2.1.

Introduction to datasets and lane change scenario construction

The dataset used for this study is the German High-D dataset, published by the Institute of Automotive Engineering at the RWTH Aachen University in Germany. The High-D dataset is a large natural vehicle trajectory data set for German motorways, collected from six different locations near Cologne, Germany, with locations varying according to the number of lanes and speed limits, and including cars and trucks in the records. The data set includes 11.5 hours of measurements and 110,000 vehicles from the six locations, with a total of 45,000 km of measured vehicle miles travelled and 5,600 complete lane change records. The data acquisition frequency was 0.1s/time. By using state-of-the-art computer vision algorithms, the positioning error is typically less than 10 cm. The data was collected from a four-lane motorway section in both directions, the road surface configuration of which is shown in Figure 1 below.

Figure 1.

Driveway map.

2.2.

Lane change safety analysis

The vehicle lane change process is mainly divided into three steps: the first step, the vehicle to determine the intention of lane change after the vehicle began to have a side acceleration and speed, the vehicle phase targets lane movement; the second step, the vehicle began to move to the target lane and continue to maintain the direction of the lane movement, until the vehicle into the target lane; the third step, the vehicle moved to the target lane of the appropriate position, the vehicle orientation acceleration and speed all to 0 and At this point, the vehicle is not moving in a side direction. Many factors need to be considered in the study of vehicle lane change, but lane change safety is the primary premise of the vehicle lane change process. The second part of the vehicle lane change process, which has safety concerns, is shown in Figure 2 below.

Figure 2.

Lane change process.

As the position of the actual vehicle travelling in the lane is highly random about its position in the target lane after changing lanes, this paper makes several assumptions about the study conditions:

The acceleration of a vehicle during a lane change varies from moment to moment and the model of Mo Zhao bin^[9]et al. is introduced to describe the dynamic acceleration and dynamic shop distance during a vehicle lane change:

is the acceleration of the target vehicle at moment t + Δt; a (max) is the maximum acceleration during the lane change; Δν (t) is the speed difference between the desired speed and the ideal speed of the target vehicle; s* (v (t), Δν (t)) the distance that the driver of the target vehicle expects to travel in Δt; T₀ is the desired headway time distance between the target vehicle and its following vehicle; b is the ideal vehicle deceleration speed.

To ensure the validity of the data used, acceleration error values are introduced to describe the authenticity of the lane change data, with smaller error values indicating that the lane change behavior of the vehicle is in line with the general lane change behavior. In this paper, data with large acceleration error values are removed to ensure that the lane change data used conforms to the general lane change pattern. As follows:

σ is the acceleration error branch; a is the actual acceleration of the vehicle; is the acceleration calculated using the lane change model.

To make the results clearer and more understandable. This paper assumes that the vehicle is in uniformly accelerated linear motion in both the x and y directions at each frequency time when changing lanes. To ensure the safety of the vehicle lane change process conditions: the vehicle in the process of lane change will not collide with the vehicle in front, but for safety considerations, this paper sets a lane change vehicle and its front vehicle safety distance when the vehicle in the process of lane change and the front vehicle safety distance is greater than s₀ vehicle lane change behaviour is not a safety hazard, the specific expression is as follows:

The X -direction has:

TheY -direction has:

x_ΔT, y_ΔT are the distance travelled by the vehicle within one frame in the corresponding direction; v₀ is the initial velocity of the vehicle in the corresponding direction at the start of the lane change; a_ΔT is the initial acceleration of the vehicle in the corresponding direction at the start of the lane change; ΔT is the frequency whose value is 0.1s; nT is the total time of the lane change; y_ΔT is the total distance travelled by the vehicle in the corresponding direction during the lane change time respectively.

The condition to ensure the safety of the vehicle lane change process is that the vehicle will not collide with the vehicle in front of it during the lane change process, but for safety considerations, this paper sets a safety distance d₀ between the lane change vehicle and its vehicle in front of it, when the vehicle in the lane change process and the safety distance of the vehicle in front of it is greater than d₀ the lane change behavior of the vehicle is not a safety hazard, as the following equation:

The X -direction has:

TheY -direction has:

d is the width of the vehicle in front; s is the distance between the lane changing vehicle and the target vehicle; T is the headway time distance between the lane changing vehicle and the vehicle in front; d₀ is the safe vehicle distance, and d₀ is 0.6m according to the road traffic management regulations of the People’s Republic of China.

2.3.

Vehicle Lane Change Carbon Emission Analysis

According to the MEET report published by the European Commission, the carbon emissions of a vehicle are related to the speed at which it is driven. The carbon emissions per unit mile (g/km) and the speed of the vehicle (km/h) are calculated using the following formula. See equation (10)

ρ₀~ρ₆ are the parameters related to the vehicle load

According to Sun Jinzhi^[8] et al. the carbon emission functions of different vehicle models were studied according to the VSP, where vehicles were divided into two models according to their vehicle weight cars with a weight of less than 3.5 tons were small cars and cars with a weight of more than 3.5 tons were medium and large cars with the following carbon emission formula:

Small cars:

Medium and large vehicles:

2.4.

