## 1 Introduction  
Since the need for the market and regulations to improve the fuel economy and smoothness of heavy-duty mining trucks, increasing the number of the forward gears is the trend of developing the new high-power hydraulic automatic transmission (AT) [1; 2; 3]. The single-transition shift (STS, that is, one clutch is going to engage while the other clutch needs to be disengaged) can no longer meet the designing requirements of a higher number of gears and more reasonable gear ratio distribution within a limited space [4]. Double-transition shift (DTS) is a dual single-transition shift process, which requires multiple clutches (typically four) for precisely coordinated control. If any clutch is not precisely controlled, power interruption or conflict may happen, and the shift quality will deteriorate [5; 6]. The DTS involving more clutch elements is more complicated than the STS of traditional transmission, which poses a higher challenge to the AT control system of heavy-duty mining trucks [7].  
In order to improve the AT shift quality, the researchers used different modeling and optimization methods to study the clutch-to-clutch control system [8; 9; 10; 11; 12]. [PERSON] et al. [13; 14] used the bond graph method to analyze the dynamics of a shift process for a ten-speed automatic transmission, and they proposed a solution by using an extra clutch to compensate the output torque, so as to assist the gear shift and suppress the excessive impact of the inertial phase. [PERSON] and [PERSON] [15] adopted subspace identification to describe the predictive equations of single-transition shift and then used the model predictive control method to optimize the shifting quality. In the research of the nonlinear dynamic characteristics of the wet clutch, a clutch pressure controller based on sliding mode control was designed to ensure a smooth clutch-to-clutch shift by [PERSON] and [PERSON] [16]. [PERSON] et al. [17] focused on the analysis of an AT electro-hydraulic control system and proposed a two-degree-of-freedom proportional-integral-derivative control optimization method to ensure that the clutch relative speed difference follows the preset trajectory curve by adjusting the proportional solenoid valve duty cycle. To achieve the balance among the sportiness, comfort, and robustness during the shift, the multi-objective genetic algorithm was used to get Pareto-optimal frontier by [PERSON] and [PERSON] [18].  
Compared with the aforementioned large amount of literature on STS, there are few studies on the double-transition shift. [PERSON] and [PERSON] [19; 20] established a DTS model based on the theory of multi-body dynamics, analyzed the motion state of the components, and proposed a parameter-based control strategy. [PERSON] et al. [6; 21] studied DTS power downshifts (10-6 gears) and proposed six different additional constraint schemes of clutch torque and speed during shift transients. Through simulation analysis, the simulation results show that the rapid pressure reduction of the two clutches to be disconnected is the optimal control scheme, but the article lacks the research on the overlap time of the two clutch sets.  
Therefore, in terms of the AT equipped on heavy-duty mining trucks with DTS, this paper uses the Lagrange method to build the dynamic model of the high-power transmission and the vehicle powertrain system at first. Secondly, the dynamic analysis of the DTS, which is composed of a group of the STS power upshift and a group of downshift, is carried out. Then, five strategies for the overlap time of the two sets of clutches in the DTS are proposed. After the multi-objective genetic algorithm optimization is performed with the shift jerk and the clutch friction loss as the performance indicators, the Pareto optimal result analysis and simulation are performed. Finally, conclusions are drawn.