Authors: Wenzel, Simone
Title: Sequential multi-objective target value optimization
Language (ISO): en
Abstract: In engineering processes the specification of optimization targets is usually reduced to minimization or maximization problems. The specfication of challenging multivariate target structures is excluded, due to the lack of algorithms that are able to handle them. Often however the optimum is a precise target instead of a minimum or maximum and it would be helpful if the deviation from the target could be penalized asymmetrically. In this thesis a new heuristic named mtEGO for multi-objective target value sequential optimization has been developed. A small initial spacefilling design is used to fit a surrogate model for each objective of the optimization problem. Based on the predictions and prediction errors of the surrogate model for the whole parameter space virtual observations with dfferent (1 ..ff) confidence levels are constructed. These virtual observations are used to roughly simulate the effect of the model uncertainty on the capability of each setting in the parameter space to be the global optimum. A transformation with desirability functions and the aggregation to a joint desirability index turns the multi-objective target value prob- lem in a simple single-objective maximization problem. Improvements are determined for this single-objective maximization problem then, which are maximized tofind the global optimum. mtEGO therefore works in a hybrid way, which means for each combination of (1...ff) confidence levels an own candidate for the global optimum is determined simultaneously. The candidates are reduced to a small number of updating points using hierarchical clustering. Finally, the model is refined with the observations from the updating points and the algorithm proceeds to generate and add new updating points until the stopping criterion is fulfilled. The mtEGO algorithm is validated successfully by means of extensive simulation studies and two case studies from mechanical engineering. Beside the fact that the two case studies demonstrate the applicability of mtEGO to real applications, they show that mtEGO even works successfully if basic conditions change in an ongoing optimization process. Further, an improved variant of mtEGO, named mtEGOimp, is developed. It does a pre-selection of reasonable confidence levels before cross-combining them. As a consequence, the computation time of the mtEGO approach is strongly reduced, which relaxes time limitations. The incorporation of a convex hull restriction method for failure points and an imputation of missing values into the mtEGO approach, finally extends it to a powerful tool for optimization problems even in the presence of unknown constraints.
Subject Headings: Concept of desirability
Multivariate optimization
Sequential optimization
Issue Date: 2011-11-14
Appears in Collections:Lehrstuhl Mathematische Statistik und naturwissenschaftliche Anwendungen

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