A Kriging Metamodel Assisted Multi-Objective Genetic Algorithm for Design Optimization

Abstract

The high computational cost of population based optimization methods, such as multi-objective genetic algorithms (MOGAs), has been preventing applications of these methods to realistic engineering design problems. The main challenge is to devise methods that can significantly reduce the number of simulation (objective∕constraint functions) calls. We present a new multi-objective design optimization approach in which the Kriging-based metamodeling is embedded within a MOGA. The proposed approach is called Kriging assisted MOGA, or K-MOGA. The key difference between K-MOGA and a conventional MOGA is that in K-MOGA some of the design points are evaluated on-line using Kriging metamodeling instead of the actual simulation model. The decision as to whether the simulation or its Kriging metamodel should be used for evaluating a design point is based on a simple and objective criterion. It is determined whether by using the objective∕constraint functions’ Kriging metamodels for a design point, its “domination status” in the current generation can be changed. Seven numerical and engineering examples with different degrees of difficulty are used to illustrate applicability of the proposed K-MOGA. The results show that on the average K-MOGA converges to the Pareto frontier with an approximately 50% fewer number of simulation calls compared to a conventional MOGA.