Package 'prioritizr'

Description

Set targets expressed as the actual value of features in the study area that need to be represented in the prioritization. For instance, setting a target of 10 requires that the solution secure a set of planning units for which their summed feature values are equal to or greater than 10.

Usage

add_absolute_targets(x, targets)

## S4 method for signature 'ConservationProblem,numeric'
add_absolute_targets(x, targets)

## S4 method for signature 'ConservationProblem,matrix'
add_absolute_targets(x, targets)

## S4 method for signature 'ConservationProblem,character'
add_absolute_targets(x, targets)

Arguments

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.

For problems associated with multiple management zones, add_absolute_targets() can be used to set targets that each pertain to a single feature and a single zone. To set targets that 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.

Value

An updated problem() object with the targets added to it.

Targets format

The targets for a problem can be specified using the following formats.

targets as a numeric vector

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

targets as a matrix object

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.

targets as a character vector

containing the column name(s) in the feature data associated with the argument to x that contain targets. This format can only be used when the feature data associated with x is a sf::st_sf() or data.frame. For problems that contain a single zone, the argument to targets must contain a single column name. Otherwise, for problems that contain multiple zones, the argument to targets must contain a column name for each zone.

See Also

See targets for an overview of all functions for adding targets.

Other targets: add_loglinear_targets(), add_manual_targets(), add_relative_targets()

Examples

## Not run: 
# set seed for reproducibility
set.seed(500)

# load data
sim_pu_raster <- get_sim_pu_raster()
sim_features <- get_sim_features()
sim_zones_pu_raster <- get_sim_zones_pu_raster()
sim_zones_features <- get_sim_zones_features()

# create minimal problem with no targets
p0 <-
  problem(sim_pu_raster, sim_features) %>%
  add_min_set_objective() %>%
  add_binary_decisions() %>%
  add_default_solver(verbose = FALSE)

# create problem with targets to secure 3 amounts for each feature
p1 <- p0 %>% add_absolute_targets(3)

# create problem with varying targets for each feature
targets <- c(1, 2, 3, 2, 1)
p2 <- p0 %>% add_absolute_targets(targets)

# solve problem
s1 <- c(solve(p1), solve(p2))
names(s1) <- c("equal targets", "varying targets")

# plot solution
plot(s1, axes = FALSE)

# create a problem with multiple management zones
p3 <-
  problem(sim_zones_pu_raster, sim_zones_features) %>%
  add_min_set_objective() %>%
  add_binary_decisions() %>%
  add_default_solver(verbose = FALSE)

# create a problem with targets that specify an equal amount of each feature
# to be represented in each zone
p4_targets <- matrix(
  2,
  nrow = number_of_features(sim_zones_features),
  ncol = number_of_zones(sim_zones_features),
  dimnames = list(
    feature_names(sim_zones_features), zone_names(sim_zones_features)
  )
)
print(p4_targets)

p4 <- p3 %>% add_absolute_targets(p4_targets)

# solve problem
s4 <- solve(p4)

# plot solution (pixel values correspond to zone identifiers)
plot(category_layer(s4), main = "equal targets", axes = FALSE)

# create a problem with targets that require a varying amount of each
# feature to be represented in each zone
p5_targets <- matrix(
  rpois(15, 1),
  nrow = number_of_features(sim_zones_features),
  ncol = number_of_zones(sim_zones_features),
  dimnames = list(
    feature_names(sim_zones_features),
    zone_names(sim_zones_features)
  )
)
print(p5_targets)

p5 <- p3 %>% add_absolute_targets(p5_targets)

# solve problem
s5 <- solve(p5)

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

## End(Not run)

Description

Add penalties to a conservation planning problem to account for asymmetric connectivity between planning units. Asymmetric connectivity data describe connectivity information that is directional. For example, asymmetric connectivity data could describe the strength of rivers flowing between different planning units. Since river flow is directional, the level of connectivity from an upstream planning unit to a downstream planning unit would be higher than that from a downstream planning unit to an upstream planning unit.

Usage

## S4 method for signature 'ConservationProblem,ANY,ANY,matrix'
add_asym_connectivity_penalties(x, penalty, zones, data)

## S4 method for signature 'ConservationProblem,ANY,ANY,Matrix'
add_asym_connectivity_penalties(x, penalty, zones, data)

## S4 method for signature 'ConservationProblem,ANY,ANY,data.frame'
add_asym_connectivity_penalties(x, penalty, zones, data)

## S4 method for signature 'ConservationProblem,ANY,ANY,dgCMatrix'
add_asym_connectivity_penalties(x, penalty, zones, data)

## S4 method for signature 'ConservationProblem,ANY,ANY,array'
add_asym_connectivity_penalties(x, penalty, zones, data)

Arguments

Details

This function adds penalties to conservation planning problem to penalize solutions that have low connectivity. Specifically, it penalizes solutions that select planning units that share high connectivity values with other planning units that are not selected by the solution (based on Beger et al. 2010).

Value

An updated problem() object with the penalties added to it.

Mathematical formulation

The connectivity penalties are implemented using the following equations. Let $I$ represent the set of planning units (indexed by $i$ or $j$), $Z$ represent the set of management zones (indexed by $z$ or $y$), and $X_{iz}$ represent the decision variable for planning unit $i$ for in zone $z$ (e.g., with binary values one indicating if planning unit is allocated or not). Also, let $p$ represent the argument to penalty, $D$ represent the argument to data, and $W$ represent the argument to zones.

If the argument to data is supplied as a matrix or Matrix object, then the penalties are calculated as:

$\sum_{i}^{I} \sum_{j}^{I} \sum_{z}^{Z} \sum_{y}^{Z} (p \times X_{iz} \times D_{ij} \times W_{zy}) - \sum_{i}^{I} \sum_{j}^{I} \sum_{z}^{Z} \sum_{y}^{Z} (p \times X_{iz} \times X_{jy} \times D_{ij} \times W_{zy})$

Otherwise, if the argument to data is supplied as an array object, then the penalties are calculated as:

$\sum_{i}^{I} \sum_{j}^{I} \sum_{z}^{Z} \sum_{y}^{Z} (p \times X_{iz} \times D_{ijzy}) - \sum_{i}^{I} \sum_{j}^{I} \sum_{z}^{Z} \sum_{y}^{Z} (p \times X_{iz} \times X_{jy} \times D_{ijzy})$

Note that when the problem objective is to maximize some measure of benefit and not minimize some measure of cost, the term $p$ is replaced with $-p$.

Data format

The argument to data can be specified using several different formats.

data as a matrix/Matrix object

where rows and columns represent different planning units and the value of each cell represents the strength of connectivity between two different planning units. Cells that occur along the matrix diagonal are treated as weights which indicate that planning units are more desirable in the solution. The argument to zones can be used to control the strength of connectivity between planning units in different zones. The default argument for zones is to treat planning units allocated to different zones as having zero connectivity.

data as a data.frame object

containing columns that are named "id1", "id2", and "boundary". Here, each row denotes the connectivity between a pair of planning units (per values in the "id1" and "id2" columns) following the Marxan format. If the argument to x contains multiple zones, then the "zone1" and "zone2" columns can optionally be provided to manually specify the connectivity values between planning units when they are allocated to specific zones. If the "zone1" and "zone2" columns are present, then the argument to zones must be NULL.

data as an array object

containing four-dimensions where cell values indicate the strength of connectivity between planning units when they are assigned to specific management zones. The first two dimensions (i.e., rows and columns) indicate the strength of connectivity between different planning units and the second two dimensions indicate the different management zones. Thus the data[1, 2, 3, 4] indicates the strength of connectivity between planning unit 1 and planning unit 2 when planning unit 1 is assigned to zone 3 and planning unit 2 is assigned to zone 4.

References

Beger M, Linke S, Watts M, Game E, Treml E, Ball I, and Possingham, HP (2010) Incorporating asymmetric connectivity into spatial decision making for conservation, Conservation Letters, 3: 359–368.

See Also

See penalties for an overview of all functions for adding penalties.

