TY - GEN

T1 - Efficient Kriging-based robust optimization of unconstrained problems

AU - Rehman, SU

AU - Langelaar, M

AU - van Keulen, F

N1 - Onder dezelfde titel in een aangepaste versie in 2014 in het tijdschrift Journal for Computational Science verschenen

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

UR - http://www.bibsonomy.org/bibtex/2ae338f2876e8c3263f7cb2940ac0ee73/dblp

M3 - Conference contribution

SN - 978-989-8565-69-3

SP - 765

EP - 773

BT - Proceedings 3rd International Conference on Simulation and Modelling Methodologies, Technologies and Applications

A2 - Oren, T

A2 - Kacprzyk, J

A2 - Leifsson, LP

A2 - et al, null

PB - SciTePress

CY - Reykjavik, Iceland

T2 - SIMULTECH 2013, Reykjavik, Iceland

Y2 - 29 July 2013 through 31 July 2013

ER -