A MULTI-OBJECTIVE SEQUENTIAL OPTIMIZATION METHOD BASED ON CLUSTERING-PARTITIONED ENSEMBLE OF METAMODELS

For the expensive multi-objective optimization problem with explicit constraints, this paper proposes a multi-objective sequential optimization method based on clustering-partitioned ensemble of metamodels (CPEM) called MOSOM-CPEM. The constrained domain optimal Latin hypercube design (CDOLHD) is introduced in MOSOM-CPEM, which enables it to obtain sample points in feasible domains with complex boundary shapes. A key challenge in utilizing ensembles of metamodels with multiple regional optimized weight factors (EM-MROWF) lies in the unequal distribution of sample points across non-rectangular domains, often resulting in a dearth of samples in certain regions and subsequently compromising the predictive accuracy of the metamodel ensemble within those areas. To mitigate this limitation, the CPEM incorporates a feasible domain division method grounded in K-means clustering, complemented by a matching boundary smoothing technique. This dual strategy ensures a more balanced and effective distribution of sample points across the entire domain, thereby enhancing the overall fitting accuracy of the model. To validate the efficacy of CPEM, its fitting accuracy is rigorously compared against several established metamodels, including the polynomial response surface (PRS), radial basis function (RBF), kriging (KRG) model, and two types of ensemble of metamodels, namely GOEL and ACAR. The results show that the fitting accuracy of CPEM is better than the compared metamodels, confirming the effectiveness of the proposed feasible domain division method. Furthermore, the performance of MOSOM-CPEM is benchmarked against other metamodel-based optimization techniques within the context of six constrained multi-objective optimization problems featured in the CEC2021 competition. The findings reveal that, when employing an identical number of sample points, the Pareto fronts yielded by MOSOM-CPEM exhibit superior convergence and distribution characteristics. MOSOM-CPEM is applied to the optimization problem of the waist rope structure of the extra-long truss boom of crawler cranes, and the results confirm its superiority, indicating that MOSOM-CPEM has high value for engineering applications.