Other penalties: add_boundary_penalties(), add_connectivity_penalties(), add_feature_weights(), add_linear_penalties()

Examples

## Not run: 
# load package
library(Matrix)

# set seed for reproducibility
set.seed(600)

# load data
sim_pu_polygons <- get_sim_pu_polygons()
sim_features <- get_sim_features()
sim_zones_pu_raster <- get_sim_zones_pu_raster()
sim_zones_features <- get_sim_zones_features()

# create basic problem
p1 <-
  problem(sim_pu_polygons, sim_features, "cost") %>%
  add_min_set_objective() %>%
  add_relative_targets(0.2) %>%
  add_default_solver(verbose = FALSE)

# create an asymmetric connectivity matrix. Here, connectivity occurs between
# adjacent planning units and, due to rivers flowing southwards
# through the study area, connectivity from northern planning units to
# southern planning units is ten times stronger than the reverse.
acm1 <- matrix(0, nrow(sim_pu_polygons), nrow(sim_pu_polygons))
acm1 <- as(acm1, "Matrix")
centroids <- sf::st_coordinates(
  suppressWarnings(sf::st_centroid(sim_pu_polygons))
)
adjacent_units <- sf::st_intersects(sim_pu_polygons, sparse = FALSE)
for (i in seq_len(nrow(sim_pu_polygons))) {
  for (j in seq_len(nrow(sim_pu_polygons))) {
    # find if planning units are adjacent
    if (adjacent_units[i, j]) {
      # find if planning units lay north and south of each other
      # i.e., they have the same x-coordinate
      if (centroids[i, 1] == centroids[j, 1]) {
        if (centroids[i, 2] > centroids[j, 2]) {
          # if i is north of j add 10 units of connectivity
          acm1[i, j] <- acm1[i, j] + 10
        } else if (centroids[i, 2] < centroids[j, 2]) {
          # if i is south of j add 1 unit of connectivity
          acm1[i, j] <- acm1[i, j] + 1
        }
      }
    }
  }
}

# rescale matrix values to have a maximum value of 1
acm1 <- rescale_matrix(acm1, max = 1)

# visualize asymmetric connectivity matrix
image(acm1)

# create penalties
penalties <- c(1, 50)

# create problems using the different penalties
p2 <- list(
  p1,
  p1 %>% add_asym_connectivity_penalties(penalties[1], data = acm1),
  p1 %>% add_asym_connectivity_penalties(penalties[2], data = acm1)
)

# solve problems
s2 <- lapply(p2, solve)

# create object with all solutions
s2 <- sf::st_sf(
  tibble::tibble(
    p2_1 = s2[[1]]$solution_1,
    p2_2 = s2[[2]]$solution_1,
    p2_3 = s2[[3]]$solution_1
 ),
 geometry = sf::st_geometry(s2[[1]])
)

names(s2)[1:3] <- c("basic problem", paste0("acm1 (", penalties,")"))

# plot solutions based on different penalty values
plot(s2, cex = 1.5)

# create minimal multi-zone problem and limit solver to one minute
# to obtain solutions in a short period of time
p3 <-
  problem(sim_zones_pu_raster, sim_zones_features) %>%
  add_min_set_objective() %>%
  add_relative_targets(matrix(0.15, nrow = 5, ncol = 3)) %>%
  add_binary_decisions() %>%
  add_default_solver(time_limit = 60, verbose = FALSE)

# crate asymmetric connectivity data by randomly simulating values
acm2 <- matrix(
  runif(ncell(sim_zones_pu_raster) ^ 2),
  nrow = ncell(sim_zones_pu_raster)
)

# create multi-zone problems using the penalties
p4 <- list(
  p3,
  p3 %>% add_asym_connectivity_penalties(penalties[1], data = acm2),
  p3 %>% add_asym_connectivity_penalties(penalties[2], data = acm2)
)

# solve problems
s4 <- lapply(p4, solve)
s4 <- lapply(s4, category_layer)
s4 <- terra::rast(s4)
names(s4) <- c("basic problem", paste0("acm2 (", penalties,")"))

# plot solutions
plot(s4, axes = FALSE)

## End(Not run)

Description

Add a binary decision to a conservation planning problem. This is the classic decision of either prioritizing or not prioritizing a planning unit. Typically, this decision has the assumed action of buying the planning unit to include in a protected area network. If no decision is added to a problem then this decision class will be used by default.

Usage

add_binary_decisions(x)

Arguments

Details

Conservation planning problems involve making decisions on planning units. These decisions are then associated with actions (e.g., turning a planning unit into a protected area). Only a single decision should be added to a problem() object. Note that if multiple decisions are added to an object, then the last one to be added will be used.

Value

An updated problem() object with the decisions added to it.

See Also

See decisions for an overview of all functions for adding decisions.

Other decisions: add_proportion_decisions(), add_semicontinuous_decisions()

Examples

## Not run: 
# set seed for reproducibility
set.seed(500)

# load data
sim_pu_raster <- get_sim_pu_raster()
sim_features <- get_sim_features()
sim_zones_pu_raster <- get_sim_zones_pu_raster()
sim_zones_features <- get_sim_zones_features()

# create minimal problem with binary decisions
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 problem
s1 <- solve(p1)

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

# create a matrix with targets for a multi-zone conservation problem
targs <- matrix(runif(15, 0.1, 0.2), nrow = 5, ncol = 3)

# build multi-zone conservation problem with binary decisions
p2 <-
  problem(sim_zones_pu_raster, sim_zones_features) %>%
  add_min_set_objective() %>%
  add_relative_targets(targs)  %>%
  add_binary_decisions() %>%
  add_default_solver(verbose = FALSE)

# solve the problem
s2 <- solve(p2)

# print solution
print(s2)

# plot solution
plot(category_layer(s2), main = "solution", axes = FALSE)

## End(Not run)

Description

Add penalties to a conservation planning problem to favor solutions that spatially clump planning units together based on the overall boundary length (i.e., total perimeter).

Usage

## S4 method for signature 'ConservationProblem,ANY,ANY,ANY,data.frame'
add_boundary_penalties(x, penalty, edge_factor, zones, data)

## S4 method for signature 'ConservationProblem,ANY,ANY,ANY,matrix'
add_boundary_penalties(x, penalty, edge_factor, zones, data)

## S4 method for signature 'ConservationProblem,ANY,ANY,ANY,ANY'
add_boundary_penalties(x, penalty, edge_factor, zones, data)

Arguments

Details

This function adds penalties to a conservation planning problem to penalize fragmented solutions. It was is inspired by Ball et al. (2009) and Beyer et al. (2016). The penalty argument is equivalent to the boundary length modifier (BLM) used in Marxan. Note that this function can only be used to represent symmetric relationships between planning units. If asymmetric relationships are required, use the add_connectivity_penalties() function.

Value

An updated problem() object with the penalties added to it.

Data format

The argument to data can be specified using the following formats. Note that boundary data must always describe symmetric relationships between planning units.

data as a NULL value

indicating that the data should be automatically calculated using the boundary_matrix() function. This argument is the default. Note that the boundary data must be supplied using one of the other formats below if the planning unit data in the argument to x do not explicitly contain spatial information (e.g., planning unit data are a data.frame or numeric class).

data as a matrix/Matrix object

where rows and columns represent different planning units and the value of each cell represents the amount of shared boundary length between two different planning units. Cells that occur along the matrix diagonal denote the total boundary length associated with each planning unit.

data as a data.frame object

with the columns "id1", "id2", and "boundary". The "id1" and "id2" columns contain identifiers (indices) for a pair of planning units, and the "boundary" column contains the amount of shared boundary length between these two planning units. Additionally, if the values in the "id1" and "id2" columns contain the same values, then the value denotes the amount of exposed boundary length (not total boundary). This format follows the the standard Marxan format for boundary data (i.e., per the "bound.dat" file).

