Exploratory landscape analysis on black-box optimization problems via Graph Neural Network

Most real-world optimization problems are poorly understood, some of which are black-box optimization problems (BBOPs). Exploratory landscape analysis (ELA) paves the way for algorithm design to deal with BBOPs. Existing ELA methods have limitations on unseen problems and lack analysis on the problem itself. To this end, this study introduces a novel ELA framework leveraging Graph Neural Network (GNN) upon BBOP’s surrogate model. Specifically, a neural network surrogate model is constructed whose architecture is utilized to represent BBOP in the form of graph. Then, GNN is responsible for capturing the relationships between the graph-represented BBOP and high-level features. As one of the most notable features in optimization, multimodality of multi-objective problems is to be identified for illustration. More than 99% accuracy on independent test set demonstrates the effectiveness of the proposed framework with simultaneously avoiding the effect of problem dimensions.