Optimal exact designs of experiments via Mixed Integer Nonlinear Programming

  • Belmiro P. M. DuarteEmail author
  • José F. O. Granjo
  • Weng Kee Wong


Optimal exact designs are problematic to find and study because there is no unified theory for determining them and studying their properties. Each has its own challenges and when a method exists to confirm the design optimality, it is invariably applicable to the particular problem only. We propose a systematic approach to construct optimal exact designs by incorporating the Cholesky decomposition of the Fisher Information Matrix in a Mixed Integer Nonlinear Programming formulation. As examples, we apply the methodology to find D- and A-optimal exact designs for linear and nonlinear models using global or local optimizers. Our examples include design problems with constraints on the locations or the number of replicates at the optimal design points.


Model-based optimal designs Exact designs Constrained designs Mixed Integer Nonlinear Programming Global Optimization 

Mathematics Subject Classification

62K05 90C47 



The research of Wong is partially supported by a grant from the National Institute of General Medical Sciences of the National Institutes of Health under Award Number R01GM107639. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health. The authors acknowledge two anonymous reviewers that contributed undoubtedly to improve the quality of the paper.

Supplementary material

11222_2019_9867_MOESM1_ESM.pdf (108 kb)
Supplementary material 1 (pdf 107 KB)


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Authors and Affiliations

  1. 1.Department of Chemical and Biological Engineering, Instituto Politécnico de CoimbraInstituto Superior de Engenharia de CoimbraCoimbraPortugal
  2. 2.Department of Chemical Engineering, CIEPQPFUniversity of CoimbraCoimbraPortugal
  3. 3.Department of Biostatistics, Fielding School of Public HealthUCLALos AngelesUSA

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