Tabu search for a partial principal balance on grouped parts

Finds a single grouped balance by tabu search over a partition of selected parts. The search is carried out on groups of parts defined by lI, using configurable neighbourhood moves.

partial_pb_tabu_search(
  X,
  lI = NULL,
  min_parts = 2,
  max_parts = NULL,
  iter = 100,
  tabu_size = length(lI),
  ini = NULL,
  remove_active = TRUE,
  add_left = TRUE,
  add_right = TRUE,
  flip_side = FALSE,
  swap_zero = FALSE,
  swap_sides = FALSE,
  debug = FALSE,
  constrained.criterion = "variance"
)

Arguments

X

A numeric matrix with strictly positive finite entries. Rows are observations and columns are compositional parts.

lI

A list defining a partition of a subset of the columns of X. If NULL, each column of X is used as a singleton group.

min_parts

Integer. Minimum number of active groups.

max_parts

Integer or NULL. Maximum number of groups from lI allowed to be active in the balance. If NULL, all groups may be active.

iter

Integer. Maximum number of tabu search iterations.

tabu_size

Integer. Maximum size of the tabu list.

ini

Initial grouped split. If NULL, the constrained principal balance of the grouped subcomposition is used.

remove_active

Logical. Allow moves from -1 or +1 to 0.

add_left

Logical. Allow moves from 0 to -1.

add_right

Logical. Allow moves from 0 to +1.

flip_side

Logical. Allow direct moves from -1 to +1 and from +1 to -1.

swap_zero

Logical. Allow swaps between one active group and one inactive group, preserving the active side.

swap_sides

Logical. Allow swaps between one left group and one right group.

debug

Logical. If TRUE, progress information is printed during the search.

constrained.criterion

Criterion used to initialise the constrained balance when ini = NULL. Either "variance" (default) or "angle".

Value

A list with the selected balance, its variance criterion, the search path, and a neighbourhoods element recording the active neighbourhood types.

Details

When ini = NULL, the constrained grouped balance is adjusted greedily so that the initial solution has exactly max_parts active groups.