Optimization: Three Tools and Two Applications
Event details
| Date | 19.09.2014 |
| Hour | 10:15 |
| Speaker | Eric Walter |
| Location | |
| Category | Conferences - Seminars |
The three tools alluded to in the title are (i) Kriging, (ii) Efficient Global Optimization and (iii) a relaxation procedure for continuous minimax optimization.
In its simplest version, Kriging is a method for building surrogate models that interpolate multivariate results. Kriging comes from mining and geostatistics, where it appeared around the middle of the last century. It is increasingly being used in industrial statistics. One of its developers was Georges Matheron, at the Ecole des mines de Paris, who called it krigeage in tribute to the seminal role of D.G. Krige, in South Africa.
Efficient global optimization (EGO) is a method based on Kriging for minimizing cost functions that are so expensive to evaluate that the budget for such evaluations is severely limited. One of the developers of EGO was Don Jones, at General Motors.
Shimizu and Aiyoshi’s procedure for continuous minimax optimization (published a long time ago in the IEEE Transactions in Automatic Control) makes it possible to find approximate worst-case solutions even when the performance index can only be evaluated numerically. J. Marzat, H. Piet-Lahanier and myself have shown how it can be combined with EGO to get approximate worst-case solutions in cases where the performance index is very costly to evaluate.
A natural application of the first two tools is the identification/estimation of the parameters of a complex knowledge-based model, which will be very briefly presented on a toy example. The robust tuning of the hyperparameters of a fault detection and isolation algorithm on a realistic aerospace test case via the use of the three tools will be presented in some more detail.
In its simplest version, Kriging is a method for building surrogate models that interpolate multivariate results. Kriging comes from mining and geostatistics, where it appeared around the middle of the last century. It is increasingly being used in industrial statistics. One of its developers was Georges Matheron, at the Ecole des mines de Paris, who called it krigeage in tribute to the seminal role of D.G. Krige, in South Africa.
Efficient global optimization (EGO) is a method based on Kriging for minimizing cost functions that are so expensive to evaluate that the budget for such evaluations is severely limited. One of the developers of EGO was Don Jones, at General Motors.
Shimizu and Aiyoshi’s procedure for continuous minimax optimization (published a long time ago in the IEEE Transactions in Automatic Control) makes it possible to find approximate worst-case solutions even when the performance index can only be evaluated numerically. J. Marzat, H. Piet-Lahanier and myself have shown how it can be combined with EGO to get approximate worst-case solutions in cases where the performance index is very costly to evaluate.
A natural application of the first two tools is the identification/estimation of the parameters of a complex knowledge-based model, which will be very briefly presented on a toy example. The robust tuning of the hyperparameters of a fault detection and isolation algorithm on a realistic aerospace test case via the use of the three tools will be presented in some more detail.
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