function to optimize the phi_p value of an array by level permutation

takes an n x m array and returns an n x m array with improved phi_p value (if possible)

phi_optimize(
  D,
  noptim.rounds = 1,
  noptim.repeats = 1,
  dmethod = "manhattan",
  p = 50
)

Arguments

D

numeric matrix or data.frame with numeric columns, n x m. A symmetric array (e.g. an OA) with nl levels for each columns. Levels must be coded as 0 to nl - 1 or as 1 to nl. levels from

noptim.rounds

number of rounds in the Weng algorithm

noptim.repeats

number of independent repeats of the Weng algorithm

dmethod

distance method for phi_p, "manhattan" (default) or "euclidean"

p

p for phi_p (the larger, the closer to maximin distance)

Value

an n x m matrix

Details

The function uses the algorithm proposed by Weng (2014) for SOA optimization:

It starts with a random permutation of column levels.

Initially, individual columns are randomly permuted (m permuted matrices, called one-neighbours), and the best permutation w.r.t. the phi_p value (manhattan distance) is is made the current optimum. This continues, until the current optimum is not improved by a set of randomly drawn one-neighbours.
Subsequently, pairs of columns are randomly permuted (choose(m,2) permuted matrices, called two-neighbours). If the current optimum can be improved or the number of optimization rounds has not yet been exhausted, a new round with one-neighbours is started with the current optimum. Otherwise, the current optimum is returned, or an independent repeat is initiated (if requested).

Limited experience suggests that an increase of noptim.rounds from the default 1 is often helpful, whereas an increase of noptim.repeats did not yield as much improvement.

References

For full detail, see SOAs-package.

Weng (2014)

Author

Ulrike Groemping

Examples

oa <- lhs::createBoseBush(8,16)
print(phi_p(oa, dmethod="manhattan"))
#> [1] 0.04838463
oa_optimized <- phi_optimize(oa)
print(phi_p(oa_optimized, dmethod="manhattan"))
#> [1] 0.04149836