Khan Noor Habib, Wang Yong, Jamal Raheela, Ebeed Mohamed, Kamel Salah, Ali Guma, Jurado Francisco, Youssef Abdel-Raheem
College of Mechanical and Electrical Engineering, Qingdao Binhai University, Shandong Sheng, 266540, China.
Department of New Energy, North China Electric Power University, Beijing, 102206, China.
Sci Rep. 2025 Apr 2;15(1):11283. doi: 10.1038/s41598-025-86881-4.
The quadratic interpolation optimization (QIO) introduces a novel approach inspired by the generalized quadratic interpolation (GQI) with dual mechanisms. Initially, QIO employs GQI in its exploration strategy, updating populations based on two randomly selected individuals. Subsequently, it incorporates another exploration strategy, updating populations based on the best solution and two randomly selected individuals. Despite QIO's effectiveness in numerous optimization tasks, it exhibits limitations when addressing highly nonlinear and multidimensional problems, such as stagnation, susceptibility to local optima, low diversity, and premature convergence. In this study, we propose three enhancement strategies to refine traditional QIO, aiming to bolster its exploration and exploitation capabilities through Weibull flight motion, chaotic mutation, and PDO mechanisms. The resultant improved QIO (IQIO) is then applied to solve the short-term hydrothermal scheduling (STHS) problem, considering system uncertainties and the potential installation of PV and wind turbine generation units to reduce fuel costs and emissions. The STHS is solved with considering the system constraints including water discharge and reservoir storage, the generated powers by the hydro and thermal units as well as balanced powers. The dependent constraints are handled using weighted summation method. The efficacy of the proposed IQIO is demonstrated using the CEC 2022 test suite, and the obtained results are benchmarked against various competitive optimization methods. Statistical analysis of the results confirms a notable enhancement in the original QIO's performance upon applying the suggested IQIO. Furthermore, the inclusion of renewable generation units by IQIO yields maximum reductions of 23.73% in costs and 45.50% in emissions, underscoring its potential for sustainable energy management.
二次插值优化（QIO）引入了一种受具有双重机制的广义二次插值（GQI）启发的新颖方法。最初，QIO在其探索策略中采用GQI，基于两个随机选择的个体更新种群。随后，它纳入了另一种探索策略，基于最优解和两个随机选择的个体更新种群。尽管QIO在众多优化任务中有效，但在处理高度非线性和多维问题时存在局限性，如停滞、易陷入局部最优、多样性低和早熟收敛。在本研究中，我们提出了三种增强策略来改进传统的QIO，旨在通过威布尔飞行运动、混沌变异和PDO机制增强其探索和利用能力。然后将所得的改进QIO（IQIO）应用于解决短期水火电调度（STHS）问题，考虑系统不确定性以及光伏和风力发电机组的潜在安装，以降低燃料成本和排放。在考虑包括排水和水库蓄水、水火电机组发电量以及平衡功率等系统约束的情况下求解STHS。使用加权求和法处理相关约束。使用CEC 2022测试套件证明了所提出的IQIO的有效性，并将获得的结果与各种竞争性优化方法进行了基准比较。结果的统计分析证实，应用建议的IQIO后，原始QIO的性能有显著提高。此外，IQIO纳入可再生发电单元可使成本最大降低23.73%，排放最大降低45.50%，突出了其在可持续能源管理方面的潜力。
