A Comparative Visual Analytics Framework for Evaluating Evolutionary Processes in Multi-objective Optimization

TL;DR

This work presents a modular visual analytics framework for comparative analysis of evolutionary multi-objective optimization (EMO) algorithms, shifting focus from final solution sets to intermediate evolutionary processes. It combines a similarity-driven preprocessing stage with an interactive, multi-view interface that captures algorithm-level, evolution-level, and solution-level insights, employing tools such as Wasserstein distance, DTW, kNN graphs, Kamada-Kawai layouts, and HCSDAN clustering. The approach is validated through case studies on the DTLZ3 and DDMOP2 problems and enriched by expert interviews, demonstrating the framework’s ability to reveal convergence patterns, inter-algorithm relationships, and solution-set distributions beyond traditional metrics like IGD and HV. The work advances explainable, multi-faceted EMO analysis with practical implications for benchmarking, algorithm design, and real-world decision support, while outlining scalability considerations and directions for extending to many-objective problems and uncertainty visualization.

Abstract

Evolutionary multi-objective optimization (EMO) algorithms have been demonstrated to be effective in solving multi-criteria decision-making problems. In real-world applications, analysts often employ several algorithms concurrently and compare their solution sets to gain insight into the characteristics of different algorithms and explore a broader range of feasible solutions. However, EMO algorithms are typically treated as black boxes, leading to difficulties in performing detailed analysis and comparisons between the internal evolutionary processes. Inspired by the successful application of visual analytics tools in explainable AI, we argue that interactive visualization can significantly enhance the comparative analysis between multiple EMO algorithms. In this paper, we present a visual analytics framework that enables the exploration and comparison of evolutionary processes in EMO algorithms. Guided by a literature review and expert interviews, the proposed framework addresses various analytical tasks and establishes a multi-faceted visualization design to support the comparative analysis of intermediate generations in the evolution as well as solution sets. We demonstrate the effectiveness of our framework through case studies on benchmarking and real-world multi-objective optimization problems to elucidate how analysts can leverage our framework to inspect and compare diverse algorithms.

Figures (6)

• Figure 1: (A) Examples of the objective space for two and three-objective problems. (B) An illustration of typical evolutionary algorithm pipelines.
• Figure 2: An overview of our visual analytics framework.
• Figure 3: The data preprocessing stage. (A) An optional down-sampling stage to reduce the number of generations. (B) Four quality measures are calculated for each generation. (C) Generation similarity and (D) Algorithm similarity are measured between individual generations or the entire evolutionary processes.
• Figure 4: The visual design of (A) the generation similarity view and (B) the scatterplot in the solution set view.
• Figure 5: The DTLZ3 problem. (A) The algorithm-level similarity analysis. (B) Comparative analysis between t-DEA and other three algorithms.