# Data-Driven Analysis of Pareto Set Topology

arXiv: https://arxiv.org/abs/1804.07179 · HTML: https://mlsanity.com/paper/1804.07179/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Apr 2018.

## Built on by (most cited first, 1 of 1)

- [On Characterizing the Evolution of Embedding Space of Neural Networks using Algebraic Topology](https://mlsanity.com/paper/2311.04592/) (2023)

## Abstract (arXiv)

When and why can evolutionary multi-objective optimization (EMO) algorithms cover the entire Pareto set? That is a major concern for EMO researchers and practitioners. A recent theoretical study revealed that (roughly speaking) if the Pareto set forms a topological simplex (a curved line, a curved triangle, a curved tetrahedron, etc.), then decomposition-based EMO algorithms can cover the entire Pareto set. Usually, we cannot know the true Pareto set and have to estimate its topology by using the population of EMO algorithms during or after the runtime. This paper presents a data-driven approach to analyze the topology of the Pareto set. We give a theory of how to recognize the topology of the Pareto set from data and implement an algorithm to judge whether the true Pareto set may form a topological simplex or not. Numerical experiments show that the proposed method correctly recognizes the topology of high-dimensional Pareto sets within reasonable population size.