaT of the first intersection
[1, 5, 20, 20]
The SPaT of the second intersection
[0, 12, 15, 15]
The slopes of the three road segments
0

Fig. 8. The simulation result of dynamic backward hierarchical speed planning control. (a) BBMOPSO target function, (b)
BBMOPSO velocity trajectory optimization, (c) SPFA collection of feasible points of passage, (d) velocity trajectory of
whole section.
As shown in Fig. 9, all three methods meet the crossing requirements; however, their speed trajectories differ
significantly. The FDS-opt and FBS-opt methods initially run at high speed and then transition to a slower speed,
whereas the DI-opt method follows a different pattern. Furthermore, Table 4 indicates that all methods ensure the
vehicle reaches the destination within the expected travel time, indicating guaranteed traffic efficiency for all eco-
driving optimization methods. Both the FDS-opt and FBS-opt methods belong to the forward hierarchical eco-
driving optimization scheme. Consequently, the optimization results of the task planning layer in the two schemes
are kept consistent, and the travel time of each road segment remains the same. The distinction lies in the approach
used to determine the specific velocity trajectory. The FDS-opt method employs DP, while the FBS-opt method
incorporates the BBMOPSO algorithm, which continuously approximates the global optimal solution. As a result,
the energy consumption cost of the velocity trajectory optimized by FBS-opt is 11.23% higher than that by FDS-
opt. However, FBS-opt significantly reduces computation time by avoiding the heavy computational load associated
with the DP algorithm. Additionally, due to the comfort evaluation index limitations in FDS-opt, the vehicle speed
trajectory optimized by FBS-opt offers improved comfort.
(c) (d)
(b)
(a)
0200 400 600 800 1000 1200
Position (m)
0
20
40
60
80
100
120
140
Time (s)
0 200 400 600 800 1000 1200
Position (m)
0
10
20
30
40
50
60
Speed ( km/h)

Fig. 9. Ve h ic l e v el o c i t y t r a j ec t o r i es o p t im i z e d b y d i ff e r e n t w h o l e-trip vehicle velocity planning methods. (a) SPaT
information in 0.8 SOC, (b) whole-trip vehicle velocity in 0.8 SOC.
Table 4 Comparison of different velocity planning methods
Method
Time (s)
Energy consumption cost (CNY)
Electricity consumption
(kW∙h)
Comfort
Calculating time (s)
FDS-opt
110. 1695
0.2180
0.1453
50.9375
847.23
FBS-opt
110. 1741
0.2425 (↑11.23%)
0.1617
42.2942
3.21
DI-opt
109.8652
0.2018 (↓7.43%)
0.1345
40.4186
5.58
Among the different approaches examined, it can be inferred that the DP method yields superior optimization
results in velocity planning compared to the BBMOPSO algorithm. However, it is worth noting that the energy
consumption cost of the velocity trajectory optimized by FDS-opt is higher than that by DI-opt. This can be
attributed to the decoupling operation of the task planning layer and the vehicle velocity planning layer in the
forward hierarchical eco-driving optimization scheme, leading to sub-optimal solutions for the travel time in each
road segment. In summary, the proposed dynamic inverse hierarchical eco-driving optimization scheme in this paper
demonstrates the advantages over existing forward hierarchical eco-driving optimization schemes. It not only
reduces vehicle energy consumption in intelligent network environments, but also significantly decreases
computational time and enhances computational efficiency. These findings highlight the potential of the proposed
scheme to improve the overall performance of eco-driving systems by achieving energy savings, reducing
computational burden, and enhancing optimization results.
B. Experimental Verifications
To f urther v erify th e p erformance of t he proposed algorithm, substantial experimental validations are
performed. The connection method of each individual parts (as shown in Fig. 10) in the experimental platform is
detailed, as follows. The PC1 employs Kvaser to connect to the NI device through CAN, and the NI device connects
to the PC2 via Ethernet [42]. Note that the driving environment information obtained by the vehicle is included in
0200 400 600 800 1000 1200
Distance (m)
0
20
40
60
80
100
120
140
Time (s)
0
10
20
30
40
50
60
Velocity (km/h)
0200 400 600 800 1000 1200
Distance (m)
(a) (b)
FDS-opt
FBS-opt
DI-opt
FDS-opt
FBS-opt
DI-opt

