Evaluate a complete quantitative-sequence initial design

Combines Euclidean distance for the quantitative portion with Hamming distance for the sequence portion. Smaller values indicate better joint separation of the design runs.

Usage

magp_joint_criterion(
  quantity,
  sequence,
  quantity_weight = 0.5,
  sequence_weight = 0.5,
  p = 15L
)

Arguments

quantity: Numeric matrix or data frame with values in [0, 1].
sequence: Numeric matrix or data frame with the same dimensions as quantity. Every row must be a permutation of 1:q.
quantity_weight: Nonnegative weight for quantitative distance.
sequence_weight: Nonnegative weight for sequence distance.
p: Positive whole-number exponent controlling emphasis on the least separated pairs of runs.

Value

One numeric criterion value. Smaller values are preferred.

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

quantity <- cbind(
  c(0.125, 0.375, 0.625, 0.875),
  c(0.625, 0.125, 0.875, 0.375),
  c(0.375, 0.875, 0.125, 0.625),
  c(0.875, 0.625, 0.375, 0.125)
)
sequence <- rbind(
  c(1, 2, 3, 4),
  c(3, 1, 4, 2),
  c(2, 4, 1, 3),
  c(4, 3, 2, 1)
)
magp_joint_criterion(quantity, sequence)
#> [1] 0.3278273