## 3 Solution Method
### Diversification  
With the aid of the RMTS metamodel, the conventional EHO can be used to select \(N\) significant solutions from the solution space. Since the EHO recursively improves the individuals in the elephant population, it is more suited to meet the needs. EHO is a biological algorithm inspired by the herding behavior of an elephant herd [7]. EHO is designed for solving and optimizing the optimizations problems by considering two herding behaviors, clan updating and separating. Clan updating operator is used to update the current positions of elephants and matriarch in each clan. Separating operator is used to upgrade the population diversity in the search process. There are many advantages of EHO, such as ease of implementation, simple control parameters and easy combination with other algorithms. EHO has been successfully employed to solve the human emotion recognition problems [22], energy-based localization problems [23] and multi-objective energy resource accommodation problem for distribution systems [24]. However, there are some issues of the original EHO, such as the low ability to retain the diversity during the search process and the cause of prematurity. Accordingly, the IEHO have been developed to improve the convergence efficiency of the original EHO. The IEHO has two control parameters that determine the influence of the matriarch and clans, which are scale factor for matriarch and scale factor for clans. The global exploration and exploitation of the IEHO are primarily dominated by the scale factor for matriarch. The IEHO adopts a large scale factor for the matriarch to increase diversification. When the scale factor for the matriarch is increased, the IEHO trends to perform global search while the probability of local search is decreased. In contrast, the IEHO utilizes a small scale factor for matriarch to increase intensification. When the scale factor for matriarch is decreased, the IEHO trends to perform local search around the optimum in a local region. The scale factor for clans defines the influence of the position for the elite elephant in a clan. Low value will generate new positions far from the center of a clan which induces a high level of exploration. Thus, a low value of scale factor for clans trends to global search, while a large value guides to local search. The following notations are used in the IEHO. \(I\) is the number of clans, \(c_{i}\) is the number of elephants in the \(i\)th clan, \(\Phi=\sum\limits_{i=1}^{I}c_{i}\) denotes the total number of elephants, \(t_{\max}\) is the number of required iterations. The position of the \(j\)th elephant in the \(i\)th clan at iteration \(t\) is denoted by \(\mathbf{x}_{j}^{i}(t)=[x_{j,1}^{i}(t),\ldots,x_{j,K}^{i}(t)]\). The position of matriarch in the \(i\)th clan at iteration \(t\) is denoted by \(\mathbf{x}_{b_{i}}^{i}(t)=[x_{b_{i},1}^{i}(t),\ldots,x_{b_{i},K}^{i}(t)]\). \(\alpha^{t}\) is a scale factor that determines the influence of matriarch at iteration \(t\), \(\alpha^{t}\in[\alpha_{\min},\alpha_{\max}]\), where \(\alpha_{\min}\) and \(\alpha_{\max}\) express the minimum and maximum values, respectively. \(\beta^{t}\) is a scale factor that determines the influence of clans at iteration \(t\), \(\beta^{t}\in[\beta_{\min},\beta_{\max}]\), where \(\beta_{\min}\) and \(\beta_{\max}\) denote the minimum and maximum values, respectively. IEHO (Algorithm 1) can be briefly summarized below. ```
Step 1: Configure parameters  Configure the values of \(I\), \(K\), \(c_{i}\), \(\alpha_{\min}\), \(\alpha_{\max}\), \(\beta_{\min}\), \(\beta_{\max}\), \(t_{\max}\), and set \(t=0\), where \(t\) expresses the iteration counter. Step 2: Initialize clan (a) A population of I clans is initialized with positions \(\mathbf{x}_{j}^{i}(0)\). For \(i=1,\ldots,I\), do  For \(j=1,\ldots,c_{



The IEHO stops when the maximum number of iterations, \(t_{\max}\), has been reached. When the IEHO has terminated, the final \(\Phi\) individuals are sorted based on their fitness.