Knee-Based Decision Making and Visualization in Many-Objective Optimization

As an essential component in multi- and many-objective optimization, decision-making process either selects a subset of solutions from the whole Pareto front or guides the search toward a small part of the Pareto front during the evolutionary process. In recent years, for many-objective optimization problems (MaOPs), a number of evolutionary algorithms have been developed to search for Pareto optimal solutions. However, there is a lack of research works focusing on designing decision-making approaches. In order to overcome this deficiency, we propose a novel knee-based decision-making method to search for several solutions of interest (SOIs) from a large number of solutions on the Pareto front, each of which contains the best convergence performance at least within its neighborhood and can be identified as a global or local knee solution. The optimization performance achieved by all SOIs approximates the performance of the whole Pareto front as much as possible. Furthermore, in order to relieve the difficulties in the decision-making process on MaOPs, a new visualization approach is developed based on this proposed decision-making approach. It provides information about the shape and location of the Pareto front, the possible bulge, as well as the convergence degree and distribution of solutions. The experimental results on several benchmark functions demonstrate the superiority of the proposed design in the selection of SOIs and visualization of high-dimensional objective space.

Automated summary

A novel knee-based decision-making method is proposed to search for solutions of interest from a large number of solutions on the Pareto front, ensuring the performance of these solutions approximates as much as possible the whole Pareto front. Additionally, a new visualization approach is developed to provide information about the shape, location, possible bulge, convergence degree, and distribution of solutions on MaOPs.