This paper presents an improved beluga whale optimization (IBWO) algorithm, which is mainly used to solve global optimization problems and engineering problems. This improvement is proposed to solve the imbalance between exploration and exploitation and to solve the problem of insufficient convergence accuracy and speed of beluga whale optimization (BWO). In IBWO, we use a new group action strategy (GAS), which replaces the exploration phase in BWO. It was inspired by the group hunting behavior of beluga whales in nature. The GAS keeps individual belugas whales together, allowing them to hide together from the threat posed by their natural enemy, the tiger shark. It also enables the exchange of location information between individual belugas whales to enhance the balance between local and global lookups. On this basis, the dynamic pinhole imaging strategy (DPIS) and quadratic interpolation strategy (QIS) are added to improve the global optimization ability and search rate of IBWO and maintain diversity. In a comparison experiment, the performance of the optimization algorithm (IBWO) was tested by using CEC2017 and CEC2020 benchmark functions of different dimensions. Performance was analyzed by observing experimental data, convergence curves, and box graphs, and the results were tested using the Wilcoxon rank sum test. The results show that IBWO has good optimization performance and robustness. Finally, the applicability of IBWO to practical engineering problems is verified by five engineering problems.
The Great Lakes are critical freshwater sources, supporting millions of people, agriculture, and ecosystems. However, climate change has worsened droughts, leading to significant economic and social consequences. Accurate multi-month drought forecasting is, therefore, essential for effective water management and mitigating these impacts. This study introduces the Multivariate Standardized Lake Water Level Index (MSWI), a modified drought index that utilizes water level data collected from 1920 to 2020. Four hybrid models are developed: Support Vector Regression with Beluga whale optimization (SVR-BWO), Random Forest with Beluga whale optimization (RF-BWO), Extreme Learning Machine with Beluga whale optimization (ELM-BWO), and Regularized ELM with Beluga whale optimization (RELM-BWO). The models forecast droughts up to six months ahead for Lake Superior and Lake Michigan-Huron. The best-performing model is then selected to forecast droughts for the remaining three lakes, which have not experienced severe droughts in the past 50 years. The results show that incorporating the BWO improves the accuracy of all classical models, particularly in forecasting drought turning and critical points. Among the hybrid models, the RELM-BWO model achieves the highest level of accuracy, surpassing both classical and hybrid models by a significant margin (7.21 to 76.74%). Furthermore, Monte-Carlo simulation is employed to analyze uncertainties and ensure the reliability of the forecasts. Accordingly, the RELM-BWO model reliably forecasts droughts for all lakes, with a lead time ranging from 2 to 6 months. The study's findings offer valuable insights for policymakers, water managers, and other stakeholders to better prepare drought mitigation strategies.