A Deep-Layered Water Flow Optimizer for Global Continuous Optimization Problems and Parameter Estimation of Solar Photovoltaic Models

The laminar operator in water flow optimizer (WFO) determines the direction of the population based on randomly selected individual pointing towards the current best individual. This random flow direction introduces uncertainty and may lead to local optima. In this paper, we introduce a deep-layered structure that guides the population towards global optima by exchanging information at each layer, proposing the deep-layered water flow optimizer (DWFO). This deep-layered structure not only determines the flow direction but also enriches population diversity to avoid local optima. In the experimental section, we compare DWFO with nine state-of-the-art algorithms on the IEEE Congress on Evolutionary Computation 2017 (CEC2017) benchmark functions and the CEC2011 real-world optimization problems. DWFO achieved average win rates of 83.62% and 78.28%, respectively, which thoroughly validates its superior performance and practicality. In the discussion section, we demonstrate the significance of hierarchical interactions between layers and the multi-layered structure in enhancing population diversity and balancing exploration and exploitation. We also analyze the impact of the deep-layered structure on algorithm complexity. Finally, we apply DWFO to solve the parameter estimation problem in solar photovoltaic models, providing a detailed introduction to four different types of photovoltaic models. We then conduct a comparative analysis of the parameter optimization results of DWFO and seven other state-of-the-art algorithms across six different photovoltaic models. DWFO achieved an average success rate of 83.33%, confirming its effectiveness in the photovoltaic field. This provides an advanced optimization method and practical application reference for research in the solar energy domain.