Abstract
Past decades have witnessed a rapid development in research on multi- and many-objective evolutionary optimization. Reference-based and preference-based strategies are both widely used in dealing with the multi- and many-objective optimization problems. However, little effort has been devoted to a critical analysis of similarities and differences between the two approaches.This paper revisits the methodologies, compares the similarities and differences, and discusses the limitations of reference-based and preference-based many-objective evolutionary algorithms. Our analyses reveal that preference information may be embedded into reference-based methods in dealing with irregular problems so that the objective space can be better explored and a solution set of interest to the user will be obtained. Meanwhile, it is far from trivial for a decision-maker to provide informed preferences without sufficient a priori knowledge of the problem in the preference-based optimization. Therefore, this paper suggests a new approach to many-objective optimization problems that integrates preference-based and reference-based methodologies, where the solutions of natural interest such as the knee regions are identified at first and then the acquired knowledge of the knee regions can be used in reference-based methods. This way, accurate, diverse and preferred solutions can be obtained, and a deeper insight into the problem can be gained.