Software for Optimal Design

by the experimental design group from Comenius University

R library OptimalDesign

• The library OptimalDesign enables the user to easily compute D-, A-, I-, and c-efficient designs of experiments including:
  • optimal approximate and exact designs with or without replications,
  • optimal designs at standard or restricted design spaces,
  • optimal designs under various kinds of simultaneous constraints, ...
• The library is free, including the free academic license for the few functions that require the commercial gurobi solver; see our gurobi installation guide. (Note that most of the computational procedures in the library OptimalDesign are open source and do not require the gurobi solver.)
• Many of the implemented algorithms have been developed by the authors of OptimalDesign themselves and substantially outperform competing methods and/or allow for solving more complex design problems.
• See a brief introduction including mathematical specifications.
• OptimalDesign can also be used to compute the solutions to some related optimization problems such as minimum-volume data-enclosing ellipsoids and t-optimal graphs.
• The package is actively maintained, continually tested and improved by the authors. See the list of known bugs and suggestions for improvement.
• We will be happy to help you with any technical or theoretical problem, or with any question related to the computation of experimental designs.

Computer source codes accompanying our academic papers

• Harman R, Rosa S (2023): Mixed-integer linear programming for computing optimal experimental designs, submitted (see the arXiv preprint for a preliminary version).
  • An R implementation of the MILP for computing optimal exact designs
  • An R implementation of the GEX algorithm used with the MILP approach in Section 5.2
  • Numerical examples
• Harman R, Filová L, Rosa S (2021): Optimal Design of Multifactor Experiments via Grid Exploration, Statistics and Computing, Volume 31, 70 (see the arXiv preprint for a preliminary version).
  • The R script to produce the GEX results of Table 4
  • The R script to produce Figure 2
• Filová L, Harman R (2020): Ascent with Quadratic Assistance for the Construction of Exact Experimental Designs, Computational Statistics, Volume 35, pp. 775–801 DOI, rdcu (pre-print: arXiv)
  • The R scripts of the numerical study (Section 6)
  • The R functions from a new version of OptimalDesign needed to perform the AQuA study
• Harman R, Filová L, Richtárik P (2020): A Randomized Exchange Algorithm for Computing Optimal Approximate Designs of Experiments, Journal of the American Statistical Association, Volume 115, pp. 348-361 DOI (pre-print: arXiv)
  • od-REX-D.r (od-REX-D.txt): The original R version as used in the manuscript
  • od-REX-A.r (od-REX-A.txt): The original R version as used in the manuscript
  • Simple commented example of using REX
  • The currently fastest R version of REX for D-optimality
  • The currently fastest R version of REX for A- and I-optimality
  • R Shiny application for computing D-, A- and I-optimal approximate designs with REX
  • R Shiny application for computing minimum volume enclosing ellipsoids with REX
• Harman R, Benková E (2017): Barycentric algorithm for computing D-optimal size- and cost-constrained designs of experiments, Metrika, Volume 80, pp. 201–225 DOI, rdcu
  • barycost.m (barycost.txt) for Matlab: Compute D-optimal approximate size-and-cost constrained designs of experiments.
• Harman R, Bachratá A, Filová L (2016): Construction of efficient experimental designs under multiple resource constraints, Applied Stochastic Models in Business and Industry, Volume 32, pp. 3-17 DOI, arXiv (older version)
  • Hugo.m (Hugo.txt) for Matlab: Compute efficient exact designs of experiments under general linear resource constraints.
  • Malab examples from the manuscript: Example1b.m (Example1b.txt), Example2.m (Example2.txt), Example3.m (Example3.txt).
  • HugoR.r (HugoR.txt) for R: Compute exact designs of experiments under the standard (size) constraint on the number of trials.
  • R example from the manuscript: Example1a.r (Example1a.txt).
• Benková E, Harman R, Müller WG (2016): Privacy sets for constrained space-filling, Journal of Statistical Planning and Inference, Volume 171, pp. 1–9 DOI
  • Henry.m for Matlab - Experimental design optimization for "bridge" constraints and the D-optimality criterion
• Harman R, Filová L (2014): Computing efficient exact designs of experiments using integer quadratic programming, Computational Statistics & Data Analysis, Volume 71, pp. 1159–1167 DOI
  • DQ_gurobi.m (DQ_gurobi.txt) for Matlab, using the Gurobi solver: Compute exact DQ-optimal designs of experiments under general linear constraints on the design weights.
  • DQ_cplex.m (DQ_cplex.txt) for Matlab, using the Cplex solver: Compute exact DQ-optimal designs of experiments under general linear constraints on the design weights.

Contact

• E-mail: harman[at]fmph.uniba.sk


• Address:
  Department of Applied Mathematics and Statistics
  Faculty of Mathematics, Physics and Informatics
  Comenius University
  Mlynská dolina
  842 48 Bratislava 4
  Slovak Republic