Add relative targets

Set targets as a proportion (between 0 and 1) of the maximum level of representation of features in the study area. Please note that proportions are scaled according to the features' total abundances in the study area (including any locked out planning units, or planning units with NA cost data) using the feature_abundances() function.

add_relative_targets(x, targets)

# S4 method for ConservationProblem,numeric
add_relative_targets(x, targets)

# S4 method for ConservationProblem,matrix
add_relative_targets(x, targets)

# S4 method for ConservationProblem,character
add_relative_targets(x, targets)

Arguments

x	problem() (i.e. ConservationProblem) object.
targets	Object that specifies the targets for each feature. See the Details section for more information.

Value

Object (i.e. ConservationProblem) with the targets added to it.

Details

Targets are used to specify the minimum amount or proportion of a feature's distribution that needs to be protected. Most conservation planning problems require targets with the exception of the maximum cover (see add_max_cover_objective()) and maximum utility (see add_max_utility_objective()) problems. Attempting to solve problems with objectives that require targets without specifying targets will throw an error.

The targets for a problem can be specified in several different ways:

numeric

vector of target values for each feature. Additionally, for convenience, this type of argument can be a single value to assign the same target to each feature. Note that this type of argument cannot be used to specify targets for problems with multiple zones.

matrix

containing a target for each feature in each zone. Here, each row corresponds to a different feature in argument to x, each column corresponds to a different zone in argument to x, and each cell contains the target value for a given feature that the solution needs to secure in a given zone.

character

containing the names of fields (columns) in the feature data associated with the argument to x that contain targets. This type of argument can only be used when the feature data associated with x is a data.frame. This argument must contain a field (column) name for each zone.

For problems associated with multiple management zones, this function can be used to set targets that each pertain to a single feature and a single zone. To set targets which can be met through allocating different planning units to multiple zones, see the add_manual_targets() function. An example of a target that could be met through allocations to multiple zones might be where each management zone is expected to result in a different amount of a feature and the target requires that the total amount of the feature in all zones must exceed a certain threshold. In other words, the target does not require that any single zone secure a specific amount of the feature, but the total amount held in all zones must secure a specific amount. Thus the target could, potentially, be met through allocating all planning units to any specific management zone, or through allocating the planning units to different combinations of management zones.

See also

targets.

Examples

# set seed for reproducibility
set.seed(500)

# load data
data(sim_pu_raster, sim_features)

# create base problem
p <- problem(sim_pu_raster, sim_features) %>%
     add_min_set_objective() %>%
     add_binary_decisions()

# create problem with 10 % targets
p1 <- p %>% add_relative_targets(0.1)

# create problem with varying targets for each feature
targets <- c(0.1, 0.2, 0.3, 0.4, 0.5)
p2 <- p %>% add_relative_targets(targets)
# \dontrun{
# solve problem
s <- stack(solve(p1), solve(p2))
#> Gurobi Optimizer version 9.0.2 build v9.0.2rc0 (linux64)
#> Optimize a model with 5 rows, 90 columns and 450 nonzeros
#> Model fingerprint: 0x6442bf6e
#> Variable types: 0 continuous, 90 integer (90 binary)
#> Coefficient statistics:
#>   Matrix range     [2e-01, 9e-01]
#>   Objective range  [2e+02, 2e+02]
#>   Bounds range     [1e+00, 1e+00]
#>   RHS range        [3e+00, 8e+00]
#> Found heuristic solution: objective 2337.9617505
#> Presolve time: 0.00s
#> Presolved: 5 rows, 90 columns, 450 nonzeros
#> Variable types: 0 continuous, 90 integer (90 binary)
#> Presolved: 5 rows, 90 columns, 450 nonzeros
#> 
#> 
#> Root relaxation: objective 1.931582e+03, 12 iterations, 0.00 seconds
#> 
#>     Nodes    |    Current Node    |     Objective Bounds      |     Work
#>  Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time
#> 
#>      0     0 1931.58191    0    4 2337.96175 1931.58191  17.4%     -    0s
#> H    0     0                    1987.3985265 1931.58191  2.81%     -    0s
#> 
#> Explored 1 nodes (12 simplex iterations) in 0.00 seconds
#> Thread count was 1 (of 4 available processors)
#> 
#> Solution count 2: 1987.4 2337.96 
#> 
#> Optimal solution found (tolerance 1.00e-01)
#> Best objective 1.987398526526e+03, best bound 1.931581908865e+03, gap 2.8085%
#> Gurobi Optimizer version 9.0.2 build v9.0.2rc0 (linux64)
#> Optimize a model with 5 rows, 90 columns and 450 nonzeros
#> Model fingerprint: 0x7b37a531
#> Variable types: 0 continuous, 90 integer (90 binary)
#> Coefficient statistics:
#>   Matrix range     [2e-01, 9e-01]
#>   Objective range  [2e+02, 2e+02]
#>   Bounds range     [1e+00, 1e+00]
#>   RHS range        [6e+00, 3e+01]
#> Found heuristic solution: objective 9439.1408525
#> Presolve removed 4 rows and 0 columns
#> Presolve time: 0.00s
#> Presolved: 1 rows, 90 columns, 90 nonzeros
#> Variable types: 0 continuous, 90 integer (90 binary)
#> Presolved: 1 rows, 90 columns, 90 nonzeros
#> 
#> 
#> Root relaxation: objective 9.190939e+03, 1 iterations, 0.00 seconds
#> 
#>     Nodes    |    Current Node    |     Objective Bounds      |     Work
#>  Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time
#> 
#>      0     0 9190.93869    0    1 9439.14085 9190.93869  2.63%     -    0s
#> 
#> Explored 0 nodes (1 simplex iterations) in 0.00 seconds
#> Thread count was 1 (of 4 available processors)
#> 
#> Solution count 1: 9439.14 
#> 
#> Optimal solution found (tolerance 1.00e-01)
#> Best objective 9.439140852480e+03, best bound 9.190938685954e+03, gap 2.6295%

