Title: An improved Harris Hawks Optimisation for the Optimal Scheduling of Cascade Pumping Stations

Authors: Xiaolian Liu; Xiaopeng Hou; Yu Zhai; Xiamin Ma; Xueni Wang; Leike Zhang; Yu Tian; Can Ding

Addresses: College of Water Resource Science and Engineering, Taiyuan University of Technology, Taiyuan, 030024, China; Shanxi Key Laboratory of Cooperative Utilization for Basin Water Resources, Taiyuan, 030024, China ' College of Civil Engineering and Architecture, Zhejiang University, Hangzhou, 310058, China ' College of Water Resource Science and Engineering, Taiyuan University of Technology, Taiyuan, 030024, China; Shanxi Key Laboratory of Cooperative Utilization for Basin Water Resources, Taiyuan, 030024, China ' School of Hydraulic Engineering, Wanjiang University of Technology, Maanshan, 243031, China ' College of Water Resource Science and Engineering, Taiyuan University of Technology, Taiyuan, 030024, China; Shanxi Key Laboratory of Cooperative Utilization for Basin Water Resources, Taiyuan, 030024, China ' College of Water Resource Science and Engineering, Taiyuan University of Technology, Taiyuan, 030024, China; Shanxi Key Laboratory of Cooperative Utilization for Basin Water Resources, Taiyuan, 030024, China ' State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, China Institute of Water Resources and Hydropower Research, Beijing, 100038, China ' Water and Environmental Engineering, Department of Built Environment, Aalto University, 00076, Aalto, Finland

Abstract: For water-conveyance projects with cascade pumping stations (CPSs), ensuring stable and efficient operation is of paramount importance. This study develops an optimal scheduling model for CPSs, integrated with a one-dimensional hydraulic model, and proposes an optimisation dispatching approach based on an enhanced Harris hawks optimisation (TFHHO). To address HHO's limitations in terms of initial population diversity and exploration, the Tent chaotic map is employed to enhance the quality and distribution of initial solutions, while a starvation rate F is introduced to escape local optima and boost global optimisation. Tests on 23 benchmark functions, TFHHO achieves 15 optimal solutions, confirming its significant superiority over PSO, GA and HHO. Applied to a CPS in Beijing, TFHHO-based optimisation schemes achieve annual operational cost reductions of $5,897 (19.4 m³/s) and $12,640 (20.0 m³/s), outperforming schemes employing PSO, GA and HHO. Thus, TFHHO algorithm provides an effective methodology for the optimal scheduling problem in CPSs.

Keywords: improved Harris hawks algorithm; cascade pumping stations; CPSs; economical operation; tent mapping; the rate of starvation.

DOI: 10.1504/IJHM.2026.152977

International Journal of Hydromechatronics, 2026 Vol.9 No.1, pp.91 - 127

Received: 15 Apr 2025
Accepted: 26 Aug 2025
Published online: 17 Apr 2026 *

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