## 4 Modeling Methodology  
Modeling methodology of this study was carried out with the following main steps (Figure 5): (1) dataset preparation, (2) initiation and model generation, (3) metaheuristic optimization, (4) fitness evaluation, (5) stopping condition, and (6) construction of the final models. A detailed description of each step is given below.  
(1) Dataset preparation:In this step, the data generated from the laboratory tests, which included 210 sets of parameters (concentration of NaOH solution, mass ratio of alkali activating solution to fly ash, mass ratio of solution Na\({}_{2}\)SiO\({}_{3}\) to solution NaOH, and compressive strength), were divided into two parts. The first part included 70% of the data which were then used to construct the models. The second part consisted of 30% of the remaining data which were then used to validate the models.  
(2) Initiation model generation:In this step, the initial ANFIS model was created using the training dataset where the Gaussian membership function was used to derived fuzzy sets and fuzzy membership values, and the fuzzy c-means clustering algorithm was used to distil natural groups from the training dataset for better training of the ANFIS.  
(3) Metaheuristic optimization:In this step, the PSO and GA optimization methods were used to find the optimal consequent and antecedent parameters of the ANFIS. To get the best optimization, a trial-and-error test was done to determine the best numbers of particles and individuals in PSO and GA. In the case of the PSO, the best number of particles was determined as \"40\". With the GA, the best number of individuals was determined as \"30\". In addition, other modeling parameters of the GA, the crossover rate and mutation rate, were set as 0.4 and 0.6, respectively, as suggested by [PERSON] et al. [59] and [PERSON] et al. [60], and another modeling parameter of the PSO, the inertia weight, was set as 0.9, as suggested by [PERSON] et al. [60].  
(4) Fitness evaluation:The RMSE function was used in this step to validate the performance of the ANFIS. In the meantime, the various combinations of consequent and antecedent parameters were explored by the PSO and GA, whereby the PSO updated the positions of particles on the basis of RMSE values to look for the best position of the swarm, and the GA generated and checked the chromosomes for the best chromosome population based on the best RMSE values.  
(5) Stopping condition:The optimization process was carried out until the maximum number of generations was set. In this study, a maximum of 1000 generations were set, and the best swarm  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Mixture No.** & **X\({}_{1}\) (M)** & **X\({}_{2}\)** & **X\({}_{3}\)** & **Y (MPa)** \\ \hline GPC 01 & 10 & 0.4 & 2 & 40.17 \\ GPC 02 & 14 & 0.4 & 2 & 49.43 \\ GPC 03 & 10 & 0.5 & 2 & 29.73 \\ GPC 04 & 14 & 0.5 & 2 & 43.17 \\ \(\cdots\) & \(\cdots\) & \(\cdots\) & \(\cdots\) & \(\cdots\) \\ \(\cdots\) & \(\cdots\) & \(\cdots\) & \(\cdots\) & \(\cdots\) \\ \(\cdots\) & \(\cdots\) & \(\cdots\) & \(\cdots\) & \(\cdots\) \\ GPC 206 & 12 & 0.45 & 3 & 35.33 \\ GPC 207 & 12 & 0.45 & 2.5 & 42.47 \\ GPC 208 & 14 & 0.40 & 3 & 48.59 \\ GPC 209 & 14 & 0.5 & 3 & 36.28 \\ GPC 210 & 14 & 0.45 & 2.5 & 49.39 \\ \hline \end{tabular}
\end{table}
Table 4: Mix proportions and compressive strength results of GPC using steel slag aggregate.  
position (PSO) and chromosomes (GA) were finally selected and compared to derive the optimal consequent and antecedent parameters.  
_(6) Construction of the final models:_ the final PSOANFIS and GAANFIS models were built using the optimal consequent and antecedent parameters in this step. Validation of the final models was also done using several methods (RMSE, MAE, and \(R\)).