Efficient Kriging-based robust optimization of unconstrained problems

Keywords: Robust optimization, Expected Improvement, Worst-case design, Implementation error, Efficient Global Optimization. Abstract: In this paper, we use Kriging and expected improvement to apply robust optimization on unconstrained problems affected by implementation error. A two-stage process is employed, where, at the first stage, a response surface of the nominal function is fitted using a design of experiments strategy such as Latin hypercube sampling (LHS). Based on this response surface, in each iteration, we construct a worst-case cost metamodel by finding the maximum realizable value of the objective with respect to the uncertainty set on the nominal metamodel. We use the total Kriging error estimate of the two metamodels to find an appropriate expected improvement criterion for robust optimization. A new sample is added at each iteration by finding the location at which this modified expected improvement measure is maximum. By means of this process, we iteratively move towards the robust optimum. We test the efficiency and convergence of the algorithm by performing hundred runs of the considered test problem for different initial sampling. These results show that the algorithm converges to the robust optimum consistently.