This function constructs efficient 2-level unblocked and blocked fractional factorial designs using a beam–search–based generator selection algorithm. It evaluates candidate generators using proxy criteria (K3, K4) and returns the top-ranked designs along with generators, scores, alias structure, and blocked designs.
dol2(n, k, max_results = 20, beam_width = 3000, verbose = TRUE)A list (invisible) of the best-ranked designs. Each element contains:
generators_str: Defining contrast used for generation of design,
design: final design matrix with renamed factor labels,
score: proxy measures (K3, K4),
key: canonical key used for uniqueness.
Integer. Total number of factors (base factors + generators).
Integer. Number of dependent generator columns to add i.e. size of the fraction.
The resulting design has r = n - k base factors.
Integer. Maximum number of final best-ranked designs to return. Default is 20.
Integer. Maximum beam width used in beam search. Default is 3000.
Logical. If TRUE, prints detailed output for every
ranked design, including alias structure and blocked design. Default is TRUE.
The function automatically:
enumerates all possible generator masks,
performs canonical ordering to avoid duplicates,
evaluates designs using moment-based proxy criteria,
selects best designs based on beam search,
prints clean summaries (rank, design matrix, aliasing, blocks),
returns a structured list of final designs.
The function internally uses:
binary encoding of columns for canonical keys,
moment-based proxies K3 and K4,
mask enumeration for generator creation,
alias structure detection for main and 2-factor effects,
automatic block generator selection (2-level).
The generated output provides experimenters with statistically efficient two-level fractional factorial designs that are well suited for both industrial and agricultural research. By reducing the total number of experimental runs while preserving the ability to estimate key main effects and low-order interactions, these designs offer a resource-efficient framework for screening factors, optimizing processes, and evaluating system performance under practical field or laboratory constraints.
Dash, S., Parsad, R. and Gupta, V. K. (2013). Row–column Designs for 2^n factorial 2-Colour Microarray Experiments for Estimation of Main Effects and Two-Factor Interactions with Orthogonal Parameterization. *Agricultural Research*, 2(2), 172–182.
National Bureau of Standards (1957). *Fractional Factorial Experiment Designs for Factors at Two Levels*. Applied Mathematics Series 48. US Government Printing Office, Washington DC.
# \donttest{
# Generate 2-level fractional factorial designs:
res <- dol2(n = 5, k = 2, max_results = 5, beam_width = 3000, verbose = TRUE)
# Access first ranked design
res[[1]]$design
res[[1]]$generators_str
# }
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