An Improved Equilibrium Optimizer for Solving Optimal Power Flow Problem

Recent Developments in Equilibrium Optimizer Algorithm: Its Variants and Applications

There have been many algorithms created and introduced in the literature inspired by various events observable in nature, such as evolutionary phenomena, the actions of social creatures or agents, broad principles based on physical processes, the nature of chemical reactions, human behavior, superiority, and intelligence, intelligent behavior of plants, numerical techniques and mathematics programming procedure and its orientation. Nature-inspired metaheuristic algorithms have dominated the scientific literature and have become a widely used computing paradigm over the past two decades. Equilibrium Optimizer, popularly known as EO, is a population-based, nature-inspired meta-heuristics that belongs to the class of Physics based optimization algorithms, enthused by dynamic source and sink models with a physics foundation that are used to make educated guesses about equilibrium states. EO has achieved massive recognition, and there are quite a few changes made to existing EOs. This article gives a thorough review of EO and its variations. We started with 175 research articles published by several major publishers. Additionally, we discuss the strengths and weaknesses of the algorithms to help researchers find the variant that best suits their needs. The core optimization problems from numerous application areas using EO are also covered in the study, including image classification, scheduling problems, and many others. Lastly, this work recommends a few potential areas for EO research in the future.

Development and application of equilibrium optimizer for optimal power flow calculation of power system

This paper proposes an enhanced version of Equilibrium Optimizer (EO) called (EEO) for solving global optimization and the optimal power flow (OPF) problems. The proposed EEO algorithm includes a new performance reinforcement strategy with the Lévy Flight mechanism. The algorithm addresses the shortcomings of the original Equilibrium Optimizer (EO) and aims to provide better solutions (than those provided by EO) to global optimization problems, especially OPF problems. The proposed EEO efficiency was confirmed by comparing its results on the ten functions of the CEC'20 test suite, to those of other algorithms, including high-performance algorithms, i.e., CMA-ES, IMODE, AGSK and LSHADE_cnEpSin. Moreover, the statistical significance of these results was validated by the Wilcoxon's rank-sum test. After that, the proposed EEO was applied to solve the the OPF problem. The OPF is formulated as a nonlinear optimization problem with conflicting objectives and subjected to both equality and inequality constraints. The performance of this technique is deliberated and evaluated on the standard IEEE 30-bus test system for different objectives. The obtained results of the proposed EEO algorithm is compared to the original EO algorithm and those obtained using other techniques mentioned in the literature. These Simulation results revealed that the proposed algorithm provides better optimized solutions than 20 published methods and results as well as the original EO algorithm. The EEO superiority was demonstrated through six different cases, that involved the minimization of different objectives: fuel cost, fuel cost with valve-point loading effect, emission, total active power losses, voltage deviation, and voltage instability. Also, the comparison results indicate that EEO algorithm can provide a robust, high-quality feasible solutions for different OPF problems.