Mathematical formulation

The boundary penalties are implemented using the following equations. Let $I$ represent the set of planning units (indexed by $i$ or $j$), $Z$ represent the set of management zones (indexed by $z$ or $y$), and $X_{iz}$ represent the decision variable for planning unit $i$ for in zone $z$ (e.g., with binary values one indicating if planning unit is allocated or not). Also, let $p$ represent the argument to penalty, $E_z$ represent the argument to edge_factor, $B_{ij}$ represent the matrix argument to data (e.g., generated using boundary_matrix()), and $W_{zz}$ represent the matrix argument to zones.

$\sum_{i}^{I} \sum_{z}^{Z} (p \times W_{zz} B_{ii}) + \sum_{i}^{I} \sum_{j}^{I} \sum_{z}^{Z} \sum_{y}^{Z} (-2 \times p \times X_{iz} \times X_{jy} \times W_{zy} \times B_{ij})$

Note that when the problem objective is to maximize some measure of benefit and not minimize some measure of cost, the term $p$ is replaced with $-p$.

References

Ball IR, Possingham HP, and Watts M (2009) Marxan and relatives: Software for spatial conservation prioritisation in Spatial conservation prioritisation: Quantitative methods and computational tools. Eds Moilanen A, Wilson KA, and Possingham HP. Oxford University Press, Oxford, UK.

Beyer HL, Dujardin Y, Watts ME, and Possingham HP (2016) Solving conservation planning problems with integer linear programming. Ecological Modelling, 228: 14–22.

See Also

See penalties for an overview of all functions for adding penalties.

Other penalties: add_asym_connectivity_penalties(), add_connectivity_penalties(), add_feature_weights(), add_linear_penalties()

Examples

## Not run: 
# set seed for reproducibility
set.seed(500)

# load data
sim_pu_raster <- get_sim_pu_raster()
sim_features <- get_sim_features()
sim_zones_pu_raster <- get_sim_zones_pu_raster()
sim_zones_features <- get_sim_zones_features()

# create minimal problem
p1 <-
  problem(sim_pu_raster, sim_features) %>%
  add_min_set_objective() %>%
  add_relative_targets(0.2) %>%
  add_binary_decisions() %>%
  add_default_solver(verbose = FALSE)

# create problem with low boundary penalties
p2 <- p1 %>% add_boundary_penalties(50, 1)

# create problem with high boundary penalties but outer edges receive
# half the penalty as inner edges
p3 <- p1 %>% add_boundary_penalties(500, 0.5)

# create a problem using precomputed boundary data
bmat <- boundary_matrix(sim_pu_raster)
p4 <- p1 %>% add_boundary_penalties(50, 1, data = bmat)

# solve problems
s1 <- c(solve(p1), solve(p2), solve(p3), solve(p4))
names(s1) <- c("basic solution", "small penalties", "high penalties",
  "precomputed data"
)

# plot solutions
plot(s1, axes = FALSE)

# create minimal problem with multiple zones and limit the run-time for
# solver to 10 seconds so this example doesn't take too long
p5 <-
  problem(sim_zones_pu_raster, sim_zones_features) %>%
  add_min_set_objective() %>%
  add_relative_targets(matrix(0.2, nrow = 5, ncol = 3)) %>%
  add_binary_decisions() %>%
  add_default_solver(time_limit = 10, verbose = FALSE)

# create zone matrix which favors clumping planning units that are
# allocated to the same zone together - note that this is the default
zm6 <- diag(3)
print(zm6)

# create problem with the zone matrix and low penalties
p6 <- p5 %>% add_boundary_penalties(50, zone = zm6)

# create another problem with the same zone matrix and higher penalties
p7 <- p5 %>% add_boundary_penalties(500, zone = zm6)

# create zone matrix which favors clumping units that are allocated to
# different zones together
zm8 <- matrix(1, ncol = 3, nrow = 3)
diag(zm8) <- 0
print(zm8)

# create problem with the zone matrix
p8 <- p5 %>% add_boundary_penalties(500, zone = zm8)

# create zone matrix which strongly favors clumping units
# that are allocated to the same zone together. It will also prefer
# clumping planning units in zones 1 and 2 together over having
# these planning units with no neighbors in the solution
zm9 <- diag(3)
zm9[upper.tri(zm9)] <- c(0.3, 0, 0)
zm9[lower.tri(zm9)] <- zm9[upper.tri(zm9)]
print(zm9)

# create problem with the zone matrix
p9 <- p5 %>% add_boundary_penalties(500, zone = zm9)

# create zone matrix which favors clumping planning units in zones 1 and 2
# together, and favors planning units in zone 3 being spread out
# (i.e., negative clumping)
zm10 <- diag(3)
zm10[3, 3] <- -1
print(zm10)

# create problem with the zone matrix
p10 <- p5 %>% add_boundary_penalties(500, zone = zm10)

# solve problems
s2 <- list(solve(p5), solve(p6), solve(p7), solve(p8), solve(p9), solve(p10))

#convert to category layers for visualization
s2 <- terra::rast(lapply(s2, category_layer))
names(s2) <- c(
  "basic solution", "within zone clumping (low)",
  "within zone clumping (high)", "between zone clumping",
  "within + between clumping", "negative clumping"
)

# plot solutions
plot(s2, axes = FALSE)

## End(Not run)

Description

Specify that the CBC (COIN-OR branch and cut) software should be used to solve a conservation planning problem (Forrest & Lougee-Heimer 2005). This function can also be used to customize the behavior of the solver. It requires the rcbc package to be installed (only available on GitHub, see below for installation instructions).

Usage

add_cbc_solver(
  x,
  gap = 0.1,
  time_limit = .Machine$integer.max,
  presolve = TRUE,
  threads = 1,
  first_feasible = FALSE,
  start_solution = NULL,
  verbose = TRUE
)

Arguments

Details

CBC is an open-source mixed integer programming solver that is part of the Computational Infrastructure for Operations Research (COIN-OR) project. This solver seems to have much better performance than the other open-source solvers (i.e., add_highs_solver(), add_rsymphony_solver(), add_lpsymphony_solver()) (see the Solver benchmarks vignette for details). As such, it is strongly recommended to use this solver if the Gurobi and IBM CPLEX solvers are not available.

Value

An updated problem() object with the solver added to it.

Installation

The rcbc package is required to use this solver. Since the rcbc package is not available on the the Comprehensive R Archive Network (CRAN), it must be installed from its GitHub repository. To install the rcbc package, please use the following code:

if (!require(remotes)) install.packages("remotes")
remotes::install_github("dirkschumacher/rcbc")

Note that you may also need to install several dependencies – such as the Rtools software or system libraries – prior to installing the rcbc package. For further details on installing this package, please consult the online package documentation.

Start solution format

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

x has numeric planning units

The argument to start_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 the argument to x. Additionally, any planning units missing cost (NA) values should also have missing (NA) values in the argument to start_solution.

x has matrix planning units

The argument to start_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 the argument to x. Additionally, any planning units missing cost (NA) values for a particular zone should also have a missing (NA) values in the argument to start_solution.

x has terra::rast() planning units

The argument to start_solution be a terra::rast() object where different grid cells (pixels) 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 the argument to x. Additionally, any planning units missing cost (NA) values for a particular zone should also have missing (NA) values in the argument to start_solution.

x has data.frame planning units

The argument to start_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 missing cost (NA) values for a particular zone should also have missing (NA) values in the argument to start_solution.

x has sf::sf() planning units

The argument to start_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, the argument to start_solution must also have the same coordinate reference system as the planning unit data. Furthermore, any planning units missing cost (NA) values for a particular zone should also have missing (NA) values in the argument to start_solution.

References

Forrest J and Lougee-Heimer R (2005) CBC User Guide. In Emerging theory, Methods, and Applications (pp. 257–277). INFORMS, Catonsville, MD. doi:10.1287/educ.1053.0020.

