multi-objective optimization problem

Self-adaptive software systems can operate continuously despite uncertainties. Control-theoretic adaptation approaches, which construct a mathematical model of the system, provide guarantees for the satisfaction of the self-adaptive system requirements, but systems undergoing frequent changes in their behavior can't use these approaches due to continuous re-identification. Therefore, researchers present adaptation approaches that combine control theory with artificial intelligence or machine learning. The adaptation solution in these approaches does not rely on the mathematical model of the system, but it does not consider the priorities of the goals, and how to provide guarantees for the goals of the self-adaptive system is not determined. This paper proposes a multi-objective data-driven adaptation method for software systems and presents a formal analysis of the guarantee of satisfying the self-adaptive system requirements. The adaptation mechanism in the method relies on the input and output data of the system and determines an adaptation decision by solving a multi-objective optimization problem. The self-adaptive software system based on the data-driven adaptation method can deal with uncertainties in the execution environment, requirements, and system parameters, and it also supports goal transformation at runtime. Two cases in different domains evaluate the data-driven adaptation method. It is also compared with one of the model-based control-theoretic adaptation approaches and a data-driven adaptation method without goal transformation. The results confirm that the requirements of the self-adaptive software system based on the proposed adaptation method are satisfied despite uncertainties.