Evaluate number of planning units selected by solution

Calculate the number of planning units selected within a solution to a conservation planning problem.

Usage

eval_n_summary(x, solution)

Arguments

x: problem() or multi_problem() object.
solution: numeric, matrix, data.frame, terra::rast(), or sf::sf() object. Note that solution must have the same format as the planning unit data in x. See the Solution format section for more information.

Value

A tibble::tibble() object containing the number of planning units selected within a solution. It contains the following columns.

summary: character description of the summary statistic. The statistic associated with the "overall" value in this column is calculated using the entire solution (including all management zones if x has multiple zones). If x has multiple management zones, then summary statistics are also provided for each zone separately (indicated using zone names).
n: numeric number of selected planning units.

Details

This summary statistic is calculated as the sum of the values in the solution. As a consequence, this metric can produce a non-integer value (e.g., 4.3) for solutions containing proportion values (e.g., generated by solving a problem() built using the add_proportion_decisions() function).

Solution format

Broadly speaking, solution must be in the same format as the planning unit data in x. Further details on the correct format are listed separately for each of the different planning unit data formats.

x has numeric planning units: Here solution must be a numeric vector with each element corresponding to a different planning unit. It should have the same number of planning units as those in x. Additionally, any planning units with missing cost (NA) values should also have missing (NA) values in the solution.
x has matrix planning units: Here solution must be a matrix vector with each row corresponding to a different planning unit, and each column correspond to a different management zone. It should have the same number of planning units and zones as those in x. Additionally, any planning units with missing cost (NA) values for a particular zone should also have a missing (NA) values in solution.
x has terra::rast() planning units: Here solution be a terra::rast() object where different cells correspond to different planning units and layers correspond to a different management zones. It should have the same dimensionality (rows, columns, layers), resolution, extent, and coordinate reference system as the planning units in x. Additionally, any planning units with missing cost (NA) values for a particular zone should also have missing (NA) values in solution.
x has data.frame planning units: Here solution must be a data.frame with each column corresponding to a different zone, each row corresponding to a different planning unit, and cell values corresponding to the solution value. This means that if a data.frame object containing the solution also contains additional columns, then these columns will need to be subsetted prior to using this function (see below for example with sf::sf() data). Additionally, any planning units with missing cost (NA) values for a particular zone should also have missing (NA) values in solution.
x has sf::sf() planning units: Here solution must be a sf::sf() object with each column corresponding to a different zone, each row corresponding to a different planning unit, and cell values corresponding to the solution value. This means that if the sf::sf() object containing the solution also contains additional columns, then these columns will need to be subsetted prior to using this function (see below for example). Additionally, solution must also have the same coordinate reference system as the planning unit data. Furthermore, any planning units with missing cost (NA) values for a particular zone should also have missing (NA) values in solution.

Examples

# set seed for reproducibility
set.seed(500)

# load data
sim_pu_raster <- get_sim_pu_raster()
sim_pu_polygons <- get_sim_pu_polygons()
sim_features <- get_sim_features()
sim_zones_pu_polygons <- get_sim_zones_pu_polygons()
sim_zones_features <- get_sim_zones_features()

# build minimal conservation problem with raster data
p1 <-
  problem(sim_pu_raster, sim_features) %>%
  add_min_set_objective() %>%
  add_relative_targets(0.1) %>%
  add_binary_decisions() %>%
  add_default_solver(verbose = FALSE)

# solve the problem
s1 <- solve(p1)

# print solution
print(s1)
#> class       : SpatRaster
#> size        : 10, 10, 1  (nrow, ncol, nlyr)
#> resolution  : 0.1, 0.1  (x, y)
#> extent      : 0, 1, 0, 1  (xmin, xmax, ymin, ymax)
#> coord. ref. : WGS 84 / Pseudo-Mercator (EPSG:3857)
#> source(s)   : memory
#> varname     : sim_pu_raster
#> name        : layer
#> min value   :     0
#> max value   :     1

# plot solution
plot(s1, main = "solution", axes = FALSE)


# calculate number of selected planning units within solution
r1 <- eval_n_summary(p1, s1)
print(r1)
#> # A tibble: 1 × 2
#>   summary     n
#>   <chr>   <dbl>
#> 1 overall    10

# build minimal conservation problem with polygon data
p2 <-
  problem(sim_pu_polygons, sim_features, cost_column = "cost") %>%
  add_min_set_objective() %>%
  add_relative_targets(0.1) %>%
  add_binary_decisions() %>%
  add_default_solver(verbose = FALSE)

