Convergence and final performances of optimization algorithms for rainfall- runoff model calibration based on the number of function calls

Abstract This study investigates the final performance and convergence behavior of 14 optimization algorithms, three of which are hybrids that combine derivative-based local search algorithms with several metaheuristics, for calibrating seven conceptual rainfall-runoff models (CRRMs) over two watersheds in Turkey. The study employs three objective functions: Nash–Sutcliffe Efficiency (NS), log-transformed NS (LNS), and Kling-Gupta Efficiency. The TOPSIS multi-criteria decision-making tool was used to rank the algorithms based on their performance across various levels of number of objective function calls (NOFCs). The study findings highlight the differential responses of optimization algorithms to NOFC variations and offer valuable insights into selecting suitable algorithms for CRRM calibration. Accordingly, as the NOFCs increased from 2500 to 10,000, differential evolution (DE) variants demonstrated remarkable adaptability, emerging as the top performers. In contrast, conventional metaheuristics struggled with improvements despite the increase in function calls, primarily due to premature convergence issues. Moreover, particle swarm optimization (PSO) variants endowed with mutation or derivative schemes performed well at lower NOFCs, but as more extensive exploration became necessary, they showed diminishing returns. The study underscores the superiority of DE variants, which include more complex mutation schemes or are derivative-based, in long-run scenarios where both computational efficiency and calibration accuracy are important.