A Graph Neural Network Assisted Evolutionary Algorithm for Expensive Multi-Objective Optimization

Surrogate-assisted evolutionary algorithms (SAEAs) have emerged as a promising approach to addressing expensive and black-box problems. Most existing SAEAs leverage regression models to predict the objective values, reducing the use of true objective functions. However, these methods focus on learning the mapping from the decision space to the objective space and may fail to reveal the relationship between solutions in the decision space. Recently, graph neural networks (GNNs) have attracted increased attention due to their powerful ability to expose sample interaction. In this paper, we propose employing a graph neural network for learning embeddings of solutions in the decision space, followed by a classification task aimed at predicting dominance relationships between solutions in the objective space and a regression task for obtaining the estimated fitness values. To this end, we generate a graph at each generation to represent the topology relationship between solutions in the decision space, where nodes represent solutions, and edges are added depending on the Euclidean distances between nodes. In addition, a new acquisition function that adaptively weights the predictions on objective values and dominance relationships is proposed to effectively identify new samples. The performance of the proposed method is examined by extensive empirical studies on a widely used test suite in comparison to its peer algorithms, and the results confirm the effectiveness of the proposed method.