## 2 Modeling
### Optimization Model Based on MPA  
The marine predator algorithm (MPA) is a novel swarm optimization algorithm that was proposed by [PERSON] et al. [36]. The core of this algorithm is a combination of three different foraging strategies proposed by the ideas of Levy flight and Brownian motion. The MPA randomly initializes the prey location, updates the prey location through three foraging strategies, and finally overcomes the prematurity problem according to the FADs or vortex effect. The foraging strategy and the effect of FADs are described as follows:  
(1) When the current iteration number is less than \(1/3\) of the maximum iteration number, the algorithm performs a global search by Brownian motion and updates the position of Prey according to Equation (33):  
\[\left\{ \begin{array}{l}\text{stepsize}_{i}=R_{B}\otimes(\text{Elite}_{i}-R _{B}\otimes\text{Prey}_{i})\\ \text{Prey}_{i}=\text{Prey}_{i}+P\cdot R\otimes\text{stepsize}_{i}\end{array} \right. \tag{33}\]  
where stepsize is the moving step of the prey; RB is a normally distributed Brownian random vector; Elite is the elite matrix; Prey\({}_{i}\) is the prey matrix; \(\otimes\) is the term-by-term multiplication operator; \(P\) is equal to 0.5; and \(R\) is the rand() function. (2) When the current number of iterations is greater than \(1/3\) and less than \(2/3\) of the maximum number of iterations, the strategy of Levy flight in parallel with Brownian motion is used to update the position of Prey, as shown in Equations (34) and (35). \[\left\{ \begin{array}{l}\text{stepsize}_{i}=R_{L}\otimes(\text{Elite}_{i}-R _{L}\otimes\text{Prey}_{i})\\ \text{Prey}_{i}=\text{Prey}_{i}+P\cdot R\otimes\text{stepsize}_{i}\end{array}  \right.i=1,2,\cdots,\frac{n}{2} \tag{34}\]  
\[\left\{ \begin{array}{l}\text{stepsize}_{i}=R_{B}\otimes(R_{B}\otimes\text {Elite}_{i}-\text{Prey}_{i})\\ \text{Prey}_{i}=\text{Elite}_{i}+P\cdot CF\otimes\text{stepsize}_{i}\end{array}  \right.i=\frac{n}{2}+1,\cdots,n \tag{35}\]  
where \(R_{L}\) is a random number with a Levy distribution; \(CF=(1-\text{Iter}/\text{MaxIter})^{(2\cdot\text{Iter}/\text{MaxIter})}\), and \(n\) is the number of prey. (3) When the current number of iterations exceeds \(2/3\) of the maximum number of iterations, the algorithm updates Prey based on the Levy motion strategy, as shown in Equation (36). \[\left\{ \begin{array}{l}\text{stepsize}_{i}=R_{L}\otimes(R_{L}\otimes\text {Elite}_{i}-\text{Prey}_{i})\\ \text{Prey}_{i}=\text{Elite}_{i}+P\cdot CF\otimes\text{stepsize}_{i}\end{array}  \right.i=1,2,\cdots,n \tag{36}\]  
(4) Finally, the algorithm overcomes the premature convergence problem through the vortex effect or fish aggregation devices (_FADs_) effect, as shown in Equation (37). \[\text{Prey}_{i}=\left\{ \begin{array}{l}\text{Prey}_{i}+CF[X_{min}+R_{L} \otimes(X_{max}-X_{min}\ )]\otimes U,r\leq FADs\\ \text{Prey}_{i}+[FADs\cdot(1-r)+r](\text{Prey}_{r1}-\text{Prey}_{r2}),r> FADs\end{array} \right. \tag{37}\]where _FADs_ (=0.2) is the probability of influencing the search process; \(U\) is a binary vector; \(r\) is a random number in the range of \([0,1]\); and \(r_{1}\) and \(r_{2}\) are the index subscripts of the prey. The support stiffness of the gears in a coaxial face gear split-torque transmission system has considerable influence on the load distribution and power flow [34; 37]. The load-sharing coefficient usually expresses the balance of the load distribution; the larger the load-sharing coefficient, the more uneven the load distribution.