Fuzzy Hierarchical Surrogate Assists Probabilistic Particle Swarm Optimization for expensive high dimensional problem

The meta-heuristic evolutionary algorithm is widely used because of its excellent global optimization ability. However, its demand for a mass of evaluation times will lead to an increase in time complexity. Especially when the dimensions of actual problems are too high, the time cost for fitness evaluation is usually minutes, hours, or even days. To improve the above shortcomings and the ability to solve high-dimensional expensive problems, a Fuzzy Hierarchical Surrogate Assisted Probabilistic Particle Swarm Optimization is proposed in this paper. This algorithm first uses Fuzzy Surrogate-Assisted (FSA), Local surrogate-assisted (LSA), and Global surrogate-assisted (GSA) models to fit the fitness evaluation function individually. Secondly, a probabilistic particle swarm optimization is implemented to predict the trained model and update the samples. FSA mainly uses a Fuzzy Clustering algorithm that divides the archive DataBase (DB) into multiple sub-archives to model separately to accurately estimate the function landscape of the function in the partial search space. LSA is mainly designed to capture the local details of the fitness function around the current individual neighborhood and enhance the local optimal accuracy estimation. GSA will build an accurate global model in the entire search space. To verify the performance of our proposed algorithm in solving high-dimensional expensive problems, experiments on seven benchmark functions are conducted in 30D, 50D, and 100D. The final test results show that our proposed algorithm is more competitive than other most advanced algorithms. •Use FCM to classify with the training set and construct FSA models respectively.•FSA, LSA, and GSA models are proposed for the first time to form the FHSA model.•The FHSA model is used to combine with the PPSO to solve the expensive problem.