## 3 Models and Methods
### Particle Swarm Optimization
The collected data are stored in a repository. A database is used to store the latest monitoring data of resources. The monitoring data stored in the database are created as historical monitoring data and time series. The preprocessor module creates these forms of monitoring data. The time-series data in raw form are transformed into supervised data by the preprocessor module to adjust the input by the neural network. A variety of mechanisms are available to be deployed that act to process the data regarding cloud workload. These include the normalized data, averaging data in the long run, grouping into multivariate time-series, and sliding window. After processing in preprocessor module, the data in output as historical resources data are fed into database collector. This historical resources data creates a model for predictions that are completed in the trainer module. For predicting the utilization of resources, the data are given to predictors. The proposed methodology includes a learning method added in the trainer module that uses FLNN. The GA-PSO mechanism trains the data into the training data. The data is stored in a repository. The data is stored in a repository. network one by one for increasing the speed of convergence and enhancing the accuracy of forecasting. The designed learning mechanism is named FLGAPSONN. When the training process is completed, the trained module predicts the utilization of resources in the future which is done in the predictor module. ## 4 Results and Discussion

This section presents details of the evaluation of the proposed hybrid model. The evaluation is carried out with publicly available Google cluster workload traces dataset [12; 28]. Each job in the dataset consists of multiple concurrent tasks that run on different machines. The dataset consists of parameters such as CPU utilization, memory consumption, disk utilization, etc. According to the previous studies [12; 28], less than 2% of the jobs take longer than one day. As used in previous experiments, a long-running job (ID 1617658948) consisting of 60,171 tasks was selected for evaluation. The job covers a 20 day period. The data of the first 15 days are used for training and the remaining data are used for testing. The evaluation consists of multivariate input where both CPU and memory are considered and univariate input where CPU or memory are considered. To evaluate the performance of the proposed hybrid GA-PSO model, we compared the results with traditional FLNN, FLGANN, and FLPSONN. The compared models consist of one input layer and one output layer with Exponential Linear Unit (ELU) as activation function. Table 1 shows the comparative results of the proposed model with other models in terms of MAE. The results are calculated with sliding window of size 5. The results show that the hybrid GA-PSO model yields smaller values for both univariate and multivariate input cases. For univariate CPU utilization prediction, the MAE of the proposed model is 0.25 which is smaller than the 0.32, 0.29, and 0.36 produced by FLPSONN, FLGANN, and FLNN models, respectively. In case of univariate memory consumption prediction, the proposed model produced MAE of 0.018 which is smaller than the compared methods. In case of multivariate CPU utilization prediction, the hybrid model produced MAE of 0.33 which is smaller than the compared methods. Similar results can be observed in case of multivariate memory consumption prediction. Figure 3: Architecture of the predictive systems. Percent improvement gain in terms of MAE of the proposed model over other compared models is presented in Figures 8 and 9 for univariate and multivariate input cases, respectively. In case of univariate CPU utilization, the proposed technique achieved percent improvement gain of 21.87, 13.75, and 30.55 over FLPSONN, FLGANN, and FLNN, respectively. In the case of memory utilization prediction, the percentage improvement gain over the compared models is 25.0, 14.28, and 33.3.