A Hybrid Feature Selection Method Using an Improved Binary Butterfly Optimization Algorithm and Adaptive β–Hill Climbing

The Butterfly Optimization Algorithm (BOA) is a recently proposed nature-inspired metaheuristic algorithm mimicking the food-foraging behavior of butterflies. Its abilities include simplicity, good convergence rate towards local optima, and avoiding the local optima stagnation problem to some extent. In earlier studies, the performance of Binary BOA (BBOA) is shown to be superior to various state-of-the-art methods in different optimization issues, such as search space reduction and solving classical engineering problems. Here, BBOA expands the original search space with all possibilities (Exploration) and seeks to determine the best one from all the produced solutions (Exploitation). Generally, the global performance of BBOA depends on the tradeoff between the Exploration and Exploitation phase and hence, produces quality solutions when a suitable tradeoff is maintained. This study introduces an improved and computationally effective variant of conventional BBOA by improving the local search ability of the Butterfly Optimization Algorithm. Initially, twelve binary variants were produced using three different transfer functions (S, U, V-shaped), and solution quality is evaluated in terms of respective fitness function scores. Next, we explored the local search ability of BOA by another recently developed optimization technique, namely, Adaptive
$\beta -$
Hill Climbing, to compute quality solutions. This optimization process employed two stochastic operators:
$N$
-operator (Neighborhood operator) and
$\beta $
-operator (Mutation operator) to generate improved offspring compared to parent solutions. This phase is iteratively implemented until the desired level of binary pattern with suitable classification accuracy is obtained. We validated the proposed approach on twenty datasets with eleven state-of-the-art feature selection algorithms. The overall results suggest that the proposed improvements increase the classification accuracy with fewer features on most datasets. In addition, the proposed approach’s time complexity was significantly reduced on eighteenth out of twenty datasets. Moreover, the proposed method effectively balances space exploration and solution exploitation in feature selection problems.