The accuracy requirements for short-term power load forecasting have been increasing due to the rapid development of the electric power industry. Nevertheless, the short-term load exhibits both elasticity and instability characteristics, posing challenges for accurate load forecasting. Meanwhile, the traditional prediction model suffers from the issues of inadequate precision and inefficient training. In this work, a proposed model called IWOA-CNN-BIGRU-CBAM is introduced. To solve the problem of the Squeeze-and-Excitation (SE) attention mechanism’s inability to collect information in the spatial dimension effectively, the Convolutional Block Attention Module (CBAM) is firstly introduced as a replacement. This change aims to enhance the ability to capture location attributes. Subsequently, we propose an improved Whale Optimization Algorithm (IWOA) that addresses its limitations, such as heavy reliance on the initial solution and susceptibility to local optimum solutions. The proposed IWOA is also applied for the hyperparameter optimization of the Convolutional Neural Network–Bidirectional Gated Recurrent Unit–Convolutional Block Attention Module (CNN-BiGRU-CBAM) to improve the precision of predictions. Ultimately, applying the proposed model to forecast short-term power demand yields results that show that the CBAM effectively addresses the problem of the SE attention mechanism’s inability to capture spatial characteristics fully. The proposed IWOA exhibits a homogeneous dispersion of the initial population and an effective capability to identify the optimal solution. Compared to other models, the proposed model improves R² by 0.00224, reduces the RMSE by 18.5781, and reduces MAE by 25.8940, and the model’s applicability and superiority are validated.

Given a graph G, the general sum-connectivity index is defined as χα(G)=∑uv∈E(G)dGu+dGvα, where dG(u) (or dG(v)) denotes the degree of vertex u (or v) in the graph G and α is a real number. In this paper, we obtain the sharp bounds for general sum-connectivity indices of several graph transformations, including the semitotal-point graph, semitotal-line graph, total graph, and eight distinct transformation graphs Guvw, where u,v,w∈+,-.

Improving urban wastewater treatment efficiency and quality is urgent for most cities. The accurate wastewater flowrate forecast of a wastewater treatment plant (WWTP) is crucial for cutting energy use and reducing pollution. In this study, two hybrid models are proposed: ARIMA–Markov and ARIMA–LSTM–Transformer. Using 5 min-interval inlet flowrate data from a WWTP in 2024, the two models were verified and compared. Forecasts for 1 day, 7 days, and 2 months ahead were made, and model accuracies were compared. Ten repetitions with the same dataset assess stability, and ARIMA–LSTM–Transformer, with better performance, were selected. Then, the Whale Optimization Algorithm (WOA), Particle Swarm Optimization (PSO) algorithm, and Sparrow Search Algorithm (SSA) were used for optimization, with the WOA excelling in accuracy and stability. Experimental results show that compared to the single model Transformer, WOA–ARIMA–LSTM–Transformer did better in forecasting wastewater flowrate. The combined model enables efficient and accurate wastewater flowrate forecasting, highlighting the combined model’s application potential.