Awesome Design of Experiments (DOE)

Adapted from Navarro-Brul et al., React. Chem. Eng., 2022

The Design of Experiments is the theory of conceiving the optimal set of trials for model-testing experimentation. DOE packages may have 4 different capabilities:

1. Generation of the design, e.g., generating factorial designs, latin hypercube, etc., upon the user request
2. Analysis of the design, e.g., the ability of comparing the sampling optimality of different designs for the model hypothesis, evaluating the aliasing of factors, etc.
3. Analysis of the response, e.g., the ability of testing the model and fitting the coefficients. Most of open-source DOE packages lack this ability, relying on well-established statistic packages such as statsmodels and scikit-learn.
4. Design augmentation, which is the typical pipeline of Active Learning (or Bayesian Optimization), using the response of the early trials to suggest a new set of trials that are a promising compromise between exploitation and exploration toward an optimum goal.

In the following we list a number of open-source packages, that focus on the generation and the analisys of designs.

Don't hesitate to open an issue to report any package (with a reasonable users base) that is missing from this list

pyDOE - GitHub, Docs

A collection of "classical" design of experiments.

We refer to a fork called pyDOE2, which is just adding the GSD method (i.e., a 3+levels fractional factorial) to pyDOE.

• Factorial Designs
  • General Full-Factorial (fullfact)
  • 2-level Full-Factorial (ff2n)
  • 2-level Fractional Factorial (fracfact)
  • Plackett-Burman (pbdesign)
  • Generalized Subset Designs (gsd)
• Response-Surface Designs
  • Box-Behnken (bbdesign)
  • Central-Composite (ccdesign)
• Randomized Designs
  • Latin-Hypercube (lhs)

DOEPY - GitHub, Docs

Another collection of "classical" design of experiments.

• Full factorial: build.full_fact()
• 2-level fractional factorial: build.frac_fact_res()
• Plackett-Burman: build.plackett_burman()
• Sukharev grid: build.sukharev()
• Box-Behnken: build.box_behnken()
• Box-Wilson (Central-composite)
  • with center-faced option: build.central_composite() with face='ccf' option
  • with center-inscribed option: build.central_composite() with face='cci' option
  • with center-circumscribed option: build.central_composite() with face='ccc' option
• Latin hypercube (simple): build.lhs()
• Latin hypercube (space-filling): build.space_filling_lhs()
• Random k-means cluster: build.random_k_means()
• Maximin reconstruction: build.maximin()
• Halton sequence based: build.halton()
• Uniform random matrix: build.uniform_random()

dexpy - GitHub, Docs

Yet another collection of "classical" design of experiments.

• Fractional Factorial: build_factorial(factor_count, run_count)
• Full Factorial: build_full_factorial(factor_count)
• Central Composite: build_ccd(factor_count, alpha='rotatable', center_points=1)
• Mixture Simplex Lattice: build_simplex_lattice(factor_count, model_order=<ModelOrder.quadratic: 2>)
• Mixture Simplex Centroid: build_simplex_centroid(factor_count)
• Optimal Designs: build_optimal(factor_count, **kwargs)

Analysis of the design:

• Statistical Power: f_power(model, design, effect_size, alpha)
• Alias list: alias_list(model, design)

diversipy - GitHub, Docs

Collection of algorithms for uniform sampling, and related topics.

• cube - Uniform sampling from the unit hypercube
  • cube.stratify_conventional: stratification of the unit hypercube
  • stratify_generalized: generalized stratification of the unit hypercube
  • cube.latin_design: generate a random latin hypercube design matrix
  • cube.improved_latin_design: generate an ‘improved’ latin hypercube design matrix
  • cube.rank1_design: design matrix for a rank-1 lattice
  • cube.sample_halton: generate a Halton point set
  • cube.sample_maximin: maximize the minimal distance in the unit hypercube with extensions
  • cube.sample_k_means: in its default setup, this algorithm converges to a centroidal Voronoi tesselation of the unit hypercube
  • cube.grid: create conventional grid in the unit hypercube
• simplex - Uniform sampling on the unit simplex
• polytope - Uniform sampling from convex polytopes
• subset - Select diverse subsets
  • subset.psa_partition: partition the data set into the given number of clusters with the part-and-select algorithm
  • subset.psa_select: select representatives points with the part-and-select algorithm
  • subset.select_greedy_maximin: greedily select a subset according to maximin criterion
  • subset.select_greedy_maxisum: greedily select a subset according to maxisum criterion.

Analysis of the design:

• indicator.solow_polasky_diversity: Solow-Polasky diversity
• indicator.weitzman_diversity: Weitzman diversity
• indicator.sum_of_dists: square root of the sum of all pairwise distances
• indicator.average_inverse_dist: average inverse distance
• indicator.separation_dist: minimal pairwise distance
• indicator.wmh_index: quality index of Wahl, Mercadier, and Helbert
• indicator.sum_of_nn_dists: sum of nearest-neighbor distances
• indicator.unanchored_L2_discrepancy: unanchored L2 discrepancy

Definitive Screening Design - GitHub

Implementation of the DSD in python: a small design aimed to screen all factors for second order models.

• dsd.generate(n_num, n_cat, factors_dict=None, method='dsd', min_13=True, n_fake_factors=0)

Analysis of the design:

• dsd.analysis.get_map_of_correlations(X, effects)

pyLHD - GitHub, Docs, WebApp

Package focused on the Latin Hypercube Design (LHD), to generate and analyze several variants of this design.

• Classical latin hypercube: pyLHD.LatinHypercube(size, seed, scramble)

Analysis of the design:

Average Absolute Correlation, Maximum Absolute Correlation, Maximum Projection Criterion (Joseph 2015), Coverage measure, Inter-site Distance, Discrepancy, MaxiMin, Mesh Ratio, Phi_p Criterion.

BoFire - GitHub, Docs

BoFire is a Bayesian Optimization Framework Intended for Real Experiments. It contains nice features to generate a DoE when starting from scratch.

• D-, A-, G-, E-, K- optimization in a constrained design space
• Space filling in a constrained design space

Analysis of the design:

• bofire.utils.doe.get_confounding_matrix()

OApackage - GitHub, Docs

The Orthogonal Array package contains functionality to generate and analyse orthogonal arrays, optimal designs and conference designs.

• Generate (oapackage.arraydata_t()) and extend (oapackage.extend_array()) orthogonal arrays
• Conference designs (oapackage.conference_t())
• D-Efficient optimized design (oapackage.Doptimize())

Analysis of the design:

• D-, Ds-, A-, E- efficiency of the design (.Defficiency(), .DsEfficiency(), .Aefficiency(), .Eefficiency())