A hybrid forecasting system using convolutional-based extreme learning with extended elephant herd optimization for time-series prediction

Accurate forecasting for the different time-series data plays a major role in predicting future analysis that can increase economic benefits. Many research models have been attempted earlier but pose certain challenges due to the random characteristics of the original time-series data in obtaining high-precision forecasting results. To this end, we propose a hybrid convolutional-based extreme learning model named Convolutional Multi-Layer Deep Extreme Learning Machine (CMDELM) adopted with the Extended Elephant Herd Optimization Algorithm (E2HOA) that performs deeper feature extraction with faster learning of optimized features. Also, an Edge-aware Attribute-based Dynamic Graph learning (EADGL) approach is proposed to ensure that the graph-structured network incorporates edge-level information for effective future learning. The CMDELM network employs stacked multiple convolutional ELM layers that use several hidden layers with dense connections to learn high-level features for enhancing forecast accuracy. Dense connections are utilized in the proposed CMDELM task of integrating ELM with CNN to aid the network in extracting feature maps from shallow layers. Moreover, the network's performance is enhanced by adjusting the convolutional kernel sizes and integrating them into the residual unit. Following the convolutional model of a fully connected network, the deep ELM layer is linked to produce the predicted classes for the forecasts. In the forecasting stage, we adopt the E2HOA strategy to optimize the computational parameters for all learning layers and predict an accurate future forecast signal. The E2HOA algorithm improves the separation and updation phases with the consideration of a newborn calf in the elephant herd. E2HOA incorporates new clans and updates them using a threshold value to determine their inclusion, thus achieving an optimal outcome. This makes the learning network achieve the final solution with the optimal key parameters of the CMDELM network. Experimental results covering different competitive models and the evaluated results indicate that our proposed hybrid forecasting system obtains satisfactory accuracy with a Root Mean Square percentage Error (RMSPE) and Symmetric Mean absolute percentage Error (SMAPE) of below 22%, respectively, for PM2.5 concentration, electricity price, and wind speed forecasting results. Hence, the experimental outcomes show that the proposed model performs well in terms of accuracy and provides constant forecasting of time-series.