Multi-objective design optimisation using multiple adaptive spatially distributed surrogates

This paper introduces an evolutionary algorithm with Multiple Adaptive Spatially Distributed Surrogates (MASDS) for multi-objective optimisation. The core optimisation algorithm is a canonical evolutionary algorithm. The solutions are evaluated using the actual analysis periodically every few generations and evaluated using surrogate models in between. An external archive of the unique solutions evaluated using actual analysis is maintained to train the surrogate models. The solutions in the archive are split into multiple partitions using k-means clustering. A surrogate model based on the Radial Basis Function (RBF) network is built for each partition and its prediction accuracy is computed using a validation set. A surrogate model for a partition is only considered valid if its prediction error is below a user-defined threshold. The performance of a new candidate solution is predicted using a valid surrogate model with the least prediction error in the neighbourhood of that point. The results of six multi-objective test problems are presented in this study, along with a welded beam design optimisation problem. A detailed comparison of the results obtained using Nondominated Sorting Genetic Algorithm II (NSGA-II), the Single Surrogate (SS) model, the Multiple Spatially Distributed Surrogate (MSDS) model and finally, the MASDS model, is presented to highlight the benefits offered by the approach.