See Also

Other solvers: add_cplex_solver(), add_default_solver(), add_gurobi_solver(), add_highs_solver(), add_lsymphony_solver, add_rsymphony_solver()

Examples

## Not run: 
# load data
sim_pu_raster <- get_sim_pu_raster()
sim_features <- get_sim_features()

# create problem
p1 <-
  problem(sim_pu_raster, sim_features) %>%
  add_min_set_objective() %>%
  add_relative_targets(0.1) %>%
  add_binary_decisions() %>%
  add_cbc_solver(gap = 0, verbose = FALSE)

# generate solution %>%
s1 <- solve(p1)

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

# create a similar problem with boundary length penalties and
# specify the solution from the previous run as a starting solution
p2 <-
  problem(sim_pu_raster, sim_features) %>%
  add_min_set_objective() %>%
  add_relative_targets(0.1) %>%
  add_boundary_penalties(10) %>%
  add_binary_decisions() %>%
  add_cbc_solver(gap = 0, start_solution = s1, verbose = FALSE)

# generate solution
s2 <- solve(p2)

# plot solution
plot(s2, main = "solution with boundary penalties", axes = FALSE)

## End(Not run)

Description

Add penalties to a conservation planning problem to account for symmetric connectivity between planning units. Symmetric connectivity data describe connectivity information that is not directional. For example, symmetric connectivity data could describe which planning units are adjacent to each other (see adjacency_matrix()), or which planning units are within threshold distance of each other (see proximity_matrix()).

Usage

## S4 method for signature 'ConservationProblem,ANY,ANY,matrix'
add_connectivity_penalties(x, penalty, zones, data)

## S4 method for signature 'ConservationProblem,ANY,ANY,Matrix'
add_connectivity_penalties(x, penalty, zones, data)

## S4 method for signature 'ConservationProblem,ANY,ANY,data.frame'
add_connectivity_penalties(x, penalty, zones, data)

## S4 method for signature 'ConservationProblem,ANY,ANY,dgCMatrix'
add_connectivity_penalties(x, penalty, zones, data)

## S4 method for signature 'ConservationProblem,ANY,ANY,array'
add_connectivity_penalties(x, penalty, zones, data)

Arguments

Details

This function adds penalties to conservation planning problem to penalize solutions that have low connectivity. Specifically, it favors pair-wise connections between planning units that have high connectivity values (based on Önal and Briers 2002).

Value

An updated problem() object with the penalties added to it.

Data format

The argument to data can be specified using several different formats.

data as a matrix/Matrix object

where rows and columns represent different planning units and the value of each cell represents the strength of connectivity between two different planning units. Cells that occur along the matrix diagonal are treated as weights which indicate that planning units are more desirable in the solution. The argument to zones can be used to control the strength of connectivity between planning units in different zones. The default argument for zones is to treat planning units allocated to different zones as having zero connectivity.

data as a data.frame object

containing columns that are named "id1", "id2", and "boundary". Here, each row denotes the connectivity between a pair of planning units (per values in the "id1" and "id2" columns) following the Marxan format. If the argument to x contains multiple zones, then the "zone1" and "zone2" columns can optionally be provided to manually specify the connectivity values between planning units when they are allocated to specific zones. If the "zone1" and "zone2" columns are present, then the argument to zones must be NULL.

data as an array object

containing four-dimensions where cell values indicate the strength of connectivity between planning units when they are assigned to specific management zones. The first two dimensions (i.e., rows and columns) indicate the strength of connectivity between different planning units and the second two dimensions indicate the different management zones. Thus the data[1, 2, 3, 4] indicates the strength of connectivity between planning unit 1 and planning unit 2 when planning unit 1 is assigned to zone 3 and planning unit 2 is assigned to zone 4.

Mathematical formulation

The connectivity penalties are implemented using the following equations. Let $I$ represent the set of planning units (indexed by $i$ or $j$), $Z$ represent the set of management zones (indexed by $z$ or $y$), and $X_{iz}$ represent the decision variable for planning unit $i$ for in zone $z$ (e.g., with binary values one indicating if planning unit is allocated or not). Also, let $p$ represent the argument to penalty, $D$ represent the argument to data, and $W$ represent the argument to zones.

If the argument to data is supplied as a matrix or Matrix object, then the penalties are calculated as:

$\sum_{i}^{I} \sum_{j}^{I} \sum_{z}^{Z} \sum_{y}^{Z} (-p \times X_{iz} \times X_{jy} \times D_{ij} \times W_{zy})$

Otherwise, if the argument to data is supplied as a data.frame or array object, then the penalties are calculated as:

$\sum_{i}^{I} \sum_{j}^{I} \sum_{z}^{Z} \sum_{y}^{Z} (-p \times X_{iz} \times X_{jy} \times D_{ijzy})$

Note that when the problem objective is to maximize some measure of benefit and not minimize some measure of cost, the term $-p$ is replaced with $p$.

Notes

In previous versions, this function aimed to handle both symmetric and asymmetric connectivity data. This meant that the mathematical formulation used to account for asymmetric connectivity was different to that implemented by the Marxan software (see Beger et al. for details). To ensure that asymmetric connectivity is handled in a similar manner to the Marxan software, the add_asym_connectivity_penalties() function should now be used for asymmetric connectivity data.

References

Beger M, Linke S, Watts M, Game E, Treml E, Ball I, and Possingham, HP (2010) Incorporating asymmetric connectivity into spatial decision making for conservation, Conservation Letters, 3: 359–368.

Önal H, and Briers RA (2002) Incorporating spatial criteria in optimum reserve network selection. Proceedings of the Royal Society of London. Series B: Biological Sciences, 269: 2437–2441.

See Also

See penalties for an overview of all functions for adding penalties. Additionally, see add_asym_connectivity_penalties() to account for asymmetric connectivity between planning units.

Other penalties: add_asym_connectivity_penalties(), add_boundary_penalties(), add_feature_weights(), add_linear_penalties()

Examples

## Not run: 
# load package
library(Matrix)

# set seed for reproducibility
set.seed(600)

# load data
sim_pu_polygons <- get_sim_pu_polygons()
sim_features <- get_sim_features()
sim_zones_pu_raster <- get_sim_zones_pu_raster()
sim_zones_features <- get_sim_zones_features()

# create basic problem
p1 <-
  problem(sim_pu_polygons, sim_features, "cost") %>%
  add_min_set_objective() %>%
  add_relative_targets(0.2) %>%
  add_default_solver(verbose = FALSE)

# create a symmetric connectivity matrix where the connectivity between
# two planning units corresponds to their shared boundary length
b_matrix <- boundary_matrix(sim_pu_polygons)

# rescale matrix values to have a maximum value of 1
b_matrix <- rescale_matrix(b_matrix, max = 1)

# visualize connectivity matrix
image(b_matrix)

# create a symmetric connectivity matrix where the connectivity between
# two planning units corresponds to their spatial proximity
# i.e., planning units that are further apart share less connectivity
centroids <- sf::st_coordinates(
  suppressWarnings(sf::st_centroid(sim_pu_polygons))
)
d_matrix <- (1 / (Matrix::Matrix(as.matrix(dist(centroids))) + 1))

# rescale matrix values to have a maximum value of 1
d_matrix <- rescale_matrix(d_matrix, max = 1)

# remove connections between planning units with values below a threshold to
# reduce run-time
d_matrix[d_matrix < 0.8] <- 0

# visualize connectivity matrix
image(d_matrix)

# create a symmetric connectivity matrix where the connectivity
# between adjacent two planning units corresponds to their combined
# value in a column of the planning unit data

# for example, this column could describe the extent of native vegetation in
# each planning unit and we could use connectivity penalties to identify
# solutions that cluster planning units together that both contain large
# amounts of native vegetation

c_matrix <- connectivity_matrix(sim_pu_polygons, "cost")

# rescale matrix values to have a maximum value of 1
c_matrix <- rescale_matrix(c_matrix, max = 1)

# visualize connectivity matrix
image(c_matrix)

# create penalties
penalties <- c(10, 25)

# create problems using the different connectivity matrices and penalties
p2 <- list(
  p1,
  p1 %>% add_connectivity_penalties(penalties[1], data = b_matrix),
  p1 %>% add_connectivity_penalties(penalties[2], data = b_matrix),
  p1 %>% add_connectivity_penalties(penalties[1], data = d_matrix),
  p1 %>% add_connectivity_penalties(penalties[2], data = d_matrix),
  p1 %>% add_connectivity_penalties(penalties[1], data = c_matrix),
  p1 %>% add_connectivity_penalties(penalties[2], data = c_matrix)
)

