In many-objective optimization, visualization of population in the high- dimensional objective space provides a critical understanding of the Pareto front. First, visualization throughout the evolutionary process can be exploited in developing effective many-objective evolutionary algorithms. Furthermore, visualization is a crucial component of multi-criteria decision making. By directly observing the performance of each solution, the trade-off between objectives, and distribution of the approximate front, the decision maker can easily decide which solution should be chosen from. In this paper, we make a detailed summary for existing visualization approaches and group them into five different categories. Then, three evaluation criteria for visualization approaches are designed, according to which, five state-of-the-arts are compared under the created data sets. Experimental results show that all approaches can satisfy each criterion to some degree but no one can fully achieve all of these criteria. There is a need to develop the new approach emphasis on fully satisfy all criteria simultaneously. Then, based on the comparison results, two future research directions for visualization approach are proposed.