# solve the problem
s2 <- solve(p2)

# plot solution
plot(s2[, "solution_1"])


# print solution
print(s2)
#> Simple feature collection with 90 features and 4 fields
#> Geometry type: POLYGON
#> Dimension:     XY
#> Bounding box:  xmin: 0 ymin: 0 xmax: 1 ymax: 1
#> Projected CRS: WGS 84 / Pseudo-Mercator
#> # A tibble: 90 × 5
#>     cost locked_in locked_out solution_1                                geometry
#>  * <dbl> <lgl>     <lgl>           <dbl>                           <POLYGON [m]>
#>  1  216. FALSE     FALSE               0     ((0 1, 0.1 1, 0.1 0.9, 0 0.9, 0 1))
#>  2  213. FALSE     FALSE               0 ((0.1 1, 0.2 1, 0.2 0.9, 0.1 0.9, 0.1 …
#>  3  207. FALSE     FALSE               0 ((0.2 1, 0.3 1, 0.3 0.9, 0.2 0.9, 0.2 …
#>  4  209. FALSE     TRUE                0 ((0.3 1, 0.4 1, 0.4 0.9, 0.3 0.9, 0.3 …
#>  5  214. FALSE     FALSE               0 ((0.4 1, 0.5 1, 0.5 0.9, 0.4 0.9, 0.4 …
#>  6  214. FALSE     FALSE               0 ((0.5 1, 0.6 1, 0.6 0.9, 0.5 0.9, 0.5 …
#>  7  210. FALSE     FALSE               0 ((0.6 1, 0.7 1, 0.7 0.9, 0.6 0.9, 0.6 …
#>  8  211. FALSE     TRUE                0 ((0.7 1, 0.8 1, 0.8 0.9, 0.7 0.9, 0.7 …
#>  9  210. FALSE     FALSE               0 ((0.8 1, 0.9 1, 0.9 0.9, 0.8 0.9, 0.8 …
#> 10  204. FALSE     FALSE               0   ((0.9 1, 1 1, 1 0.9, 0.9 0.9, 0.9 1))
#> # ℹ 80 more rows

# calculate number of selected planning units within solution
r2 <- eval_n_summary(p2, s2[, "solution_1"])
print(r2)
#> # A tibble: 1 × 2
#>   summary     n
#>   <chr>   <dbl>
#> 1 overall     9

# manually calculate number of selected planning units
r2_manual <- sum(s2$solution_1, na.rm = TRUE)
print(r2_manual)
#> [1] 9

# build multi-zone conservation problem with polygon data
p3 <-
  problem(
    sim_zones_pu_polygons, sim_zones_features,
    cost_column = c("cost_1", "cost_2", "cost_3")
  ) %>%
  add_min_set_objective() %>%
  add_relative_targets(matrix(runif(15, 0.1, 0.2), nrow = 5, ncol = 3)) %>%
  add_binary_decisions() %>%
  add_default_solver(verbose = FALSE)

# solve the problem
s3 <- solve(p3)

# print solution
print(s3)
#> Simple feature collection with 90 features and 9 fields
#> Geometry type: POLYGON
#> Dimension:     XY
#> Bounding box:  xmin: 0 ymin: 0 xmax: 1 ymax: 1
#> Projected CRS: WGS 84 / Pseudo-Mercator
#> # A tibble: 90 × 10
#>    cost_1 cost_2 cost_3 locked_1 locked_2 locked_3 solution_1_zone_1
#>  *  <dbl>  <dbl>  <dbl> <lgl>    <lgl>    <lgl>                <dbl>
#>  1   216.   183.   205. FALSE    FALSE    FALSE                    0
#>  2   213.   189.   210. FALSE    FALSE    FALSE                    0
#>  3   207.   194.   215. TRUE     FALSE    FALSE                    0
#>  4   209.   198.   219. FALSE    FALSE    FALSE                    0
#>  5   214.   200.   221. FALSE    FALSE    FALSE                    0
#>  6   214.   203.   225. FALSE    FALSE    FALSE                    0
#>  7   211.   209.   223. FALSE    FALSE    FALSE                    0
#>  8   210.   212.   222. TRUE     FALSE    FALSE                    0
#>  9   204.   218.   214. FALSE    FALSE    FALSE                    0
#> 10   213.   183.   206. FALSE    FALSE    FALSE                    0
#> # ℹ 80 more rows
#> # ℹ 3 more variables: solution_1_zone_2 <dbl>, solution_1_zone_3 <dbl>,
#> #   geometry <POLYGON [m]>

# create new column representing the zone id that each planning unit
# was allocated to in the solution
s3$solution <- category_vector(
  s3[, c("solution_1_zone_1", "solution_1_zone_2", "solution_1_zone_3")]
)
s3$solution <- factor(s3$solution)

# plot solution
plot(s3[, "solution"])


# calculate number of selected planning units within solution
r3 <- eval_n_summary(
  p3, s3[, c("solution_1_zone_1", "solution_1_zone_2", "solution_1_zone_3")]
)
print(r3)
#> # A tibble: 4 × 2
#>   summary     n
#>   <chr>   <dbl>
#> 1 overall    51
#> 2 zone_1     17
#> 3 zone_2     17
#> 4 zone_3     17