Equilibrium optimizer: a comprehensive survey

Equilibrium optimizer (EO) is a recent optimization method inspired by the physical equation of the mass balance that provides the conservation of mass entering, leaving, and generating in a control volume and the system always reaches an equilibrium point. It is a fast-growing algorithm that has been adopted by several researchers due to its successful features, such as simplicity, parameter-less, derivative-free, and sound-and-complete. In this survey paper, a comprehensive analysis of EO and its evolution, since its introduction in 2020 until now, is provided. Its performance and convergence behavior are initially studied and compared against eight well-established methods using 23 mathematical optimization functions which reveals its superiority. Since EO is established to deal with a single objective and free optimization problems of the continuous domain, a comprehensive analysis of the different EO versions which are either modified versions or hybridized versions are introduced to deal with different search spaces of optimization problems. Furthermore, this research aims to provide a deep analysis of the applications of the EO algorithm, including the population type, the optimizer version used, and the main contribution. This is realized by its successful applications in different domains such as scheduling and planning, power and electrical engineering, civil and environmental engineering, communication and networking, image processing, etc. A discussion about the different EO versions and applications is provided to highlight the pros and cons of such algorithms. This discussion leads this survey to end up providing several possible research directions that can be followed in the future. Overall, this survey provides a comprehensive analysis of Equilibrium Optimizer performance and applications and contributes to the broader field of optimization algorithms.