Parallel binary arithmetic optimization algorithm and its application for feature selection

Arithmetic Optimization Algorithm (AOA) has simple structure, few parameters and is easy to implement. It utilizes the distribution behavior of the main arithmetic operators in mathematics. The Multiplication and Division operators are used for exploration, while the Subtraction and Addition are used for exploitation. In this manuscript, the AOA algorithm was converted into binary form with the Multiplication Mathematical Optimizer Operator (MOO) redesigned for better exploration. Then, four families of transfer functions are used in the binary AOA (BAOA). Moreover, in order to further improve the performance, the parallel mechanism is introduced to the BAOA and proposed the Parallel Binary AOA (PBAOA) algorithm. The proposed algorithms are applied for feature selection problem on 10 low-dimensional and 10 high-dimensional datasets from UCI and scikit-feature repository. The results show that the proposed BAOA and PBAOA algorithms are superior to the classical and state-of-the-art algorithms. The Z-shaped transfer functions are more suitable for the proposed algorithms on low-dimensional datasets, while the V-shaped transfer functions are more suitable for high-dimensional datasets. Moreover, no matter what transfer function is used, the parallel mechanism is effective for BAOA.