Algorithms for computing optimal designs of experiments under constraints
Eva Benková
PhD thesis advisor:
Radoslav Harman
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PhD thesis - Full text 
Abstract:
In this dissertation thesis, we study several problems of finding the optimal experimental design under various design constraints. First, we introduce a multiplicative algorithm for constructing D-optimal approximate size- and cost-constrained designs, that
is, designs restricted on the number of trials and, simultaneously, on the total cost of the experiment. The proposed method is a non-trivial specification of the “barycentric” algorithm introduced in [31], which includes also reducing the design space by removal of unnecessary design points. We analytically prove its convergence and demonstrate its performance in comparison to the competing methods. A different type of linearly constrained designs are space-filling designs frequently
used in computer experiments. We propose a general exchange-type heuristic framework for computing exact designs, which is based on the notion of “privacy sets” and can be adapted for various space-filling restrictions. Our specification of the framework for the
so-called Bridge designs significantly outperforms the state-of-the-art method. Moreover, we implemented the general framework for the so-called Minimum-distance designs by the use of Voronoi diagrams and their generalizations - power diagrams. We explain the role of these diagrams in constructing efficient Minimum-distance designs by deriving some crucial theoretical properties. Performance of the heuristic for both kinds of constraints is compared against competing algorithms in numerical studies.
References
[1] Eva Benková, Radoslav Harman: Barycentric algorithm for computing D-optimal size- and cost-constrained designs of experiments, Metrika 80(2017), pp. 201-225.
[2] Eva Benková, Radoslav Harman, Werner G. Müller: Privacy sets for constrained space-filling, Journal of Statistical Planning and Inference 171(2016), pp. 1-9.
[3] Werner G. Müller, Eva Benková, Radoslav Harman: Discussion of "Space-filling designs for computer experiments: A review", Quality Engineering 28(2016), pp. 36-38.