Lévy Arithmetic Algorithm: An enhanced metaheuristic algorithm and its application to engineering optimization

Lévy Arithmetic Algorithm is an upgraded metaheuristic optimization approach proposed to enhance the Arithmetic Optimization Algorithm using the Lévy random step. Arithmetic Optimization Algorithm addresses diverse optimization problems by employing arithmetic operators. However, its linear search capability might hinder attaining optimal solutions, which leads to stagnation. In this study, the Lévy Arithmetic Algorithm is introduced by combining the Arithmetic Optimization Algorithm and the Lévy random step to enhance search capabilities and minimize computational demands for improved outcomes. The evaluation encompassed ten CEC2019 benchmark functions, four established real-world engineering problems, and the Economic Load Dispatch of microgrids with renewable energy integration. Using evaluation metrics such as standard deviation and mean, along with hypothesis tests, the study conducts a thorough comparison between the performance of the proposed algorithm and that of the conventional Arithmetic Optimization Algorithm. The results show that the Lévy Arithmetic Algorithm achieves optimization with a minimized number of evaluations in terms of standard deviation and mean, compared to the Arithmetic Optimization Algorithm. Additionally, the proposed method was compared with various well-known and recent metaheuristics algorithms, and the Lévy Arithmetic Algorithm consistently demonstrates superior performance, especially in contrast to the Arithmetic Optimization Algorithm.