A novel metamodel-based multi-objective optimization method using adaptive multi-regional ensemble of metamodels

The optimization of the engineering system is becoming more and more significant as time progresses, and a large number of metamodel-based multi-objective optimization methods have been proposed during the past decades. For a metamodel-based multi-objective optimization method, the accuracy of the solution is greatly influenced by the prediction accuracy of the metamodels. This study developed a novel metamodel-based multi-objective optimization method using an adaptive multi-regional ensemble of metamodels (AMEM) to get an optimization method with higher accuracy and efficiency. Two strategies were employed in this new metamodel-based multi-objective optimization method. One strategy is that several stand-alone metamodels, i.e., polynomial regression (PR), radial basis function (RBF), and Kriging (KRG) were combined into an ensemble of metamodels (EM) using the weight sum approach. The other strategy is that new design points were dynamically added into various local regions where the Pareto optimal designs are located, and each basis model and its weight factors were regenerated simultaneously, which adaptively improved the accuracy of the constructed adaptive multi-regional ensemble of metamodels. Besides, two novel approaches for selecting new design points from Pareto optimal set were proposed in this study. The performance of this novel metamodel-based multi-objective optimization method was evaluated using twelve mathematical functions and two practical engineering optimization problems. The twelve mathematical functions were typically selected from previous studies, and the two practical engineering optimization problems are crashworthiness optimization of triply periodic minimal surface (TPMS)-filled tube (one design variable) and buffer performance optimization of airbags used in the re-entry capsule (two design variables). To compare the advantages of this method, the optimization of these problems was also implemented by common metamodel-based methods. The results showed that the adaptive multi-regional ensemble of metamodels-based multi-objective optimization method is more accurate than the common methods in both mathematical functions and engineering optimization problems. In addition, the adaptive multi-regional ensemble of metamodels-based multi-objective optimization method has better efficiency than the common method, especially in practical engineering optimization problems.