Hyperbolic Neural Network-Based Preselection for Expensive Multiobjective Optimization

A series of surrogate-assisted evolutionary algorithms (SAEAs) have been proposed for the expensive multiobjective optimization problems (EMOPs), building cheap surrogate models to replace the expensive real function evaluations (FEs). However, the search efficiency of these SAEAs is not yet satisfactory. More efforts are needed to further exploit useful information from the real FEs in order to better guide the search process. Facing this challenge, this article proposes a hyperbolic neural network (HNN)-based preselection operator to accelerate the optimization process based on the limited evaluated solutions. First, the preselection task is modeled as a multilabel classification problem where solutions are classified into different layers (ordinal categories) through the $\epsilon $ -relaxed objective aggregation. Second, in order to resemble the hierarchical structure of candidate solutions, a HNN is applied to tackle the multilabel classification problem. The reason for using HNN is that hyperbolic spaces more closely resemble hierarchical structures than the Euclidean spaces. Moreover, to alleviate the data deficiency issue, a data augmentation strategy is employed for training the HNN. In order to evaluate its performance, the proposed HNN-based preselection operator is embedded into two SAEAs. Experimental results on the two benchmark test suites and three real-world problems with up to 11 objectives and 150 decision variables involving seven state-of-the-art algorithms demonstrate the effectiveness of the proposed method.