Solve

Solve a conservation planning problem.

Usage

# S3 method for ConservationProblem
solve(a, b, ..., run_checks = TRUE, force = FALSE)

Arguments

a: problem() object.
b: missing.
...: arguments passed to compile().
run_checks: logical flag indicating whether presolve checks should be run prior solving the problem. These checks are performed using the presolve_check() function. Defaults to TRUE. Skipping these checks may reduce run time for large problems.
force: logical flag indicating if an attempt to should be made to solve the problem even if potential issues were detected during the presolve checks. Defaults to FALSE.

Value

A numeric, matrix, data.frame, sf::st_sf(), or terra::rast() object containing the solution to the problem. Additionally, the returned object has attributes that describe optimization process or solution (see below for examples on accessing these attributes). These attributes provide the following information.

objective: numeric mathematical objective value for the solution used to evaluate the prioritization during optimization.
runtime: numeric total amount of time elapsed while during the optimization process (reported in seconds). Note that this measure of time does not include any data pre-processing or post-processing steps.
status: character status of the optimization process. This status typically describes the reason why the optimization process terminated. For example, it might indicate that the optimization process terminated because an optimal solution was found, or because a pre-specified time limit was reached. These status values are (mostly) obtained directly from the solver software, and so we recommend consulting the solver's documentation for further information on what particular status values mean. Note that some solvers (e.g., Gurobi and HiGHS) will return an "OPTIMAL" status when the solver has found a solution within the pre-specified optimality gap (e.g., it has found a solution within 10% of optimality), even though the solution itself may not be strictly optimal.
gap: numeric optimality of the solution. This gap value provides an upper bound of how far the solution is from optimality. For example, you might specify a 10% optimality gap for the optimization process (e.g., using add_highs_solver(gap = 0.1)), and this might produce a solution that is actually 5% from optimality. As such, the solution might have a gap value of 0.05 (corresponding to 5%). Because this value represents an upper bound, it is also possible that the solution in this example -- even though it is actually 5% from optimality -- might have a gap value of 7% (i.e., 0.07). Note that only some solvers are able to provide this information (i.e., the Gurobi and HiGHS solvers), and the gap value for other solvers will contain missing (NA) values.

Details

After formulating a conservation planning problem(), it can be solved using an exact algorithm solver (see solvers for available solvers). If no solver has been explicitly specified, then the best available exact algorithm solver will be used by default (see add_default_solver()). Although these exact algorithm solvers will often display a lot of information that isn't really that helpful (e.g., nodes, cutting planes), they do display information about the progress they are making on solving the problem (e.g., the performance of the best solution found at a given point in time). If potential issues were detected during the presolve checks (see presolve_check()) and the problem is being forcibly solved (i.e., with force = TRUE), then it is also worth checking for any warnings displayed by the solver to see if these potential issues are actually causing issues (e.g., Gurobi can display warnings that include "Warning: Model contains large matrix coefficient range" and "Warning: Model contains large rhs").

Output format

This function will output solutions in a similar format to the planning units associated with a. Specifically, it will return solutions based on the following types of planning units.

a has numeric planning units: The solution will be returned as a numeric vector. Here, each element in the vector corresponds to a different planning unit. Note that if a portfolio is used to generate multiple solutions, then a list of such numeric vectors will be returned.
a has matrix planning units: The solution will be returned as a matrix object. Here, rows correspond to different planning units, and columns correspond to different management zones. Note that if a portfolio is used to generate multiple solutions, then a list of such matrix objects will be returned.
a has terra::rast() planning units: The solution will be returned as a terra::rast() object. If the argument to x contains multiple zones, then the object will have a different layer for each management zone. Note that if a portfolio is used to generate multiple solutions, then a list of terra::rast() objects will be returned.
a has sf::sf(), or data.frame planning units: The solution will be returned in the same data format as the planning units. Here, each row corresponds to a different planning unit, and columns contain solutions. If the argument to a contains a single zone, then the solution object will contain columns named by solution. Specifically, the column names containing the solution values be will named as "solution_XXX" where "XXX" corresponds to a solution identifier (e.g., "solution_1"). If the argument to a contains multiple zones, then the columns containing solutions will be named as "solution_XXX_YYY" where "XXX" corresponds to the solution identifier and "YYY" is the name of the management zone (e.g., "solution_1_zone1").

Examples

# \dontrun{
# 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_raster <- get_sim_zones_pu_raster()
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 
#> dimensions  : 10, 10, 1  (nrow, ncol, nlyr)
#> resolution  : 0.1, 0.1  (x, y)
#> extent      : 0, 1, 0, 1  (xmin, xmax, ymin, ymax)
#> coord. ref. : Undefined Cartesian SRS 
#> source(s)   : memory
#> varname     : sim_pu_raster 
#> name        : layer 
#> min value   :     0 
#> max value   :     1 

# print attributes describing the optimization process and the solution
print(attr(s1, "objective"))
#> solution_1 
#>   1987.399 
print(attr(s1, "runtime"))
#> solution_1 
#>      0.005 
print(attr(s1, "status"))
#> solution_1 
#>  "OPTIMAL" 
print(attr(s1, "gap"))
#> solution_1 
#> 0.02808527 

# calculate feature representation in the solution
r1 <- eval_feature_representation_summary(p1, s1)
print(r1)
#> # A tibble: 5 × 5
#>   summary feature   total_amount absolute_held relative_held
#>   <chr>   <chr>            <dbl>         <dbl>         <dbl>
#> 1 overall feature_1         83.3          8.91         0.107
#> 2 overall feature_2         31.2          3.13         0.100
#> 3 overall feature_3         72.0          7.34         0.102
#> 4 overall feature_4         42.7          4.35         0.102
#> 5 overall feature_5         56.7          6.01         0.106

