# Application of Three Metaheuristic Techniques in Simulation of Concrete Slump
## 4 Results and Discussion
### ALO, BBO, and GOA Conventional Methods for Optimizing the NN  
When it comes to hybrid optimization techniques, population size is considered an influential parameter which highly affects the performance of the proposed algorithm. In fact, this value indicates the number of the individuals in the society (e.g., the number of ant lions in the ALO technique). Each network was tested by nine different population sizes (i.e., 10, 25, 50, 75, 100, 200, 300, 400, and 500) [46]. The RMSE was defined as the objective function to measure the error of the performance at the end of each iteration. Each model performed within 1000 repetitions to optimize the neural parameters (i.e., connecting weights and biases) of the proposed NN. More clearly, at each iteration, the found solution contained the mentioned parameters. The NN was reconstructed by means of the obtained parameters and performed to estimate slump. Then, the RMSE between the targets and outputs was measured as the objective function. The result was a convergence curve showing the decrease of the error. Figure 5a-c shows the obtained convergence curves of the implemented BBO-NN, GOA-NN, and ALO-NN ensembles, respectively. Figure 5: _Cont._  
As is illustrated, all three models decreased the majority of the RMSE within the first 600 iterations. For better illustration, Figure 6 denotes the best response of the tested networks in terms of the RMSE. Accordingly, the ALO, BBO, and GOA with population sizes of 400, 50, and 300 performed more efficiently than other versions. It is also seen that the overall behavior of the RMSE is downward for GOA-NN, while it fluctuates for the two other algorithms. The proposed ALO-NN achieved the RMSE of 4.955 at the 678 th try, and remained steady thereafter. As for the BBO and GOA, the RMSE was obtained 4.4508 and 4.9552, respectively. Notably, the implementation time (for all 1000 repetitions) were obtained 32,784.89, 645.38, and 4273.3 seconds on an operating system at 2.5 GHz and 6 Gigabytes of RAM. Figure 5: The sensitivity analysis based on the model complexity for the (**a**) BBO-NN, (**b**) GOA-NN, and (**c**) ALO-NN. Figure 6: The final root mean square error (RMSE) values versus the population size. The calculated RMSEs for the training samples (4.4509, 4.9553, and 4.8051, respectively, for the BBO-NN, GOA-NN, and ALO-NN) indicate that the computational parameters suggested by all three metaheuristic algorithms develop an MLP with an acceptable accuracy. This claim can also be supported by the training MAEs (3.5513, 3.8576, and 3.8055). From a comparison viewpoint, regarding the lower error values, the BBO acquired a better understanding of the relationship between slump and its effective factors, compared to the two other networks. Moreover, the ALO outperformed GOA in this phase. As for the testing phase, the computed RMSEs (4.1859, 4.0171, and 3.7788) showed disagreement between the learning and generalization power of the used ensembles. In this sense, despite the higher accuracy of the BBO in the training phase, the ALO produced more consistent results for concretes with unseen conditions. Furthermore, GOA performed more efficiently than BBO in the testing stage. Figure 8: The testing results obtained for (**a,b**) BBO-NN, (**c,d**) GOA-NN, and (**e,f**) ALO-NN predictions. In addition to RMSE, the obtained MAEs (3.3465, 3.2013, and 3.0286) revealed that the ALO was the most effective evolutionary algorithm for optimizing MLP, followed by GOA and BBO. Overall, it was concluded that, although the BBO trained the ANN more effectively than the two other techniques, the ALO was found to have the highest generalization capability. However, investigating the reason for this requires further analysis and expert coding knowledge; one possible reason could be the greater number of steps taken by ALO to achieve the target, because it is an obvious distinction between the mechanisms of the mentioned techniques.