Skip to contents

Automatic Zoning Procedure (AZP)

Source: R/region_azp.R
azp.Rd

Performs regionalization using the Automatic Zoning Procedure algorithm. AZP uses local search to minimize within-region heterogeneity while maintaining spatial contiguity. Three variants are available: basic (greedy), tabu search, and simulated annealing.

Usage

azp(
  data,
  attrs = NULL,
  n_regions,
  weights = "queen",
  bridge_islands = FALSE,
  method = c("tabu", "basic", "sa"),
  max_iterations = 100L,
  tabu_length = 10L,
  cooling_rate = 0.99,
  initial_temperature = 0,
  scale = TRUE,
  seed = NULL,
  verbose = FALSE
)

Arguments

data

An sf object with polygon or point geometries.

attrs

Character vector of column names to use for clustering (e.g., c("var1", "var2")). If NULL, uses all numeric columns.

n_regions

Integer. Number of regions (clusters) to create.

weights

Spatial weights specification. Can be:

  • "queen" (default): Polygons sharing any boundary point are neighbors

  • "rook": Polygons sharing an edge are neighbors

  • An nb object from spdep or created with sp_weights()

  • A list for other weight types: list(type = "knn", k = 6) for k-nearest neighbors, or list(type = "distance", d = 5000) for distance-based weights

bridge_islands

Logical. If TRUE, automatically connect disconnected components (e.g., islands) using nearest-neighbor edges. If FALSE (default), the function will error when the spatial weights graph is disconnected.

method

Character. Optimization method: "basic" (greedy local search), "tabu" (tabu search), or "sa" (simulated annealing). Default is "tabu".

max_iterations

Integer. Maximum number of iterations (default 100).

tabu_length

Integer. Length of tabu list for tabu method (default 10).

cooling_rate

Numeric. Cooling rate for SA method, between 0 and 1 (default 0.99).

initial_temperature

Numeric. Initial temperature for SA method. If 0 (default), automatically set based on initial objective.

scale

Logical. If TRUE (default), standardize attributes before clustering.

seed

Optional integer for reproducibility.

verbose

Logical. Print progress messages.

Value

An sf object with a .region column containing cluster assignments. Metadata is stored in the "spopt" attribute, including:

  • algorithm: "azp"

  • method: The optimization method used

  • n_regions: Number of regions created

  • objective: Total within-region sum of squared deviations

  • solve_time: Time to solve in seconds

Details

The Automatic Zoning Procedure (AZP) was introduced by Openshaw (1977) and refined by Openshaw & Rao (1995). It is a local search algorithm that:

  1. Starts with an initial random partition into n_regions

  2. Iteratively moves border areas between regions to reduce heterogeneity

  3. Maintains spatial contiguity throughout

  4. Terminates when no improving moves are found

Three variants are available:

  • basic: Greedy local search that only accepts improving moves

  • tabu: Tabu search that can accept non-improving moves to escape local optima, with a tabu list preventing cycling

  • sa: Simulated annealing that accepts worse moves with decreasing probability as temperature cools

References

Openshaw, S. (1977). A geographical solution to scale and aggregation problems in region-building, partitioning and spatial modelling. Transactions of the Institute of British Geographers, 2(4), 459-472.

Openshaw, S., & Rao, L. (1995). Algorithms for reengineering 1991 Census geography. Environment and Planning A, 27(3), 425-446.

Examples

if (FALSE) { # \dontrun{
library(sf)
nc <- st_read(system.file("shape/nc.shp", package = "sf"))

# Basic AZP with 8 regions
result <- azp(nc, attrs = c("SID74", "SID79"), n_regions = 8)

# Tabu search (often finds better solutions)
result <- azp(nc, attrs = c("SID74", "SID79"), n_regions = 8,
              method = "tabu", tabu_length = 15)

# Simulated annealing
result <- azp(nc, attrs = c("SID74", "SID79"), n_regions = 8,
              method = "sa", cooling_rate = 0.95)

# View results
plot(result[".region"])
} # }