# solve problems
s2 <- lapply(p2, solve)

# create single object with all solutions
s2 <- sf::st_sf(
  tibble::tibble(
    p2_1 = s2[[1]]$solution_1,
    p2_2 = s2[[2]]$solution_1,
    p2_3 = s2[[3]]$solution_1,
    p2_4 = s2[[4]]$solution_1,
    p2_5 = s2[[5]]$solution_1,
    p2_6 = s2[[6]]$solution_1,
    p2_7 = s2[[7]]$solution_1
  ),
  geometry = sf::st_geometry(s2[[1]])
)

names(s2)[1:7] <- c(
  "basic problem",
  paste0("b_matrix (", penalties,")"),
  paste0("d_matrix (", penalties,")"),
  paste0("c_matrix (", penalties,")")
)

# plot solutions
plot(s2)

# create minimal multi-zone problem and limit solver to one minute
# to obtain solutions in a short period of time
p3 <-
  problem(sim_zones_pu_raster, sim_zones_features) %>%
  add_min_set_objective() %>%
  add_relative_targets(matrix(0.15, nrow = 5, ncol = 3)) %>%
  add_binary_decisions() %>%
  add_default_solver(time_limit = 60, verbose = FALSE)

# create matrix showing which planning units are adjacent to other units
a_matrix <- adjacency_matrix(sim_zones_pu_raster)

# visualize matrix
image(a_matrix)

# create a zone matrix where connectivities are only present between
# planning units that are allocated to the same zone
zm1 <- as(diag(3), "Matrix")

# print zone matrix
print(zm1)

# create a zone matrix where connectivities are strongest between
# planning units allocated to different zones
zm2 <- matrix(1, ncol = 3, nrow = 3)
diag(zm2) <- 0
zm2 <- as(zm2, "Matrix")

# print zone matrix
print(zm2)

# create a zone matrix that indicates that connectivities between planning
# units assigned to the same zone are much higher than connectivities
# assigned to different zones
zm3 <- matrix(0.1, ncol = 3, nrow = 3)
diag(zm3) <- 1
zm3 <- as(zm3, "Matrix")

# print zone matrix
print(zm3)

# create a zone matrix that indicates that connectivities between planning
# units allocated to zone 1 are very high, connectivities between planning
# units allocated to zones 1 and 2 are moderately high, and connectivities
# planning units allocated to other zones are low
zm4 <- matrix(0.1, ncol = 3, nrow = 3)
zm4[1, 1] <- 1
zm4[1, 2] <- 0.5
zm4[2, 1] <- 0.5
zm4 <- as(zm4, "Matrix")

# print zone matrix
print(zm4)

# create a zone matrix with strong connectivities between planning units
# allocated to the same zone, moderate connectivities between planning
# unit allocated to zone 1 and zone 2, and negative connectivities between
# planning units allocated to zone 3 and the other two zones
zm5 <- matrix(-1, ncol = 3, nrow = 3)
zm5[1, 2] <- 0.5
zm5[2, 1] <- 0.5
diag(zm5) <- 1
zm5 <- as(zm5, "Matrix")

# print zone matrix
print(zm5)

# create vector of penalties to use creating problems
penalties2 <- c(5, 15)

# create multi-zone problems using the adjacent connectivity matrix and
# different zone matrices
p4 <- list(
  p3,
  p3 %>% add_connectivity_penalties(penalties2[1], zm1, a_matrix),
  p3 %>% add_connectivity_penalties(penalties2[2], zm1, a_matrix),
  p3 %>% add_connectivity_penalties(penalties2[1], zm2, a_matrix),
  p3 %>% add_connectivity_penalties(penalties2[2], zm2, a_matrix),
  p3 %>% add_connectivity_penalties(penalties2[1], zm3, a_matrix),
  p3 %>% add_connectivity_penalties(penalties2[2], zm3, a_matrix),
  p3 %>% add_connectivity_penalties(penalties2[1], zm4, a_matrix),
  p3 %>% add_connectivity_penalties(penalties2[2], zm4, a_matrix),
  p3 %>% add_connectivity_penalties(penalties2[1], zm5, a_matrix),
  p3 %>% add_connectivity_penalties(penalties2[2], zm5, a_matrix)
)

# solve problems
s4 <- lapply(p4, solve)
s4 <- lapply(s4, category_layer)
s4 <- terra::rast(s4)
names(s4) <-  c(
  "basic problem",
  paste0("zm", rep(seq_len(5), each = 2), " (", rep(penalties2, 2), ")")
)

# plot solutions
plot(s4, axes = FALSE)

# create an array to manually specify the connectivities between
# each planning unit when they are allocated to each different zone

# for real-world problems, these connectivities would be generated using
# data - but here these connectivity values are assigned as random
# ones or zeros
c_array <- array(0, c(rep(ncell(sim_zones_pu_raster[[1]]), 2), 3, 3))
for (z1 in seq_len(3))
  for (z2 in seq_len(3))
    c_array[, , z1, z2] <- round(
      runif(ncell(sim_zones_pu_raster[[1]]) ^ 2, 0, 0.505)
    )

# create a problem with the manually specified connectivity array
# note that the zones argument is set to NULL because the connectivity
# data is an array
p5 <- list(
  p3,
  p3 %>% add_connectivity_penalties(15, zones = NULL, c_array)
)

# solve problems
s5 <- lapply(p5, solve)
s5 <- lapply(s5, category_layer)
s5 <- terra::rast(s5)
names(s5) <- c("basic problem", "connectivity array")

# plot solutions
plot(s5, axes = FALSE)

## End(Not run)

Description

Add constraints to a conservation planning problem to ensure that all selected planning units are spatially connected with each other and form a single contiguous unit.

Usage

## S4 method for signature 'ConservationProblem,ANY,ANY'
add_contiguity_constraints(x, zones, data)

## S4 method for signature 'ConservationProblem,ANY,data.frame'
add_contiguity_constraints(x, zones, data)

## S4 method for signature 'ConservationProblem,ANY,matrix'
add_contiguity_constraints(x, zones, data)

Arguments

Details

This function uses connection data to identify solutions that form a single contiguous unit. It was inspired by the mathematical formulations detailed in Önal and Briers (2006).

Value

An updated problem() object with the constraints added to it.

Data format

The argument to data can be specified using the following formats.

data as a NULL value

indicating that connection data should be calculated automatically using the adjacency_matrix() function. This is the default argument. Note that the connection data must be manually defined using one of the other formats below when the planning unit data in the argument to x is not spatially referenced (e.g., in data.frame or numeric format).

data as a matrix/Matrix object

where rows and columns represent different planning units and the value of each cell indicates if the two planning units are connected or not. Cell values should be binary numeric values (i.e., one or zero). Cells that occur along the matrix diagonal have no effect on the solution at all because each planning unit cannot be a connected with itself.

data as a data.frame object

containing columns that are named "id1", "id2", and "boundary". Here, each row denotes the connectivity between two planning units following the Marxan format. The "boundary" column should contain binary numeric values that indicate if the two planning units specified in the "id1" and "id2" columns are connected or not. This data can be used to describe symmetric or asymmetric relationships between planning units. By default, input data is assumed to be symmetric unless asymmetric data is also included (e.g., if data is present for planning units 2 and 3, then the same amount of connectivity is expected for planning units 3 and 2, unless connectivity data is also provided for planning units 3 and 2).

Notes

In early versions, this function was named as the add_connected_constraints() function.

References

Önal H and Briers RA (2006) Optimal selection of a connected reserve network. Operations Research, 54: 379–388.

See Also

See constraints for an overview of all functions for adding constraints.

