The automatic zoning procedure (AZP) was initially outlined in Openshaw (1977) as a way to address some of the consequences of the modifiable areal unit problem (MAUP). In essence, it consists of a heuristic to find the best set of combinations of contiguous spatial units into p regions, minimizing the within sum of squares as a criterion of homogeneity. The number of regions needs to be specified beforehand.

```
azp_sa(
p,
w,
df,
cooling_rate,
sa_maxit = 1,
bound_variable = data.frame(),
min_bound = 0,
inits = 0,
initial_regions = vector("numeric"),
scale_method = "standardize",
distance_method = "euclidean",
random_seed = 123456789,
rdist = numeric()
)
```

- p
The number of spatially constrained clusters

- w
An instance of Weight class

- df
A data frame with selected variables only. E.g. guerry[c("Crm_prs", "Crm_prp", "Litercy")]

- cooling_rate
The cooling rate of a simulated annealing algorithm. Defaults to 0.85

- sa_maxit
(optional): The number of iterations of simulated annealing. Defaults to 1

- bound_variable
(optional) A data frame with selected bound variabl

- min_bound
(optional) A minimum bound value that applies to all clusters

- inits
(optional) The number of construction re-runs, which is for ARiSeL "automatic regionalization with initial seed location"

- initial_regions
(optional) The initial regions that the local search starts with. Default is empty. means the local search starts with a random process to "grow" clusters

- scale_method
(optional) One of the scaling methods 'raw', 'standardize', 'demean', 'mad', 'range_standardize', 'range_adjust' to apply on input data. Default is 'standardize' (Z-score normalization).

- distance_method
(optional) The distance method used to compute the distance betwen observation i and j. Defaults to "euclidean". Options are "euclidean" and "manhattan"

- random_seed
(optional) The seed for random number generator. Defaults to 123456789.

- rdist
(optional) The distance matrix (lower triangular matrix, column wise storage)

A names list with names "Clusters", "Total sum of squares", "Within-cluster sum of squares", "Total within-cluster sum of squares", and "The ratio of between to total sum of squares".

```
if (FALSE) {
library(sf)
guerry_path <- system.file("extdata", "Guerry.shp", package = "rgeoda")
guerry <- st_read(guerry_path)
queen_w <- queen_weights(guerry)
data <- guerry[c('Crm_prs','Crm_prp','Litercy','Donatns','Infants','Suicids')]
azp_clusters <- azp_sa(5, queen_w, data, cooling_rate = 0.85)
azp_clusters
}
```