Improvement Strategies for Visualizing Solution Sets in Many-Objective Optimization Problems

Abstract

In real-world multi-objective optimization, dealing with many objectives and a large number of solutions is a common challenge that complicates data visualization and analysis. This study aims to simplify decision-making by analyzing tools to better explore Pareto optimal solutions in many-objective scenarios, integrating clustering, filtering, and ranking with existing graphics techniques. The dynamic combination of these tools should reduce complexity and highlight significant patterns in the data set, allowing decision-makers to tailor the visualization to their specific needs and preferences. Central to the approach presented in this work is the innovative application of shape-based clustering to organize the solution set and the use of this clustering to define distinct types of filters. Additionally, ranking methods originally proposed to enhance search in many-objective evolutionary algorithms are used here to identify the best solutions based on predefined criteria in combination with other techniques. The efficacy of the proposed integrated approach was evaluated using an application developed with this aim and considering a five-objective problem as a case study. The analysis suggests that using these combined strategies aids interactive visual exploration, effectively reducing solution volume and improving data understanding, potentially facilitating decision-making tasks.

Keywords

• Multi-objective optimization
• many-objective optimization
• data visualization
• shape-based clustering
• decision-making
• filtering methods