Other constraints: add_feature_contiguity_constraints(), add_linear_constraints(), add_locked_in_constraints(), add_locked_out_constraints(), add_mandatory_allocation_constraints(), add_manual_bounded_constraints(), add_manual_locked_constraints(), add_neighbor_constraints()

Examples

## Not run: 
# load data
sim_pu_raster <- get_sim_pu_raster()
sim_features <- get_sim_features()
sim_zones_pu_raster <- get_sim_zones_pu_raster()
sim_zones_features <- get_sim_zones_features()

# create minimal problem
p1 <-
  problem(sim_pu_raster, sim_features) %>%
  add_min_set_objective() %>%
  add_relative_targets(0.2) %>%
  add_binary_decisions() %>%
  add_default_solver(verbose = FALSE)

# create problem with added connected constraints
p2 <- p1 %>% add_contiguity_constraints()

# solve problems
s1 <- c(solve(p1), solve(p2))
names(s1) <- c("basic solution", "connected solution")

# plot solutions
plot(s1, axes = FALSE)

# create minimal problem with multiple zones, and limit the solver to
# 30 seconds to obtain solutions in a feasible period of time
p3 <-
  problem(sim_zones_pu_raster, sim_zones_features) %>%
  add_min_set_objective() %>%
  add_relative_targets(matrix(0.2, ncol = 3, nrow = 5)) %>%
  add_binary_decisions() %>%
  add_default_solver(time_limit = 30, verbose = FALSE)

# create problem with added constraints to ensure that the planning units
# allocated to each zone form a separate contiguous unit
z4 <- diag(3)
print(z4)
p4 <- p3 %>% add_contiguity_constraints(z4)

# create problem with added constraints to ensure that the planning
# units allocated to each zone form a separate contiguous unit,
# except for planning units allocated to zone 3 which do not need
# form a single contiguous unit
z5 <- diag(3)
z5[3, 3] <- 0
print(z5)
p5 <- p3 %>% add_contiguity_constraints(z5)

# create problem with added constraints that ensure that the planning
# units allocated to zones 1 and 2 form a contiguous unit
z6 <- diag(3)
z6[1, 2] <- 1
z6[2, 1] <- 1
print(z6)
p6 <- p3 %>% add_contiguity_constraints(z6)

# solve problems
s2 <- lapply(list(p3, p4, p5, p6), solve)
s2 <- lapply(s2, category_layer)
s2 <- terra::rast(s2)
names(s2) <- c("basic solution", "p4", "p5", "p6")

# plot solutions
plot(s2, axes = FALSE)

# create a problem that has a main "reserve zone" and a secondary
# "corridor zone" to connect up import areas. Here, each feature has a
# target of 50% of its distribution. If a planning unit is allocated to the
# "reserve zone", then the prioritization accrues 100% of the amount of
# each feature in the planning unit. If a planning unit is allocated to the
# "corridor zone" then the prioritization accrues 40% of the amount of each
# feature in the planning unit. Also, the cost of managing a planning unit
# in the "corridor zone" is 30% of that when it is managed as the
# "reserve zone". Finally, the problem has constraints which
# ensure that all of the selected planning units form a single contiguous
# unit, so that the planning units allocated to the "corridor zone" can
# link up the planning units allocated to the "reserve zone"

# create planning unit data
pus <- sim_zones_pu_raster[[c(1, 1)]]
pus[[2]] <- pus[[2]] * 0.3
print(pus)

# create biodiversity data
fts <- zones(
  sim_features, sim_features * 0.4,
  feature_names = names(sim_features),
  zone_names = c("reserve zone", "corridor zone")
)
print(fts)

# create targets
targets <- tibble::tibble(
  feature = names(sim_features),
  zone = list(zone_names(fts))[rep(1, 5)],
  target = terra::global(sim_features, "sum", na.rm = TRUE)[[1]] * 0.5,
  type = rep("absolute", 5)
)
print(targets)

# create zones matrix
z7 <- matrix(1, ncol = 2, nrow = 2)
print(z7)

# create problem
p7 <-
  problem(pus, fts) %>%
  add_min_set_objective() %>%
  add_manual_targets(targets) %>%
  add_contiguity_constraints(z7) %>%
  add_binary_decisions() %>%
  add_default_solver(verbose = FALSE)

# solve problems
s7 <- category_layer(solve(p7))

# plot solutions
plot(s7, main = "solution", axes = FALSE)

## End(Not run)

Description

Specify that the IBM CPLEX software should be used to solve a conservation planning problem (IBM 2017) . This function can also be used to customize the behavior of the solver. It requires the cplexAPI package to be installed (see below for installation instructions).

Usage

add_cplex_solver(
  x,
  gap = 0.1,
  time_limit = .Machine$integer.max,
  presolve = TRUE,
  threads = 1,
  verbose = TRUE
)

Arguments

Details

IBM CPLEX is a commercial optimization software. It is faster than the available open source solvers (e.g., add_lpsymphony_solver() and add_rsymphony_solver(). Although formal benchmarks examining the performance of this solver for conservation planning problems have yet to be completed, preliminary analyses suggest that it performs slightly slower than the Gurobi solver (i.e., add_gurobi_solver()). We recommend using this solver if the Gurobi solver is not available. Licenses are available for the IBM CPLEX software to academics at no cost (see < https://www.ibm.com/products/ilog-cplex-optimization-studio/cplex-optimizer>).

Value

An updated problem() object with the solver added to it.

Installation

The cplexAPI package is used to interface with IBM CPLEX software. To install the package, the IBM CPLEX software must be installed (see https://www.ibm.com/products/ilog-cplex-optimization-studio/cplex-optimizer). Next, the CPLEX_BIN environmental variable must be set to specify the file path for the IBM CPLEX software. For example, on a Linux system, this variable can be specified by adding the following text to the ⁠~/.bashrc⁠ file:

  export CPLEX_BIN="/opt/ibm/ILOG/CPLEX_Studio128/cplex/bin/x86-64_linux/cplex"

Please Note that you may need to change the version number in the file path (i.e., "CPLEX_Studio128"). After specifying the CPLEX_BIN environmental variable, the cplexAPI package can be installed. Since the cplexAPI package is not available on the the Comprehensive R Archive Network (CRAN), it must be installed from its GitHub repository. To install the cplexAPI package, please use the following code:

if (!require(remotes)) install.packages("remotes")
remotes::install_github("cran/cplexAPI")

For further details on installing this package, please consult the installation instructions.

References

IBM (2017) IBM ILOG CPLEX Optimization Studio CPLEX User's Manual. Version 12 Release 8. IBM ILOG CPLEX Division, Incline Village, NV.

See Also

Other solvers: add_cbc_solver(), add_default_solver(), add_gurobi_solver(), add_highs_solver(), add_lsymphony_solver, add_rsymphony_solver()

Examples

## Not run: 
# load data
sim_pu_raster <- get_sim_pu_raster()
sim_features <- get_sim_features()

# create problem
p <-
  problem(sim_pu_raster, sim_features) %>%
  add_min_set_objective() %>%
  add_relative_targets(0.1) %>%
  add_binary_decisions() %>%
  add_cplex_solver(gap = 0.1, time_limit = 5, verbose = FALSE)

# generate solution
s <- solve(p)

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

## End(Not run)

Description

Generate a portfolio of solutions for a conservation planning problem using Bender's cuts (discussed in Rodrigues et al. 2000). This is recommended as a replacement for add_gap_portfolio() when the Gurobi software is not available.

Usage

add_cuts_portfolio(x, number_solutions = 10)

Arguments

Details

This strategy for generating a portfolio of solutions involves solving the problem multiple times and adding additional constraints to forbid previously obtained solutions. In general, this strategy is most useful when problems take a long time to solve and benefit from having multiple threads allocated for solving an individual problem.

Value

An updated problem() object with the portfolio added to it.

Notes

In early versions (< 4.0.1), this function was only compatible with Gurobi (i.e., add_gurobi_solver()). To provide functionality with exact algorithm solvers, this function now adds constraints to the problem formulation to generate multiple solutions.

References

Rodrigues AS, Cerdeira OJ, and Gaston KJ (2000) Flexibility, efficiency, and accountability: adapting reserve selection algorithms to more complex conservation problems. Ecography, 23: 565–574.

