Visualization, Clustering, and Graph Generation of Optimization Search Trajectories for Evolutionary Computation Through Topological Data Analysis: Application of the Mapper

Abstract

Topological Data Analysis (TDA) is an analytical technique that can reveal the skeletal structure inherent in complex or high-dimensional data. In this study, we considered the optimization search trajectories obtained from multiple trials of evolutionary computation as a single data set and challenged to represent the similarities and differences of each search trajectory as a topological network. Mapper is one of TDA tools and it includes the dimensionality reduction of data and clustering during graph generation. We modified Mapper to apply into this problem. The proposed framework is Mapper for evolutionary computation (EvoMapper). In the numerical experiments, multiple searches were conducted at different initial points to provide a basic review of the effectiveness of EvoMapper. The test functions were the One-max and Rastrigin function. A graph providing intuitive insights on the analysis results was constructed and visualized. In addition, the trials that reached the optimal solution and those that did not were clustered and found to have similar topology.