A novel approach to minimum attribute reduction based on quantum-inspired self-adaptive cooperative co-evolution

Attribute reduction in rough set theory is an important feature selection method. However it has been proven as an NP-hard problem to find minimum attribute reduction. It is therefore necessary to investigate efficient heuristic algorithms to find near-optimal solutions. In this paper, a novel and efficient minimum attribute reduction algorithm based on quantum-inspired self-adaptive cooperative co-evolution incorporated into shuffled frog leaping algorithm is proposed. First, evolutionary frog individuals are represented by multi-state quantum bits, and self-adaptive quantum rotation angle and quantum mutation probability strategy are adopted to update the operation of quantum revolving door. Second, a self-adaptive cooperative co-evolutionary model for minimum attribute reduction is designed to divide the evolutionary attribute sets into reasonable subsets. The subsets are assigned the self-adaptive mechanism according to their historical performance records, and each of them is evolved by the quantum-inspired shuffled frog leaping algorithm. So the reasonable decompositions are more easily produced by exploiting any correlation and interdependency between attribute subsets interaction. Finally, global convergence of the proposed algorithm is proved in theory, and its performance is investigated on some global optimization functions, UCI datasets and magnetic resonance images (MRIs), compared with existing state-of-the-art algorithms. The results demonstrate that the proposed algorithm can achieve a higher performance on the convergence rate and stability of attribute reduction. So it can be considered as a more competitive heuristic algorithm on the efficiency and accuracy of minimum attribute reduction.