ENBIS-8 in Athens

21 – 25 September 2008 Abstract submission: 14 March – 11 August 2008

Multivariate Expected Improvement Using Two-Sided Desirabilities

22 September 2008, 14:40 – 15:00


Submitted by
Simone Wenzel
Simone Wenzel and Joachim Kunert
Technical University of Dortmund, Germany
Efficient global optimization has become a widely used technique in engineering applications, especially in automotive and aerospace industry. In 1998 Schonlau, Welch and Jones introduced an efficient global optimization algorithm (EGO). Based on a small initial design a surrogate model is fitted and updated sequentially to find the global optimum. Updating points are obtained balancing the exploitation of the model information (which area is optimal) with the need of exploration where the uncertainty is high, i.e. the point with the largest expected improvement. Since 1998, many variations of the expected improvement criterion have been published adapting the EGO-algorithm for noisy or multi-objective problems. We consider a multivariate situation, where quality is measured by several variables. A common practice for such multi-objective problems is to transform the multivariate data into a univariate desirability index. However, the distribution of the desirability index and hence the calculation of an expected improvement is not easy. Some results on the distribution exist for one-sided desirabilities, but not for the two-sided cases. A full Monte Carlo Simulation is not feasible, because we need the expected improvement for every possible design point. Hence, a Monte Carlo Simulation would lead to too many simulations and be too time consuming. We therefore propose to get only a rough impression by calculating the improvement for only a small number of virtual observations at each design points. These observations are chosen using the mean and the variances of the surrogate model.
The usability of the approach is demonstrated with a multi-objective optimization problem from mechanical engineering.
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