Multi-objective planning

The vehicle lane change benefits studied in this paper are the vehicle’s benefits and environmental benefits, there are three indicators of comfort, efficiency and carbon emission rate, comfort and efficiency are the vehicle’s benefits, its carbon emission is the environmental benefits, the first order derivative of acceleration is introduced to quantify the comfort of each vehicle, the difference between the current speed and the desired speed is used to describe the efficiency; the carbon emission per unit time of the vehicle lane change process to describe the carbon emission rate.

The three-lane change benefits for lane-change vehicles are as follows:

B_comfortable, B_carbon denote the comfort, efficiency, and safety of the vehicle lane change, respectively; is the average of the first-order inverse of the acceleration during the lane change; is the desired speed of the vehicle lane change; and v_t is the current speed of the vehicle.

The lane change benefits for the target vehicle are as follows:

B₁, B₂ are the vehicle benefits and environmental benefits of vehicle lane change respectively; N is the normalized parameter of comfort to efficiency, which is taken as 10m/s in this paper.

2.5.

Modelling and analysis of the risks and benefits of vehicle lane change

Vehicle lane change benefit analysis for a multi-objective problem, most according to the driver’s primary goal is to improve the speed of the vehicle, but the lane change will lead to changes in the relationship between the vehicles on the road to follow, the vehicle’s lateral traffic flow is also affected by the vehicle lane change, that is, the vehicle lane change will produce lane change risk, therefore, the premise of solving the maximum benefit of the vehicle lane change to ensure the safety of the vehicle lane change, although the vehicle lane changes carbon emissions is not the driver’s goal to consider, but the study of vehicle carbon emissions is of great importance to environmental protection, to vehicle lane change the vehicle’s own benefits and vehicle carbon emission rate as the goal to establish multi-objective planning as follows:

s.t.

v_max, v_min, a_max, a_min, t_max, t_min represent the maximum and minimum speed, acceleration, and lane change duration of the vehicle, respectively. The values taken in this paper are: 25m/s, 5m/s, 6m/s²,2m/s²,8s,4s.The parameter values are taken from the literature ^[4].

3.1.

Pareto solution

The objective of this paper is to find a Pareto feasible solution for a vehicle lane change concerning both vehicle benefit and environmental gain that is more objective. The mutual constraints between the objectives in a Pareto-solved multi-objective optimisation problem improve the performance of one objective often come at the expense of the performance of other objectives, and there cannot be a solution that makes the performance of all objectives optimal, so for a multi-objective optimisation problem, the solution is usually a set of non-inferior solutions. In the presence of multiple Pareto-optimal solutions, all Pareto-optimal solutions can be considered equally important, and it is, therefore, necessary to find as many Pareto-optimal solutions to the optimisation problem as possible. In addition to the requirement that the solution to the optimisation problem converges to an approximate Pareto-optimal domain, the solution obtained must also be uniformly sparsely distributed over the Pareto-optimal domain, and a set of well-agreed solutions between multiple objectives is based on a set of diverse solutions.

3.2.

NSGA-II algorithm

The NSGA-II^[10] algorithm is introduced to solve the Pareto solution. The NSGA-II algorithm is superior to the NSGA algorithm: it adopts a fast non-dominated sorting algorithm, which greatly reduces the computational complexity compared to NSGA; it adopts the crowding degree and crowding degree comparison operator instead of the shared radius share Q that needs to be specified, and it is used as the winning criterion in the peer comparison after the fast sorting, so that the individuals in the quasi-Pareto individuals in the domain can be extended to the whole Pareto domain and evenly distributed, maintaining the diversity of the population; an elite strategy is introduced to expand the sampling space, preventing the loss of the best individuals and improving the computational speed and robustness of the algorithm.NSGA-II is an improvement on the first generation of non-dominated sorting genetic algorithms, whose algorithm is based on the following three main steps:

3.3.

Analysis of results

Through multi-objective solutions, the Pareto solutions for different desired speeds are obtained in this paper. The Pareto feasible solutions and the actual solutions for the desired speeds of 55m/s, 45m/s, 35m/s and 25m/s are shown in Figures 1, 2 and 3 respectively, and Table 1 is shown in.

Figure 3.

Pareto feasible solution versus actual solution of the data.

Table 1.

Table comparing the Pareto feasible scenario with the actual scenario for the data.

Vehicle driver’s lane change primary pursuit for higher speed and driving comfort, the actual data set of solutions are mainly concentrated in the upper right side of the Pareto solution, that is, high speed, high efficiency and high vehicle carbon emissions of lane change behaviour, but the pursuit of excessive speed and efficiency will cause high carbon emissions, this paper selected the right side of the Pareto surface solution analysis, its Pareto solution set and the actual data values are shown in the table, from the table can be seen to ensure that the vehicle lane change gains high at the same time reduce when the vehicle change lane environmental impact lane change initial headway spacing, headway time distance, maximum acceleration, maximum speed should be in,