A New Visualization for Many-Objective Optimization

The visualization of the approximations in high-dimensional space is a critical issue in many-objective optimization. As a popular visualization method, the parallel coordinates plots (PCPs) have been widely used in displaying the high-dimensional approximations. However, it is not as straightforward as the classic scatter plot for well-presenting the information contained in an approximation. One observation for PCPs is that their presented information changes when the axes order changes. In this paper, we propose a kernel-based visualization (KBV) method for many-objective optimization, in terms of comparing the quality of approximations, understanding the distribution of a solution set, and reflecting the relationship between different objectives. In KBV, the kernel feature map is combined with a re-order method for improving the effectiveness of the PCPs and providing more insightful information among different objectives, which is clearly beneficial for decision makers. The experimental analysis of KBV is also given in this paper. Finally, we introduce KBV to visualize the approximation on water resource problem (WRP).