Evaluate a sequence initial design

Measures two properties of a sequence design: how evenly ordered adjacent component pairs are represented and how well separated the design rows are under Hamming distance. Smaller values indicate a better design.

Usage

magp_sequence_criterion(
  sequence,
  pair_weight = 0.2,
  space_weight = 0.8,
  p = 15L
)

Arguments

sequence

Numeric matrix or data frame. Every row must be a permutation of 1:q.

pair_weight

Nonnegative weight for ordered adjacent-pair balance.

space_weight

Nonnegative weight for Hamming-distance space filling.

p

Positive whole-number exponent controlling emphasis on the weakest pair counts and the smallest distances.

Value

One numeric criterion value. Smaller values are preferred.

Details

Each row uses the same sequence format as the fitting functions. The value in column j is the position assigned to component j, and every row must be a permutation of 1:q.

References

Xiao, Q., Wang, Y., Mandal, A., and Deng, X. (2024). Modeling and Active Learning for Experiments with Quantitative-Sequence Factors. Journal of the American Statistical Association. doi:10.1080/01621459.2022.2123335 .

Examples

sequence <- rbind(
  c(1, 2, 3, 4),
  c(3, 1, 4, 2),
  c(2, 4, 1, 3),
  c(4, 3, 2, 1)
)
magp_sequence_criterion(sequence)
#> [1] 0.5300508