Joint optimization of multiple responses based on loss functions
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Date
2011-03-02
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Abstract
Most of the existing methods for the analysis and optimization of multiple
responses require some kind of weighting of these responses, for instance in
terms of cost or desirability. Particularly at the design stage, such information
is hardly available or will rather be subjective. Kuhnt and Erdbrugge
(2004) present an alternative strategy using loss functions and a penalty
matrix which can be decomposed into a standardizing (data-driven) and a
weight matrix. The effect of different weight matrices is displayed in joint
optimization plots in terms of predicted means and variances of the response
variables. In this article, we propose how to choose weight matrices for two
and more responses. Furthermore we prove the Pareto optimality of every
point that minimizes the conditional mean of the loss function.
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Keywords
Different weight matrix, Loss function, Multiple response, Pareto optimality, Penalty matrix