In this study, we have compared six state-of-the-art Multiobjective Evolutionary Algorithms (MOEAs) designed specifically for many-objective optimization problems under a number of carefully crafted benchmark problems. Using the performance metrics ensemble, we aim at providing a comprehensive measure and more importantly revealing insight pertaining to specific problem characteristics that the underlying MOEA could perform the best. The experimental results confirm the finding from the No Free Lunch theorem: any algorithm's elevated performance over one class of problems is exactly paid for in loss over another class. In addition, the experimental results show that the performance of MOEA to solve many-objective optimization problems depends on two distinct aspects: the ability of MOEA to tackle the specific characteristics of the problem and the ability of MOEA to handle high-dimensional objective space.
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