# Application of Three Metaheuristic Techniques in Simulation of Concrete Slump
## 4 Results and Discussion
### ALO, BBO, and GOA Conventional Methods for Optimizing the NN
As explained, six major steps are needed to implement the ALO, whilst both BBO and GOA execute the optimization with two steps. Focusing on the range of the products, there are some negative values in the training data. In details, the actual slump values in the training phase vary from 0 to 29 cm, while the predicted values by the BBO-NN, GOA-NN, and ALO-NN range in, [-1.922, 28.761], [-3.113, 27.742], and [-5.346, 29.722], respectively. Needless to say, negative slump values do not indicate any physical meaning. The authors believe that the reason for this can be sought in the wide range of actual slumps (sample variance = 76.57). The distribution of input data might be another misleading parameter. Referring to Figure 4d-f, for instance, it can be seen that there is a considerable number of concrete specimens which did not show any sensitivity to the changes in the amount of slag and fly ash (slump equals 0 for these data). However, it should be noted that the slump is a function of all input parameters. In comparison with some of previous studies which have used the same dataset to train their intelligent approaches, or same statistical indexes to assess their model performance [47; 48; 49; 50; 51], the result of our study are more promising. [PERSON] [24], for example, found that the ANN with an RMSE of 4.12 cm is a capable tool for simulating the slump. Likewise, [PERSON] [25] and [PERSON] [2] achieved the RMSEs of 4.03 and 8.51 by employing ANN in their research. This is because the RMSE of the elite model of the current study was less than 4 cm (i.e., 3.7788 cm) obtained by the proposed ALO-NN ensemble. Another item which could be pointed out is the enhancement of the ANN performance in incorporation with the ALO optimization algorithm. In other words, the weights and biases suggested by ALO constructed a more capable ANN compared to those suggested through its regular learning model. Noting that the current study was carried out for typical concrete mixture (i.e. used Portland cement), and it is found that the employed metaheuristic sciences have excellent performance and potential to predict the slump simulation of special concrete like self-compacting concrete (SCC) [47], high strength concrete (HSC) [23], and so on. Testing the used networks for the mentioned aims could be an appropriate idea for future studies. Moreover, according to [PERSON] [25], the American Concrete Pavement Association (ACPA) [53] has considered that measured differences in slumps of lower than 2 inches (5.08 cm) are typical for sampling, testing, and material variation. Therefore, the prediction error of the all three implemented models, and especially the ALO-NN, is relatively low, and lies in an acceptable extent. Hence, the suggested models are potent enough to be properly used in the industry. As difficulties have been associated with laboratory models, and considering the high robustness of soft computing methods in the field of slump modelling, intelligent tools may be accurate and inexpensive alternatives to traditional approaches. In the last part of this study, a slump predictive formula is presented (Equation (12)). Note that, this formula is developed based on the weights and biases that have been suggested by the most successful neural ensemble (i.e., the ALO-NN). More specifically, this equation indicates the neural relationship established in the unique output neuron of the used MLP network. Therefore, utilizing it entails calculating some middle parameters which are the outputs of the hidden neurons. \[\text{Slump}=-0.1317\times Z1-0.8109\times Z2+0.5922\times Z3+0.3680\times Z4 +0.8241\times Z5-0.5218\times Z6-0.2127 \tag{12}\]  
In above formula, Z1, Z2,... Z6 are middle parameters and are obtained by Equation (13). This is worth noting that the activation function of the hidden neurons is \"Tangent-Sigmoid\" (briefly Tansig) which is expressed by Equation (14). * _ASCE Task Committee_ (2000)_ _ASCE Task Committee. Artificial neural networks in hydrology. II: Hydrologic applications._ J. Hydrol.