An improved butterfly optimization algorithm and its application in cascade hydropower generation operation

Cascade reservoir operation is an effective nonstructural countermeasure for water resources management. In recent years, many meta-heuristic algorithms are introduced to handle reservoir optimal operation due to their strong search capability and high efficiency. The butterfly optimization algorithm (BOA) is a newly developed metaheuristic method which has been widely used in solving various optimiz-ation problems. But it has local convergence and premature problems. Therefore, this paper proposed an improved version of BOA where three strategies are introduced: (1) the self-adaptive strategy to improve the initial population, (2) the dynamic switch strategy to balance exploration and exploitation, (3) the Levy-flight and standardized fragrance operators for position updating. The feasibility of the BOA, and IBOA are verified and compared with several commonly used algorithms (PSO, SCA, WOA and TSA) based on 19 test functions. Then, these methods are applied to address the optimization of cascade reservoirs that aims to maximize total hydropower generation. The results show that the proposed IBOA produces higher hydropower output and more stable results, indicating better scheduling schemes than BOA and the other four algorithms. In conclusion, IBOA is an effective and robust alternative optimization tool for cascade reservoir operation problems.