Background. Multi-cloud environments present complex challenges in optimal resource allocation and provider selection. Previous research has established a comprehensive ontological model and evaluation criteria for distributed data storage, however efficient provider selection remains a significant challenge due to the dynamic nature of cloud services and the multitude of interdependent factors affecting performance and cost-effectiveness. Objective. The purpose of the paper is to develop and validate a sophisticated optimization function for cloud provider selection in multi-cloud environments, incorporating both Reinforcement Learning (RL) and Multi-Objective Evolutionary Algorithms (MOEAs) to address the complexity of provider selection while considering multiple competing objectives and constraints. Methods. The research employs an ontological approach to formalize domain concepts, relationships, and properties in multi-cloud environments. Additionally, an optimization function is developed incorporating multiple weighted criteria derived from the established ontological model. The study focuses on the implementation of the RL algorithm to adapt to dynamic changes in cloud provider characteristics and integration of MOEAs to handle multiple competing objectives as well as providing a comparative analysis with traditional selection methods and alternative optimization approaches for multi-cloud storage settings. Results. The proposed ontological model successfully formalizes the domain's concepts, relationships, and properties in multi-cloud environments. The optimization function demonstrates effectiveness in selecting the most suitable public cloud provider based on the proposed features, enhancing data management practices automation and decision-making processes. Conclusions. The developed optimization function and suggested methodology significantly advance the state-of-the-art in distributed multi-cloud data storage. The integration of RL and MOEAs provides a robust framework for addressing the complexity of multi-cloud environments while offering superior performance compared to existing approaches. The methodology successfully balances multiple objectives while adapting to dynamic changes in cloud provider characteristics.