ModelBased OnlineOptimization
The mbminimize algorithm is a fully automatic online optimization algorithm for complex nonlinear realworld systems with nontrivial search space dimension, such as combustion engines.
The algorithm was developed in a cooperation with the BMW Group Munich in order to meet the increasing demands of the calibration of modern combustion engines. The working principle is modelbased in the sense that a global model of the objective function is maintained and improved during the optimization process. On the one hand this reduces the number of measurements, which is desirable since measuring is extremely expensive and timeconsuming. On the other hand this enables a noise filtering and thus improves the optimization results. Measuring points are determined by methods from active learning. Moreover, the algorithm incorporates highly flexible methods for limit handling, which is crucial for the optimization of combustion engines, since not all parameter combinations are drivable.
In the sequel, the highlights of the mbminimize algorithm are illustrated.
Experimental design:Before the optimization can start, a initial set of measuring points has to be determined. This is carried out by means of statistical experimental design, where both spacefilling and Doptimal criteria are taken into account. 

Model Committees and Active Learning:For the global model, heterogeneous committees of different model types are used. Employing a model committee instead of a single model normally reduces the model error. Additionally, using heterogeneous committees significantly reduces the risk of a high model bias, i.e. a totally wrong model output in spite of good fitting due to an inappropriate model type. Currently, third order polynomial models with local error correction and feedforward neural networks are used for the mbminimize algorithm. A further benefit of a model committee is the query by committee method which is a strategy for active learning. In empirical comparisons, this strategy outperforms other active learning algorithms with respect to both computation time and quality. 

Limit handling:Limit handling is a central point for a fully automatic online optimization, since not all parts of the search space are drivable and test beds for combustion engines are quite sensitive to limit violations. It is therefore important to detect, model and subsequently avoid limit violations. On the other hand the constraint models should not be too restrictive, since optima are often located near the limit. A further problem is the extremely sparse data available for limit models, in fact it is desirable to produce as few limit violations as possible and thus as few data as possible. The mbminimize algorithm contains limit models relying on regression models, classification models, and geometric models. The special technique of confidence terms allows to control the restrictiveness of the models with arbitrary precision. Moreover, stepback strategies assure that the engine is restored to a safe operation state if a limit occurs. 
Detailed description of the algorithm and the methods can be found in:
 Jan Poland: Modellgestützte und Evolutionäre Optimierungsverfahren für die Motorentwicklung,
PhD thesis, 2002, LogosVerlag, ISBN 3832500154  Kosmas Knödler: Methoden der restringierten OnlineOptimierung zur Basisapplikation moderner Verbrennungsmotoren,
PhD thesis, 2004, LogosVerlag, ISBN 3832507159
Contact
Alexander Sung, Sand 1, Raum 318, Tel. (07071) 2978979, sung at informatik.unituebingen.de