A new hybrid Lévy Quantum-behavior Butterfly Optimization Algorithm and its application in NL5 Muskingum model

This paper presents a novel hybrid algorithm that combines the Butterfly Optimization Algorithm (BOA) and Quantum-behavior Particle Swarm Optimization (QPSO) algorithms, leveraging $gbest$ to establish an algorithm communication channel for cooperation. Initially, the population is split into two equal subgroups optimized by BOA and QPSO respectively, with the latter incorporating the Lévy flight for enhanced performance. Subsequently, a hybrid mechanism comprising a weight hybrid mechanism, a elite strategy, and a diversification mechanism is introduced to blend the two algorithms. Experimental evaluation on 12 benchmark test functions and the Muskin model demonstrates that the synergy between BOA and QPSO significantly enhances algorithm performance. The hybrid mechanism further boosts algorithm performance, positioning the new algorithm as a high-performance method. In the Muskingum model experiment, the algorithm proposed in this article can give the best sum of the square of deviation (SSQ) and is superior in the comparison of other indicators. Overall, through benchmark test function experiments and Muskin model evaluations, it is evident that the algorithm proposed in this paper exhibits strong optimization capabilities and is effective in addressing practical problems.