A gradient-descent-like learning-based framework in surrogate-assisted evolutionary algorithms for expensive many-objective optimization

Surrogate-assisted evolutionary algorithms (SAEAs) commonly depend on traditional offspring generation methods such as simulated binary crossover and polynomial mutation, which often lead to suboptimal search efficiencies. This paper introduces the gradient-descent-like learning-based SAEA (GDL-SAEA) designed for expensive multiobjective optimization problems. Our method aims to determine the learned possibly fastest convergence (i.e., gradient-descent-like) direction for each solution via a trained neural network, leveraging prior knowledge from the relationships within the current population and surrogate model. The population is segmented into three subgroups, generating triple training data through cosine similarity and the Mahalanobis distance. Notably, each elite solution within these groups serves as a label for the corresponding poor solution with a midpoint acting as an anchor, thereby enhancing the supervised learning of the convergence process. To implement the proposed framework, three representative SAEAs are embedded into the GDL-SAEA. Experimental evaluations on multiobjective benchmarks and real-world problems with up to 10 objectives reveal that GDL-SAEA outperforms seven state-of-the-art and classic algorithms.