## Appendix A Modified Multi-Objective Dragonfly Algorithm  
In order to solve the problems associated with the MODA of easily falling into local optimal solutions and having slower convergence speeds, a steps-based strategy based on an exponential function and an elite opposition learning strategy were used for modification. First, the elite opposition learning strategy was used to generate a broader search scope and diversify the population identified as the next generation and to improve the global search capacity and search accuracy of the MODA [62]. Then, a steps-based strategy based on an exponential function was applied to enhance the convergence speed of the algorithm in the later stages. The specific implementation scheme is as follows:  
1. Elite Opposition Learning Strategy  
To improve the global search capacity and search accuracy of the MODA, the elite opposition learning strategy was applied to produce various elite opposition individuals and further develop an unplanned opposition population that can hunt in neighborhood space and enhance the local mining capacity. During the running of the MODA, the elite opposition learning strategy can define the elite dragonfly as the top dragonfly with the best fitness value. This is expressed by \(\mathbf{ex}_{m}^{t}=[ex_{m,1}^{t},ex_{m,2}^{t},\cdots,ex_{m,D}^{t}]\), \(m=1,2,\ldots,EN\), where \(ex_{i,j}^{t}\) indicates the elite solutions corresponding to individuals \(x_{i,j}^{t}\), \(t\) is the present iteration, and \(D\) represents the dimension of the algorithm space. Moreover, an elite opposition solution \(\mathbf{ex}_{i}^{t}=[e\overset{\times}{x}_{i,1}^{t},e\overset{\times}{x}_{i,2 }^{t},\cdots,e\overset{\times}{x}_{i,D}^{t}]\) with respect to a certain dragonfly in the current solution \(x_{i}^{t}=[x_{i,1}^{t},x_{i,2}^{t},\cdots,x_{i,D}^{t}]\) can be mathematically modeled by:  
\[e\overset{\times}{x}_{i,j}^{t}=k\cdot(\mathbf{ea}_{j}^{t}+\mathbf{eb}_{j}^{t })-x_{i,j}^{t}. \tag{1}\]  
\[\mathbf{ea}_{j}^{t}=min(ex_{m,j}^{t}),\mathbf{eb}_{j}^{t}=max(ex_{m,j}^{t}). \tag{2}\]  
\[e\overset{\times}{x}_{i,j}^{t}=rand\cdot(\mathbf{eb}_{j}^{t}-\mathbf{ea}_{j}^ {t})+\mathbf{ea}_{j}^{t},\text{ if }e\overset{\times}{x}_{i,j}^{t}<L\mathbf{b}_{i}. \tag{3}\]  
where \(i=1,2,\ldots,SN\), \(j=1,2,\ldots,EN\), \(k=rand(0,1)\), \(SN\) represents the population size of the dragonflies, and, generally, \(EN\) represents the selected number of elite individuals with the value of \(SN^{*}0.1\). \(k\) represents a generalized argument that is subject to a uniform distribution. The elite opposition learning strategy is used in the basic MODA to effectively expand the search area, diversify the population, and enhance the optimization performance and global search capability. 1. Steps-based Strategy based on an Exponential Function  
In a basic MODA, there are several parameters \((s,a,c,f,e,\text{ and }w)\), as described by \(\Delta\mathbf{x}_{i+1}=(sS_{i}+aA_{i}+cC_{i}+fF_{i}+eE_{i})+w\mathbf{x}_{i}\), which are adaptively adjusted at random; hence, the dragonfly individuals update themselves according to a stochastic linear step size in the course of iteration. This means that the position update of the dragonfly completely relies on the site of the present individual and the stochastic linear step size, which can be determined, respectively. Despite the above strategy being conducive to finding a globally optimal solution to some degree, it cannot ensure that the solution is optimal; thus, this situation causes a slow convergence rate [51]. To expedite the convergence rate of theMODA, the exponential step strategy is applied to replace the original linear step strategy. This means that an exponential function is added to the original step and generates an exponential function steps-based strategy. It should be noted that a vital parameter \(\mu\) is adopted to renew the step, so that the local and global hunt capacities can be improved, and the convergence rate can be further accelerated. Hence, it is pivotal to set a suitable \(\mu\).