# plot solution
plot(s, main = c("10 % targets", "varying targets"), axes = FALSE,
     box = FALSE)
# }
# create a problem with multiple management zones
p3 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
      add_min_set_objective() %>%
      add_binary_decisions()

# create a problem with targets that specify an equal amount of each feature
# to be represented in each zone
p4_targets <- matrix(0.1, nrow = 5, ncol = 3,
                     dimnames = list(feature_names(sim_features_zones),
                                     zone_names(sim_features_zones)))
print(p4_targets)
#>           zone_1 zone_2 zone_3
#> feature_1    0.1    0.1    0.1
#> feature_2    0.1    0.1    0.1
#> feature_3    0.1    0.1    0.1
#> feature_4    0.1    0.1    0.1
#> feature_5    0.1    0.1    0.1

p4 <- p3 %>% add_relative_targets(p4_targets)

# solve problem
# \dontrun{
# solve problem
s4 <- solve(p4)
#> Gurobi Optimizer version 9.0.2 build v9.0.2rc0 (linux64)
#> Optimize a model with 105 rows, 270 columns and 1620 nonzeros
#> Model fingerprint: 0x60594edc
#> Variable types: 0 continuous, 270 integer (270 binary)
#> Coefficient statistics:
#>   Matrix range     [2e-01, 1e+00]
#>   Objective range  [2e+02, 2e+02]
#>   Bounds range     [1e+00, 1e+00]
#>   RHS range        [1e+00, 8e+00]
#> Found heuristic solution: objective 7019.1222763
#> Presolve time: 0.00s
#> Presolved: 105 rows, 270 columns, 1620 nonzeros
#> Variable types: 0 continuous, 270 integer (270 binary)
#> Presolved: 105 rows, 270 columns, 1620 nonzeros
#> 
#> 
#> Root relaxation: objective 5.935429e+03, 100 iterations, 0.00 seconds
#> 
#>     Nodes    |    Current Node    |     Objective Bounds      |     Work
#>  Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time
#> 
#>      0     0 5935.42867    0   13 7019.12228 5935.42867  15.4%     -    0s
#> H    0     0                    6082.2792264 5935.42867  2.41%     -    0s
#> 
#> Explored 1 nodes (100 simplex iterations) in 0.01 seconds
#> Thread count was 1 (of 4 available processors)
#> 
#> Solution count 2: 6082.28 7019.12 
#> 
#> Optimal solution found (tolerance 1.00e-01)
#> Best objective 6.082279226435e+03, best bound 5.935428674960e+03, gap 2.4144%

# plot solution (pixel values correspond to zone identifiers)
plot(category_layer(s4), main = c("equal targets"))
# }
# create a problem with targets that require a varying amount of each
# feature to be represented in each zone
p5_targets <- matrix(runif(15, 0.01, 0.2), nrow = 5, ncol = 3,
                     dimnames = list(feature_names(sim_features_zones),
                                     zone_names(sim_features_zones)))
print(p5_targets)
#>               zone_1     zone_2     zone_3
#> feature_1 0.16838399 0.04908221 0.06359158
#> feature_2 0.14775224 0.10731456 0.17964011
#> feature_3 0.19530969 0.18583855 0.15529418
#> feature_4 0.09884473 0.16747797 0.04122594
#> feature_5 0.16433284 0.14519964 0.14909414

p5 <- p3 %>% add_relative_targets(p4_targets)
# solve problem
# \dontrun{
# solve problem
s5 <- solve(p5)
#> Gurobi Optimizer version 9.0.2 build v9.0.2rc0 (linux64)
#> Optimize a model with 105 rows, 270 columns and 1620 nonzeros
#> Model fingerprint: 0x60594edc
#> Variable types: 0 continuous, 270 integer (270 binary)
#> Coefficient statistics:
#>   Matrix range     [2e-01, 1e+00]
#>   Objective range  [2e+02, 2e+02]
#>   Bounds range     [1e+00, 1e+00]
#>   RHS range        [1e+00, 8e+00]
#> Found heuristic solution: objective 7019.1222763
#> Presolve time: 0.00s
#> Presolved: 105 rows, 270 columns, 1620 nonzeros
#> Variable types: 0 continuous, 270 integer (270 binary)
#> Presolved: 105 rows, 270 columns, 1620 nonzeros
#> 
#> 
#> Root relaxation: objective 5.935429e+03, 100 iterations, 0.00 seconds
#> 
#>     Nodes    |    Current Node    |     Objective Bounds      |     Work
#>  Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time
#> 
#>      0     0 5935.42867    0   13 7019.12228 5935.42867  15.4%     -    0s
#> H    0     0                    6082.2792264 5935.42867  2.41%     -    0s
#> 
#> Explored 1 nodes (100 simplex iterations) in 0.01 seconds
#> Thread count was 1 (of 4 available processors)
#> 
#> Solution count 2: 6082.28 7019.12 
#> 
#> Optimal solution found (tolerance 1.00e-01)
#> Best objective 6.082279226435e+03, best bound 5.935428674960e+03, gap 2.4144%

# plot solution (pixel values correspond to zone identifiers)
plot(category_layer(s5), main = c("varying targets"))
# }