Pareto Optimization for Subset Selection via Steering Mutation With Theoretical Guarantee [Research Frontier]

Subset selection, which refers to the selection of a finite number of variables to optimize a given objective function, is a fundamental problem in various applications. Among the existing algorithms for solving this problem, evolutionary algorithms (EAs) based on Pareto optimization have demonstrated good performance in acquiring high-quality subsets with a theoretical guarantee. However, most existing EAs ignore the importance of variables in designing evolutionary operators (for example, mutations), which makes the search inefficient. To fill this gap, this study proposes a steering mutation-based evolutionary algorithm called SMSS for subset selection, where the importance of variables is fully utilized to ensure both the effectiveness and theoretical guarantee of the algorithm. Specifically, a novel steering mutation operator is designed in SMSS to effectively select items of high importance and discard those of low importance in the Pareto optimization process, which provides the generation of final subsets with better quality. In addition, it is proved that SMSS can attain a $(1-e^{-\gamma })$(1-e-γ)-optimal polynomial-time approximation guarantee in scenarios where the objective function exhibits monotonicity. Extensive experiments on two subset selection applications (unsupervised feature selection and sparse regression) demonstrate the superiority of the proposed algorithm over state-of-the-art algorithms.