[Paper Review] Clustering-Based Subset Selection in Evolutionary Multiobjective Optimization

Weiyu Chen, Hisao Ishibuchi+1 more|arXiv (Cornell University)|Aug 19, 2021

Advanced Multi-Objective Optimization Algorithms4 citations

TL;DR

This paper proposes a systematic evaluation of clustering-based subset selection in evolutionary multiobjective optimization (EMO), demonstrating that IGD-based subset selection is equivalent to clustering. It compares multiple clustering algorithms across diverse scenarios and shows that K-means++ and greedy IGD-based selection outperform others in terms of hypervolume and computational efficiency, while also introducing a preference-aware K-medoids variant that prioritizes knee-region solutions for decision-makers.

ABSTRACT

Subset selection is an important component in evolutionary multiobjective optimization (EMO) algorithms. Clustering, as a classic method to group similar data points together, has been used for subset selection in some fields. However, clustering-based methods have not been evaluated in the context of subset selection from solution sets obtained by EMO algorithms. In this paper, we first review some classic clustering algorithms. We also point out that another popular subset selection method, i.e., inverted generational distance (IGD)-based subset selection, can be viewed as clustering. Then, we perform a comprehensive experimental study to evaluate the performance of various clustering algorithms in different scenarios. Experimental results are analyzed in detail, and some suggestions about the use of clustering algorithms for subset selection are derived. Additionally, we demonstrate that decision maker's preference can be introduced to clustering-based subset selection.

Motivation & Objective

• To evaluate the performance of various clustering algorithms in subset selection for EMO algorithms.
• To demonstrate that IGD-based subset selection can be interpreted as a form of clustering.
• To provide practical guidelines for selecting clustering algorithms based on data set size and dimensionality.
• To extend clustering-based subset selection to incorporate decision-maker preferences, particularly for knee-region solutions.
• To identify gaps in existing clustering methods for EMO and suggest future algorithmic developments.

Proposed method

• Review and analyze classic clustering algorithms, including K-means, K-means++, K-medoids, DBSCAN, and hierarchical clustering.
• Reframe IGD-based subset selection as a clustering problem using a modified similarity measure based on the IGD+ indicator.
• Implement and compare multiple clustering-based subset selection methods on benchmark multiobjective test problems (e.g., DTLZ, MaF3, DEB2DK).
• Modify the K-medoids algorithm by replacing Euclidean distance with an IGD+-based similarity measure that emphasizes inferior objective differences.
• Use weighted average linkage in hierarchical clustering to improve efficiency for small data sets.
• Integrate decision-maker preferences by prioritizing solutions in knee regions through reweighted distance computation in medoid selection.

Experimental results

Research questions

• RQ1 How do different clustering algorithms perform in subset selection for EMO algorithms across varying data set sizes and dimensions?
• RQ2 Can IGD-based subset selection be formally interpreted as a clustering-based method?
• RQ3 Which clustering algorithm offers the best trade-off between convergence quality (hypervolume) and computational cost in low- and high-dimensional problems?
• RQ4 How can decision-maker preferences—particularly for knee-region solutions—be effectively integrated into clustering-based subset selection?
• RQ5 What are the performance trade-offs between clustering-based methods and traditional indicator-based subset selection in EMO?

Key findings

• For small data sets, hierarchical clustering with weighted average linkage achieves the best hypervolume performance in low-dimensional problems.
• In high-dimensional problems, greedy IGD-based subset selection outperforms all clustering methods in terms of hypervolume quality.
• For large data sets (e.g., from unbounded external archives), K-means++ provides the best balance of performance and efficiency in low-dimensional cases.
• In high-dimensional cases, greedy IGD-based subset selection remains the top-performing method in terms of both hypervolume and computation time.
• The modified K-medoids algorithm successfully prioritizes solutions in knee regions by using an IGD+-based similarity measure, aligning subset selection with decision-maker preferences.
• The study confirms that IGD-based subset selection is equivalent to a clustering process, providing a theoretical foundation for unifying these approaches.