Data-Driven Analysis of Pareto Set Topology
This addresses a major concern for EMO researchers and practitioners by enabling topology analysis without prior knowledge of the true Pareto set, though it is incremental as it builds on existing theoretical insights.
The paper tackles the problem of determining when evolutionary multi-objective optimization algorithms can cover the entire Pareto set by analyzing its topology, presenting a data-driven method that correctly recognizes high-dimensional Pareto set topologies as topological simplices with reasonable population sizes.
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.