Objective Reduction in Many-Objective Optimization: Evolutionary Multiobjective Approaches and Comprehensive Analysis

Many-objective optimization problems bring great difficulties to the existing multiobjective evolutionary algorithms, in terms of selection operators, computational cost, visualization of the high-dimensional tradeoff front, and so on. Objective reduction can alleviate such difficulties by removing the redundant objectives in the original objective set, which has become one of the most important techniques in many-objective optimization. In this paper, we suggest to view objective reduction as a multiobjective search problem and introduce three multiobjective formulations of the problem, where the first two formulations are both based on preservation of the dominance structure and the third one utilizes the correlation between objectives. For each multiobjective formulation, a multiobjective objective reduction algorithm is proposed by employing the nondominated sorting genetic algorithm II to generate a Pareto front of nondominated objective subsets that can offer decision support to the user. Moreover, we conduct a comprehensive analysis of two major categories of objective reduction approaches based on several theorems, with the aim of revealing their strengths and limitations. Lastly, the performance of the proposed multiobjective algorithms is studied extensively on various benchmark problems and two real-world problems. Numerical results and comparisons are then shown to highlight the effectiveness and superiority of the proposed multiobjective algorithms over existing state-of-the-art approaches in the related field.