## 2 Dehghani Method (DM)  
In this section, first DM is explained and then its mathematical modeling is presented. DM shows that all population members of the optimization algorithm, even the worst one, can contribute to the development of the population of algorithm. \begin{table}
\begin{tabular}{c c} \hline \hline \multicolumn{2}{c}{General description: Designed based on the ideation of various laws of physics.} \\ \hline \(\bullet\) & Spring Search Algorithm \\  & (SSA) [39; 40], Curved Space \\  & Optimization (CSO) [41], Black \\  & Hole (BH) [42], Ray \\ Physics-based & Optimization (RO) [43] \\  & algorithm, Artificial Chemical \\  & Reaction Optimization \\  & Algorithm (ACROA) [44], \\  & Galaxy-based Search \\  & Algorithm (GbSA) [45], and \\  & Small World Optimization \\  & Algorithm (SWOA) [46] \\ \hline \multicolumn{2}{c}{General description: They have involved evolution of a population in order to create new generations of genetically superior individuals [47].} \\ \hline \(\bullet\) & Biogeography-based \\ Evolutionary-based & Optimizer (BBO) [48], \\  & Differential Evolution \\  & (DE) [49], Genetic Algorithm \\  & (GA) [50], Evolution Strategy \\  & (ES) [51], and Genetic \\  & Programming (GP) [52]. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Cont. Each population-based optimization algorithm has a matrix called the population matrix, which each row of this matrix represents a population member. Each member of the population is actually a vector which represents the values of the problem variables. Given that each member of the population is a random vector in the problem search space, it is a suggested solution (SS) to the problem. After the formation of the population matrix, the values proposed by each population member for the problem variables are evaluated in the objective function (OF). The population matrix and values of the objective functions are defined in Equation (1). \[\text{SS}=X=\left[ \begin{array}{cccccc}SS_{1}=X_{1}&x_{1}^{1}&\cdots&x_{1}^{d }&\cdots&x_{1}^{m}&OF_{1}\\ \vdots&\vdots&\ddots&\vdots&&\vdots&\vdots\\ SS_{i}=X_{i}&x_{i}^{1}&\cdots&x_{i}^{d}&\cdots&x_{i}^{m}&OF_{i}\\ \vdots&\vdots&&\vdots&\ddots&\vdots&\vdots\\ SS_{N}=X_{N}&x_{N}^{1}&\cdots&x_{N}^{d}&\cdots&x_{N}^{m}&OF_{N}\\ \end{array} \right], \tag{1}\]  
where, SS is the suggested solutions matrix, \(X\) is the population matrix, \(\text{SS}_{i}\) is the \(i\)'th suggested solution, \(X_{i}\) is the \(i\)'th population member, \(x_{i}^{d}\) is the value of \(d\)'th variables of optimization problem suggested by \(i\)'th population member, \(N\) is the number of population members or suggested solutions, \(m\) is the number of variables, and \(OF_{i}\) is the value of objective function for the \(i\)'th suggested solution. Different values for the objective function are obtained based on the values proposed for the variables by the population members. The member that offers the best-suggested solution (BSS) to the optimization problem plays an important role in improving the algorithm population. The row number of this member in the population matrix is determined using Equation (2). \[\text{{best}}=\left\{ \begin{array}{ll}\text{{the row number of }}X\text{ matrix with}\text{min}OF,&\text{{for minimization problems}}\\ \text{{the row number of }}X\text{ matrix with}\text{max}OF,&\text{{for maximization problems}}\\ \end{array} \right., \tag{2}\]  
where, _best_ is the row number of the member with BSS. The BSS and it's \(OF\) are specified by Equations (3) and (4). \[X_{best}\ :\text{variables value of}\text{min}objective\ function, \tag{3}\]  
\[F_{best}\ :\text{value of}\text{min}objective\ function, \tag{4}\]  
where, \(X_{best}\) is the BSS or best population member and \(F_{best}\) is the value of \(OF\) for BSS. As mentioned, the best member of the population plays an important role in improving the population of the algorithm and thus the performance of the optimization algorithm.