A fuzzy transfer function based on the behavior of meta-heuristic algorithm and its application for high-dimensional feature selection problems

Abstract

Many discrete optimization problems are in the class of NP-hard problems; therefore, exact algorithms cannot achieve an optimum solution in reasonable time. Approximate algorithms like binary meta-heuristic algorithms have provided good results in these problems. Since many meta-heuristic algorithms have been introduced for continuous search spaces, employing a transfer function is one of the simplest methods to map the search space to the binary one. Many transfer functions have been introduced, divided in atomic and compound transfer functions. In the atomic transfer functions, a single function is applied in the algorithm, such as S-shaped, U-shaped, V-shaped, Z-shaped and so on. Compound transfer functions employ more than one atomic transfer function in their structures, such as Mirrored Time-Varying S-shaped, χ-shaped, and Upgrade transfer functions. An improper transfer function decreases the algorithm's performance in the binary search space. Hence, several transfer functions are usually evaluated for solving a binary problem to select the best one. In this study, a fuzzy transfer function is proposed and applied in Binary Particle Swarm Optimization (FBPSO). The behavior of PSO is analyzed, and the fuzzy transfer function and its rules create a new binary position. The performance of atomic and compound transfer functions employed in BPSO and some recently introduced binary meta-heuristic algorithms are compared with FBPSO in high-dimensional feature selection problems. The experimental results show that FBPSO achieves the best solution in terms of minimum error and feature selection rate compared with other comparative algorithms.