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


# 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)

# 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: Undefined Cartesian SRS
#> # A tibble: 90 × 5
#>     cost locked_in locked_out solution_1                                    geom
#>    <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 feature representation in the solution
r2 <- eval_feature_representation_summary(p2, s2[, "solution_1"])
print(r2)
#> # A tibble: 5 × 5
#>   summary feature   total_amount absolute_held relative_held
#>   <chr>   <chr>            <dbl>         <dbl>         <dbl>
#> 1 overall feature_1         74.5          8.05         0.108
#> 2 overall feature_2         28.1          2.83         0.101
#> 3 overall feature_3         64.9          6.65         0.103
#> 4 overall feature_4         38.2          3.87         0.101
#> 5 overall feature_5         50.7          5.41         0.107

# plot solution
plot(s2[, "solution_1"], main = "solution", axes = FALSE)


# build multi-zone conservation problem with raster data
p3 <-
  problem(sim_zones_pu_raster, sim_zones_features) %>%
  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)
#> class       : SpatRaster 
#> dimensions  : 10, 10, 3  (nrow, ncol, nlyr)
#> resolution  : 0.1, 0.1  (x, y)
#> extent      : 0, 1, 0, 1  (xmin, xmax, ymin, ymax)
#> coord. ref. : Undefined Cartesian SRS 
#> source(s)   : memory
#> varnames    : sim_zones_pu_raster 
#>               sim_zones_pu_raster 
#>               sim_zones_pu_raster 
#> names       : zone_1, zone_2, zone_3 
#> min values  :      0,      0,      0 
#> max values  :      1,      1,      1 

# calculate feature representation in the solution
r3 <- eval_feature_representation_summary(p3, s3)
print(r3)
#> # A tibble: 20 × 5
#>    summary feature   total_amount absolute_held relative_held
#>    <chr>   <chr>            <dbl>         <dbl>         <dbl>
#>  1 overall feature_1        250.          48.0          0.192
#>  2 overall feature_2         93.6         18.2          0.195
#>  3 overall feature_3        216.          43.0          0.199
#>  4 overall feature_4        128.          23.1          0.181
#>  5 overall feature_5        170.          31.7          0.186
#>  6 zone_1  feature_1         83.3         16.9          0.203
#>  7 zone_1  feature_2         31.2          5.75         0.184
#>  8 zone_1  feature_3         72.0         15.2          0.211
#>  9 zone_1  feature_4         42.7          6.70         0.157
#> 10 zone_1  feature_5         56.7         11.0          0.194
#> 11 zone_2  feature_1         83.3         15.9          0.191
#> 12 zone_2  feature_2         31.2          6.12         0.196
#> 13 zone_2  feature_3         72.0         14.3          0.199
#> 14 zone_2  feature_4         42.7          8.38         0.196
#> 15 zone_2  feature_5         56.7         10.3          0.182
#> 16 zone_3  feature_1         83.3         15.2          0.183
#> 17 zone_3  feature_2         31.2          6.37         0.204
#> 18 zone_3  feature_3         72.0         13.4          0.187
#> 19 zone_3  feature_4         42.7          8.03         0.188
#> 20 zone_3  feature_5         56.7         10.4          0.184

# plot solution
plot(category_layer(s3), main = "solution", axes = FALSE)


# build multi-zone conservation problem with polygon data
p4 <-
  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
s4 <- solve(p4)

# print solution
print(s4)
#> 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: Undefined Cartesian SRS
#> # 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>,
#> #   geom <POLYGON [m]>

# calculate feature representation in the solution
r4 <- eval_feature_representation_summary(
  p4, s4[, c("solution_1_zone_1", "solution_1_zone_2", "solution_1_zone_3")]
)
print(r4)
#> # A tibble: 20 × 5
#>    summary feature   total_amount absolute_held relative_held
#>    <chr>   <chr>            <dbl>         <dbl>         <dbl>
#>  1 overall feature_1        225.          37.7          0.167
#>  2 overall feature_2         83.9         14.8          0.177
#>  3 overall feature_3        195.          33.3          0.171
#>  4 overall feature_4        114.          19.2          0.168
#>  5 overall feature_5        154.          25.0          0.163
#>  6 zone_1  feature_1         75.1         12.3          0.164
#>  7 zone_1  feature_2         28.0          4.47         0.160
#>  8 zone_1  feature_3         65.0         10.7          0.164
#>  9 zone_1  feature_4         38.0          6.20         0.163
#> 10 zone_1  feature_5         51.2          8.06         0.158
#> 11 zone_2  feature_1         75.1         11.3          0.150
#> 12 zone_2  feature_2         28.0          5.28         0.189
#> 13 zone_2  feature_3         65.0         10.1          0.156
#> 14 zone_2  feature_4         38.0          6.85         0.180
#> 15 zone_2  feature_5         51.2          7.77         0.152
#> 16 zone_3  feature_1         75.1         14.1          0.188
#> 17 zone_3  feature_2         28.0          5.07         0.181
#> 18 zone_3  feature_3         65.0         12.5          0.193
#> 19 zone_3  feature_4         38.0          6.12         0.161
#> 20 zone_3  feature_5         51.2          9.16         0.179

# create new column representing the zone id that each planning unit
# was allocated to in the solution
s4$solution <- category_vector(
  s4[, c("solution_1_zone_1", "solution_1_zone_2", "solution_1_zone_3")]
)
s4$solution <- factor(s4$solution)

# plot solution
plot(s4[, "solution"])

# }