the velocity planning method, as such there is no need to interact with the environment in this experiment. At the
beginning of the experiment, the controller is started, and the Ve r i s ta n d is loaded to run the PHEV vehicle model
installed in the NI-PXI system. After that, the controller starts to call the proposed algorithm immediately, outputs
the first velocity trajectory after 4 s, and starts the optimization of the second velocity at the same time. The PC1
transmits the planned reference velocity trajectory to the vehicle model through CAN communication. Then, the
PID control algorithm is applied to solve the vehicle acceleration, which is sent to the energy management layer for
torque distribution, and finally the PHEV operation state information is updated. During the experiment, the
experimental data are recorded by the Ve r is t a n d s o f t wa r e installed in PC2.
Fig. 10. Schematic diagram of experimental platform.
The experimental scene setting is shown in Fig. 11, and the total trip (the length is 8 km) involves 11 road
segments and 10 intersections (including 5 straight intersections, 3 left-turn intersections, and 2 right-turn
intersections). The settings of road status information are shown in Table 5, and the SPaT information is shown in
Table 6. Note that the green phase duration is set to infinity to indicate that the intersection is a right-turn intersection,
as shown in intersections 6 and 9 in Table 6.
Fig. 11. Veh i c l e d r i v i ng r o u te .
Table 5 Road status information settings for each road segment
Serial number
1
2
3
4
5
6
7
8
9
10
11
Length (m)
460
500
880
900
610
800
650
830
690
780
900
Limiting-velocity (km/h)
60
60
60
80
80
80
60
60
60
80
80
Gradient
0
0
2
0
0
1
0
3
0
0
0
Table 6 SPaT information settings at each intersection
Matlab/Simulink
PC1 PC2
NI MAX Veristand
Ethernet
Dynamic Inverse
Hierarchical Eco-driving
optimization scheme
USB
Energy
Management
System Model
Speed Tracking
Control
Signal protocol
conversion
CAN
CAN
Kvaser USBcan NI Equipment
Vehicle
Running
Status
Reference
Velocity
Starting Point
Destination
1
2
34 5
6
7 8 9
10
11

Serial number
1
2
3
4
5
6
7
8
9
10
aa (s)
1
0
1
0
0
1
1
0
1
1
bb (s)
10
45
20
30
50
5
3
30
5
10
cc (s)
30
45
60
50
45
inf
30
40
inf
30
dd (s)
45
60
60
60
60
0
60
60
0
50
Fig. 12. Comparison of vehicle velocity and acceleration of simulation and experiment. (a) velocity, (b) acceleration.
Fig. 13. Comparison of battery SOC and energy consumption of simulation and experiment. (a) SOC, (b) energy consumption
cost
Fig. 14. Experimental operating point optimized by the dynamic inverse hierarchical eco-driving optimization method.
(a) the driving motor, (b) the engine.
After experiment, the calculation time of the simulation optimization is 3.96 s, and the calculation time of the
experiment optimization is 30.71 s, adequately manifesting that the proposed eco-driving optimization scheme can
meet the requirements of real-time application. In addition, as shown in Figs. 12 and 13, the results of simulation
and experiment are roughly the same, verifying the effectiveness of the proposed method in practical application.
0200 400 600 800 1000
Time (s)
0
10
20
30
40
50
60
70
Velocity (km/h)
(a)
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
Acceleration (m/s2)
0200 400 600 800 1000
Time (s)
(b)
Reference
Experiment
Middle Reference
Experiment
Time (s)
400
0200 600 800 1000
0.395
0.400
0.405
0.410
0.415
0.420
SOC
(a)
0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
Energy consumption cost (CNY)
0200 400 600 800 1000
Time (s)
(b)
1.8
Reference
Experiment
Reference
Experiment
Torque (N」m)
Rotational Speed (r/min)
(a) (b)
Torque (N」m)
Rotational Speed (r/min)

