Efficient Feature Selection with Multiple Equivalent Subsets Using a Multi-objective Quantum-inspired Evolutionary Approach

Abstract

Abstract In many real-world applications, it is useful to identify multiple distinct feature subsets that achieve the same classification accuracy with the same number of features. This gives domain experts more flexibility to choose feature combinations based on cost, availability, or application-specific requirements. However, finding several equally good feature subsets is a challenging task. Multimodal multi-objective optimization algorithms are well suited for this purpose, but many existing methods converge too early, fail to preserve multiple promising solutions, and do not explore the feature space effectively, which often leads to suboptimal results. In this paper, a novel multimodal multi-objective quantum-inspired Whale Optimization Algorithm for feature selection, called MMQFS, is proposed. The method includes a new convergence strategy that modifies the shrinking phase using randomly selected neighboring whales. To improve diversity, a modified crowding distance based on Hamming distance is adopted. In addition, a new environmental selection mechanism is introduced to allow lower-ranked solutions to survive into the next generations, which helps enhance multimodality. A new evaluation measure, Meas_Mod, is also proposed to assess the quality and extent of modality in the obtained solutions. The performance of MMQFS is evaluated against 10 state-of-the-art multi-objective algorithms on 25 diverse datasets using four existing performance measures together with Meas_Mod. The experimental results show that MMQFS performs strongly in terms of estimated Pareto-front coverage, convergence, and modality. The statistical tests further confirm the effectiveness of the proposed algorithm.