Surrogate Assisted Evolutionary Algorithm for Multiobjective Optimization

Abstract

Multidisciplinary design optimization (MDO) typically requires assessment of numerous designs, each of which involves computationally expensive analyses (computational fluid dynamics (CFD), finite element based methods (FEM), computational electromagnetics (CEM) etc.). Apart from using multiple processors, one way to contain the computational time of a MDO problem is to use cheaper approximations (surrogates) in lieu of the actual analyses during the course of optimization. A major problem in using surrogates within an evolutionary algorithm lies with its representation accuracy and the problem is far more acute for multiobjective (MO) problems where both the proximity to the Pareto front and the diversity of the solutions along the nondominated front are equally important. In this paper, we introduce a surrogate assisted evolutionary algorithm for multiobjective optimization that relies on a surrogate model based on Radial Basis Function (RBF) network. The optimization algorithm performs K generations based on actual function evaluations followed by S generations based on the surrogate model and is referred as K-S model. The accuracy of the surrogate model is maintained via periodic retraining and the number of data points required to create the surrogate model is identified by a k-means clustering algorithm. We compare the performance of our algorithm with and without surrogates on a number of standard MO test cases and engineering design examples.