While it is necessary to note that there exists a certain gap. From the enlarged green circle in Fig. 12 (a), we can
find that in the first 4 s of the experiment, the velocity is zero, which corresponds to the calculation time of the first
optimization mentioned above. As shown in the enlarged red circle in Fig. 12 (a), the speed difference between the
two results is quite large, which is caused by the communication lag when the speed control variable is transferred
through the CAN bus in the experiment. The accuracy of the vehicle velocity information transmitted by CAN
communication is 0.1 m/s, therefore there exists a slight error between the information received by the PHEV model
and the value sent by the controller, whereas it is within an acceptable range. In addition, as can be found from Fig.
12 (a), the PID control algorithm can track the reference vehicle speed trajectory quite accurately. Similarly, as
shown in Fig. 12 (b), the acceleration of simulation and experiment exhibit similar changing tendency. However,
compared with the simulation results, the experimental results showcase some distinct fluctuations, which are
mainly caused by the data transmission during the experimental equipment, rather than the strategy itself. The
trajectories of battery SOC and energy consumption cost depicted in Fig. 13 verify the effectiveness of the proposed
eco-driving optimization scheme, however the deviation is resulted, which is primarily attributed to the presence of
oscillations in the acceleration signal during the experimental process, and caused by overshooting in the control
process. As a result, this error manifests in the final results of SOC and energy consumption. In Fig. 13 (a), the
existence of deviation, the SOC trajectory of the vehicle keeps the similar varying trend, and returns to the specified
SOC range ultimately. Fig. 14 represents the operating points of the driving motor and the engine in the experiment.
It is evident that the vehicle primarily operates in the pure electric mode, while the engine operates predominantly
along the lowest fuel consumption curve in series mode. This enables the engine to recharge the traction battery and
maintain the vehicle's SOC stable at around 0.4. In summary, the trajectory of battery SOC and energy consumption
cost can also demonstrate the effectiveness of the proposed full-range vehicle speed planning method. Through
extensive experimental verification, it can be concluded that the method proposed in this paper is capable of
planning the globally optimal vehicle speed trajectory with a high computational efficiency, meeting the
requirements of eco-driving, energy consumption saving and the comfort guarantee of driving.
V. CONCLUSIONS
This paper explores a real-time eco-driving optimization scheme for PHEVs at multi-intersections, and the
proposed method is validated to promote energy consumption economy and operation comfort while ensuring traffic

efficiency. Notably, it significantly reduces calculation time and ensures real-time performance. The utilization of
inverse layering and dynamic output of optimization results, facilitated by a fast energy consumption model and
efficient optimization algorithm, emphasizes the real-time application capability of the proposed method. By
combining a heuristic algorithm with the Pareto theory, the proposed method achieves a balance between energy
economy, comfort, and traffic efficiency, eliminating the need for a tedious weight factor determination process.
Moreover, it effectively solves the energy-saving velocity trajectory problem in the spatial domain for multiple
intersections. Simulation results demonstrate a 7.43% reduction in energy consumption cost compared to FDS-opt.
The consistency between simulation and experimental results further confirms the effectiveness of the proposed
method in practical applications.
In future studies, the vehicle’s economic efficiency and performance will be further enhanced by upgrading
the algorithm, thereby enabling to adapt to increasingly intricate and dynamic traffic scenarios. Additionally, the
research focus is extended to include the optimization of energy management strategies for PHEVs. By integrating
speed planning and energy management, comprehensive optimization can be anticipated.
ACKNOWLEDGEMENTS
The work is funded by the National Natural Science Foundation of China (No. 52002046 and 52272395) in
part, Chongqing Fundamental Research and Frontier Exploration Project (No. CSTC2019JCYJ-MSXMX0642) in
part, Science and Technology Research Program of Chongqing Municipal Education Commission (No.
KJQN201901539) in part.
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