Construct a quantitative-sequence initial design — magp_initial

Builds an initial design in three steps. It first generates the sequence permutations, then constructs a maximin-style Latin hypercube for the quantitative levels, and finally aligns the two fixed designs by permuting whole quantitative rows. The final alignment preserves both the Latin hypercube and every sequence permutation.

Usage

magp_initial_design(
  n,
  q,
  pair_weight = 0.2,
  sequence_space_weight = 0.8,
  quantity_weight = 0.5,
  sequence_weight = 0.5,
  p = 15L,
  sequence_maxit = 10000L,
  quantity_maxit = 10000L,
  alignment_maxit = 10000L,
  sequence_temp = 0.1,
  quantity_temp = 0.01,
  alignment_temp = 0.001,
  tmax = 10L,
  initial_sequence = NULL,
  initial_quantity = NULL,
  seed = NULL,
  sequence_method = c("sann", "random", "sfta"),
  sfta_control = list()
)

Arguments

n: Number of design runs. Must be at least two.
q: Number of components. Must be at least three.
pair_weight: Nonnegative weight for ordered adjacent-pair balance in the sequence search.
sequence_space_weight: Nonnegative weight for Hamming-distance space filling in the sequence search.
quantity_weight: Nonnegative quantitative-distance weight in the joint criterion.
sequence_weight: Nonnegative sequence-distance weight in the joint criterion.
p: Positive whole-number exponent used in all three criteria.
sequence_maxit: Positive whole number of sequence-search iterations.
quantity_maxit: Positive whole number of quantitative-search iterations.
alignment_maxit: Positive whole number of row-alignment iterations.
sequence_temp: Positive initial temperature for the sequence search.
quantity_temp: Positive initial temperature for the quantitative search.
alignment_temp: Positive initial temperature for the alignment search.
tmax: Positive whole number of evaluations at each temperature.
initial_sequence: Optional n by q matrix of sequence positions.
initial_quantity: Optional n by q Latin hypercube in [0, 1].
seed: Optional nonnegative whole-number seed. Separate deterministic seeds are used for the three stages, and the caller's random-number state is preserved.
sequence_method: Method for the sequence portion. Choose "random", "sfta" for space-filling threshold accepting, or "sann" for simulated annealing. The default is "sann" for backward compatibility.
sfta_control: Named list of SFTA settings, passed to magp_sequence_design(). Used only for sequence_method = "sfta".

Value

An object of class magp_initial_design. Its design element is an n by 2*q matrix ready to use as the input to a MAGP fitting function. The first q columns contain quantitative levels and the last q columns contain sequence positions. The component searches and their criterion values are retained for inspection.

Details

The sequence method does not change how quantitative levels are generated. With a fixed seed, all three methods use the same quantitative design before the final row-alignment step. The alignment can change its row order but not its values or Latin-hypercube structure.

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

design <- magp_initial_design(
  n = 8,
  q = 4,
  sequence_maxit = 500,
  quantity_maxit = 500,
  alignment_maxit = 500,
  seed = 1
)
design$design
#>      quantity_1 quantity_2 quantity_3 quantity_4 sequence_1 sequence_2
#> [1,]     0.3125     0.8125     0.0625     0.4375          4          1
#> [2,]     0.0625     0.1875     0.4375     0.3125          3          2
#> [3,]     0.1875     0.6875     0.6875     0.8125          1          4
#> [4,]     0.4375     0.5625     0.9375     0.0625          1          4
#> [5,]     0.5625     0.0625     0.8125     0.6875          3          1
#> [6,]     0.9375     0.9375     0.5625     0.5625          1          2
#> [7,]     0.8125     0.3125     0.3125     0.1875          4          2
#> [8,]     0.6875     0.4375     0.1875     0.9375          3          4
#>      sequence_3 sequence_4
#> [1,]          2          3
#> [2,]          1          4
#> [3,]          3          2
#> [4,]          2          3
#> [5,]          4          2
#> [6,]          4          3
#> [7,]          3          1
#> [8,]          2          1
design$criteria
#>               sequence           quantitative joint_before_alignment 
#>              0.4509175              1.5794435              0.4611254 
#>                  joint 
#>              0.4521889 

random <- magp_initial_design(
  8, 4, sequence_method = "random", seed = 1,
  quantity_maxit = 100, alignment_maxit = 100
)
sfta <- magp_initial_design(
  8, 4, sequence_method = "sfta", seed = 1, sequence_maxit = 200,
  quantity_maxit = 100, alignment_maxit = 100,
  sfta_control = list(nstarts = 2, ncalibrate = 50)
)
rbind(random = random$criteria, sfta = sfta$criteria)
#>         sequence quantitative joint_before_alignment     joint
#> random 0.4933127     1.734591              0.4814744 0.4651859
#> sfta   0.4514109     1.734591              0.4725987 0.4539948