Grid Classification-Based Surrogate-Assisted Particle Swarm Optimization for Expensive Multiobjective Optimization

Surrogate-assisted evolutionary algorithms (SAE-As), mainly including regression-based SAEAs and classification-based SAEAs, are promising for solving expensive multi-objective optimization problems (EMOPs). Regression-based SAEAs usually use complex regression models to approximate the fitness evaluation, which will suffer from high training costs to obtain a fine-accuracy surrogate. In contrast, classification-based SAEAs can achieve solution selection via coarse binary relations predicted by classifiers, thus avoiding high requirements in prediction accuracy and training costs. However, most of the binary relations in existing classification-based SAEAs mainly only involve convergence comparison whereas diversity maintenance is neglected. Considering the capacity of the grid technique in maintaining both convergence and diversity, we propose a new classification method called grid classification to discretize the objective space into grids and train a lightweight grid classification-based surrogate (GCS), for which low training costs are needed. The GCS can evaluate the solution performance in terms of both convergence and diversity simultaneously according to the predicted grid locations, which opens up a new field for follow-up research on classification-based SAEAs. Following this, a GCS-assisted particle swarm optimization algorithm is proposed for tackling EMOPs. Experimental results on widely-used benchmark problems (including high-dimensional EMOPs) and a 222-high-dimensional real-world application problem show its competitiveness in terms of both optimization performance and computational cost.