See Also

See portfolios for an overview of all functions for adding a portfolio.

Other portfolios: add_default_portfolio(), add_extra_portfolio(), add_gap_portfolio(), add_shuffle_portfolio(), add_top_portfolio()

Examples

## Not run: 
# set seed for reproducibility
set.seed(500)

# load data
sim_pu_raster <- get_sim_pu_raster()
sim_features <- get_sim_features()
sim_zones_pu_raster <- get_sim_zones_pu_raster()
sim_zones_features <- get_sim_zones_features()

# create minimal problem with cuts portfolio
p1 <-
  problem(sim_pu_raster, sim_features) %>%
  add_min_set_objective() %>%
  add_relative_targets(0.2) %>%
  add_cuts_portfolio(10) %>%
  add_default_solver(gap = 0.2, verbose = FALSE)

# solve problem and generate 10 solutions within 20% of optimality
s1 <- solve(p1)

# convert portfolio into a multi-layer raster object
s1 <- terra::rast(s1)

# plot solutions in portfolio
plot(s1, axes = FALSE)

# build multi-zone conservation problem with cuts portfolio
p2 <-
 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_cuts_portfolio(10) %>%
 add_default_solver(gap = 0.2, verbose = FALSE)

# solve the problem
s2 <- solve(p2)

# print solution
str(s2, max.level = 1)

# convert each solution in the portfolio into a single category layer
s2 <- terra::rast(lapply(s2, category_layer))

# plot solutions in portfolio
plot(s2, main = "solution", axes = FALSE)

## End(Not run)

Description

Generate a portfolio containing a single solution.

Usage

add_default_portfolio(x)

Arguments

Details

By default, this is portfolio is added to problem() objects if no other portfolios is manually specified.

Value

An updated problem() object with the portfolio added to it.

See Also

See portfolios for an overview of all functions for adding a portfolio.

Other portfolios: add_cuts_portfolio(), add_extra_portfolio(), add_gap_portfolio(), add_shuffle_portfolio(), add_top_portfolio()

Description

Specify that the best solver currently available should be used to solve a conservation planning problem.

Usage

add_default_solver(x, ...)

Arguments

Details

Ranked from best to worst, the available solvers that can be used are: add_gurobi_solver(), add_cplex_solver(), add_cbc_solver(), add_highs_solver(), add_lpsymphony_solver(), and finally add_rsymphony_solver(). For information on the performance of different solvers, please see Schuster et al. (2020).

Value

An updated problem() object with the solver added to it.

References

Schuster R, Hanson JO, Strimas-Mackey M, and Bennett JR (2020). Exact integer linear programming solvers outperform simulated annealing for solving conservation planning problems. PeerJ, 8: e9258.

See Also

See solvers for an overview of all functions for adding a solver.

Other solvers: add_cbc_solver(), add_cplex_solver(), add_gurobi_solver(), add_highs_solver(), add_lsymphony_solver, add_rsymphony_solver()

Description

Generate a portfolio of solutions for a conservation planning problem by storing feasible solutions discovered during the optimization process. This method is useful for quickly obtaining multiple solutions, but does not provide any guarantees on the number of solutions, or the quality of solutions.

Usage

add_extra_portfolio(x)

Arguments

Details

This strategy for generating a portfolio requires problems to be solved using the Gurobi software suite (i.e., using add_gurobi_solver(). Specifically, version 8.0.0 (or greater) of the gurobi package must be installed.

Value

An updated problem() object with the portfolio added to it.

See Also

See portfolios for an overview of all functions for adding a portfolio.

Other portfolios: add_cuts_portfolio(), add_default_portfolio(), add_gap_portfolio(), add_shuffle_portfolio(), add_top_portfolio()

Examples

## Not run: 
# set seed for reproducibility
set.seed(600)

# load data
sim_pu_raster <- get_sim_pu_raster()
sim_features <- get_sim_features()
sim_zones_pu_raster <- get_sim_zones_pu_raster()
sim_zones_features <- get_sim_zones_features()

# create minimal problem with a portfolio for extra solutions
p1 <-
  problem(sim_pu_raster, sim_features) %>%
  add_min_set_objective() %>%
  add_relative_targets(0.05) %>%
  add_extra_portfolio() %>%
  add_default_solver(gap = 0, verbose = FALSE)

# solve problem and generate portfolio
s1 <- solve(p1)

# convert portfolio into a multi-layer raster object
s1 <- terra::rast(s1)

# print number of solutions found
print(terra::nlyr(s1))

# plot solutions
plot(s1, axes = FALSE)

# create multi-zone problem with a portfolio for extra solutions
p2 <-
  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_extra_portfolio() %>%
  add_default_solver(gap = 0, verbose = FALSE)

# solve problem and generate portfolio
s2 <- solve(p2)

# convert each solution in the portfolio into a single category layer
s2 <- terra::rast(lapply(s2, category_layer))

# print number of solutions found
print(terra::nlyr(s2))

# plot solutions in portfolio
plot(s2, axes = FALSE)

## End(Not run)

Description

Add constraints to a problem to ensure that each feature is represented in a contiguous unit of dispersible habitat. These constraints are a more advanced version of those implemented in the add_contiguity_constraints() function, because they ensure that each feature is represented in a contiguous unit and not that the entire solution should form a contiguous unit. Additionally, this function can use data showing the distribution of dispersible habitat for each feature to ensure that all features can disperse throughout the areas designated for their conservation.

Usage

## S4 method for signature 'ConservationProblem,ANY,data.frame'
add_feature_contiguity_constraints(x, zones, data)

## S4 method for signature 'ConservationProblem,ANY,matrix'
add_feature_contiguity_constraints(x, zones, data)

## S4 method for signature 'ConservationProblem,ANY,ANY'
add_feature_contiguity_constraints(x, zones, data)

Arguments

Details

This function uses connection data to identify solutions that represent features in contiguous units of dispersible habitat. It was inspired by the mathematical formulations detailed in Önal and Briers (2006) and Cardeira et al. 2010. For an example that has used these constraints, see Hanson et al. (2019). Please note that these constraints require the expanded formulation and therefore cannot be used with feature data that have negative vales. Please note that adding these constraints to a problem will drastically increase the amount of time required to solve it.

Value

An updated problem() object with the constraints added to it.

Data format

The argument to data can be specified using the following formats.

data as a NULL value

connection data should be calculated automatically using the adjacency_matrix() function. This is the default argument and means that all adjacent planning units are treated as potentially dispersible for all features. Note that the connection data must be manually defined using one of the other formats below when the planning unit data in the argument to x is not spatially referenced (e.g., in data.frame or numeric format).

data as amatrix/Matrix object

where rows and columns represent different planning units and the value of each cell indicates if the two planning units are connected or not. Cell values should be binary numeric values (i.e., one or zero). Cells that occur along the matrix diagonal have no effect on the solution at all because each planning unit cannot be a connected with itself. Note that pairs of connected planning units are treated as being potentially dispersible for all features.

data as a data.frame object

containing columns that are named "id1", "id2", and "boundary". Here, each row denotes the connectivity between two planning units following the Marxan format. The "boundary" column should contain binary numeric values that indicate if the two planning units specified in the "id1" and "id2" columns are connected or not. This data can be used to describe symmetric or asymmetric relationships between planning units. By default, input data is assumed to be symmetric unless asymmetric data is also included (e.g., if data is present for planning units 2 and 3, then the same amount of connectivity is expected for planning units 3 and 2, unless connectivity data is also provided for planning units 3 and 2). Note that pairs of connected planning units are treated as being potentially dispersible for all features.

data as a list object

containing matrix, Matrix, or data.frame objects showing which planning units should be treated as connected for each feature. Each element in the list should correspond to a different feature (specifically, a different target in the problem), and should contain a matrix, Matrix, or data.frame object that follows the conventions detailed above.

Notes

In early versions, it was named as the add_corridor_constraints function.

References

Önal H and Briers RA (2006) Optimal selection of a connected reserve network. Operations Research, 54: 379–388.

Cardeira JO, Pinto LS, Cabeza M and Gaston KJ (2010) Species specific connectivity in reserve-network design using graphs. Biological Conservation, 2: 408–415.

Hanson JO, Fuller RA, & Rhodes JR (2019) Conventional methods for enhancing connectivity in conservation planning do not always maintain gene flow. Journal of Applied Ecology, 56: 913–922.

See Also

See constraints for an overview of all functions for adding constraints.

Other constraints: add_contiguity_constraints(), add_linear_constraints(), add_locked_in_constraints(), add_locked_out_constraints(), add_mandatory_allocation_constraints(), add_manual_bounded_constraints(), add_manual_locked_constraints(), add_neighbor_constraints()

Examples

## Not run: 
# load data
sim_pu_raster <- get_sim_pu_raster()
sim_features <- get_sim_features()
sim_zones_pu_raster <- get_sim_zones_pu_raster()
sim_zones_features <- get_sim_zones_features()

# create minimal problem
p1 <-
  problem(sim_pu_raster, sim_features) %>%
  add_min_set_objective() %>%
  add_relative_targets(0.3) %>%
  add_binary_decisions() %>%
  add_default_solver(verbose = FALSE)

# create problem with contiguity constraints
p2 <- p1 %>% add_contiguity_constraints()

# create problem with constraints to represent features in contiguous
# units
p3 <- p1 %>% add_feature_contiguity_constraints()

# create problem with constraints to represent features in contiguous
# units that contain highly suitable habitat values
# (specifically in the top 5th percentile)
cm4 <- lapply(seq_len(terra::nlyr(sim_features)), function(i) {
  # create connectivity matrix using the i'th feature's habitat data
  m <- connectivity_matrix(sim_pu_raster, sim_features[[i]])
  # convert matrix to 0/1 values denoting values in top 5th percentile
  m <- round(m > quantile(as.vector(m), 1 - 0.05, names = FALSE))
  # remove 0s from the sparse matrix
  m <- Matrix::drop0(m)
  # return matrix
  m
})
p4 <- p1 %>% add_feature_contiguity_constraints(data = cm4)

# solve problems
s1 <- c(solve(p1), solve(p2), solve(p3), solve(p4))
names(s1) <- c(
  "basic solution", "contiguity constraints",
  "feature contiguity constraints",
  "feature contiguity constraints with data"
)
# plot solutions
plot(s1, axes = FALSE)

# create minimal problem with multiple zones, and limit the solver to
# 30 seconds to obtain solutions in a feasible period of time
p5 <-
  problem(sim_zones_pu_raster, sim_zones_features) %>%
  add_min_set_objective() %>%
  add_relative_targets(matrix(0.1, ncol = 3, nrow = 5)) %>%
  add_binary_decisions() %>%
  add_default_solver(time_limit = 30, verbose = FALSE)

# create problem with contiguity constraints that specify that the
# planning units used to conserve each feature in different management
# zones must form separate contiguous units
p6 <- p5 %>% add_feature_contiguity_constraints(diag(3))

# create problem with contiguity constraints that specify that the
# planning units used to conserve each feature must form a single
# contiguous unit if the planning units are allocated to zones 1 and 2
# and do not need to form a single contiguous unit if they are allocated
# to zone 3
zm7 <- matrix(0, ncol = 3, nrow = 3)
zm7[seq_len(2), seq_len(2)] <- 1
print(zm7)
p7 <- p5 %>% add_feature_contiguity_constraints(zm7)

# create problem with contiguity constraints that specify that all of
# the planning units in all three of the zones must conserve first feature
# in a single contiguous unit but the planning units used to conserve the
# remaining features do not need to be contiguous in any way
zm8 <- lapply(
  seq_len(number_of_features(sim_zones_features)),
  function(i) matrix(ifelse(i == 1, 1, 0), ncol = 3, nrow = 3)
)
print(zm8)
p8 <- p5 %>% add_feature_contiguity_constraints(zm8)

# solve problems
s2 <- lapply(list(p5, p6, p7, p8), solve)
s2 <- terra::rast(lapply(s2, category_layer))
names(s2) <- c("p5", "p6", "p7", "p8")
# plot solutions
plot(s2, axes = FALSE)

## End(Not run)

Description

Add features weights to a conservation planning problem. Specifically, some objective functions aim to maximize (or minimize) a metric that measures how well a set of features are represented by a solution (e.g., maximize the number of features that are adequately represented, add_max_features_objective()). In such cases, it may be desirable to prefer the representation of some features over other features (e.g., features that have higher extinction risk might be considered more important than those with lower extinction risk). To achieve this, weights can be used to specify how much more important it is for a solution to represent particular features compared with other features.

Usage

## S4 method for signature 'ConservationProblem,numeric'
add_feature_weights(x, weights)

## S4 method for signature 'ConservationProblem,matrix'
add_feature_weights(x, weights)

Arguments

Details

Weights can only be applied to problems that have an objective that is budget limited (e.g., add_max_cover_objective(), add_min_shortfall_objective()). They can also be applied to problems that aim to maximize phylogenetic representation (add_max_phylo_div_objective()) to favor the representation of specific features over the representation of some phylogenetic branches. Weights cannot be negative values and must have values that are equal to or larger than zero. Note that planning unit costs are scaled to 0.01 to identify the cheapest solution among multiple optimal solutions. This means that the optimization process will favor cheaper solutions over solutions that meet feature targets (or occurrences) when feature weights are lower than 0.01.

Value

An updated problem() with the weights added to it.

Weights format

The argument to weights can be specified using the following formats.

weights as a numeric vector

containing weights for each feature. Note that this format cannot be used to specify weights for problems with multiple zones.

weights as a matrix object

containing weights 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 weight value for a given feature that the solution can to secure in a given zone. Note that if the problem contains targets created using add_manual_targets() then a matrix should be supplied containing a single column that indicates that weight for fulfilling each target.

See Also

See penalties for an overview of all functions for adding penalties.

Other penalties: add_asym_connectivity_penalties(), add_boundary_penalties(), add_connectivity_penalties(), add_linear_penalties()

Examples

## Not run: 
# load package
require(ape)

# load data
sim_pu_raster <- get_sim_pu_raster()
sim_features <- get_sim_features()
sim_phylogeny <- get_sim_phylogeny()
sim_zones_pu_raster <- get_sim_zones_pu_raster()
sim_zones_features <- get_sim_zones_features()

# create minimal problem that aims to maximize the number of features
# adequately conserved given a total budget of 3800. Here, each feature
# needs 20% of its habitat for it to be considered adequately conserved
p1 <-
  problem(sim_pu_raster, sim_features) %>%
  add_max_features_objective(budget = 3800) %>%
  add_relative_targets(0.2) %>%
  add_binary_decisions() %>%
  add_default_solver(verbose = FALSE)

# create weights that assign higher importance to features with less
# suitable habitat in the study area
w2 <- exp((1 / terra::global(sim_features, "sum", na.rm = TRUE)[[1]]) * 200)

# create problem using rarity weights
p2 <- p1 %>% add_feature_weights(w2)

# create manually specified weights that assign higher importance to
# certain features. These weights could be based on a pre-calculated index
# (e.g., an index measuring extinction risk where higher values
# denote higher extinction risk)
w3 <- c(0, 0, 0, 100, 200)
p3 <- p1 %>% add_feature_weights(w3)

# solve problems
s1 <- c(solve(p1), solve(p2), solve(p3))
names(s1) <- c("equal weights", "rarity weights", "manual weights")

# plot solutions
plot(s1, axes = FALSE)

# plot the example phylogeny
par(mfrow = c(1, 1))
plot(sim_phylogeny, main = "simulated phylogeny")

# create problem with a maximum phylogenetic diversity objective,
# where each feature needs 10% of its distribution to be secured for
# it to be adequately conserved and a total budget of 1900
p4 <-
  problem(sim_pu_raster, sim_features) %>%
  add_max_phylo_div_objective(1900, sim_phylogeny) %>%
  add_relative_targets(0.1) %>%
  add_binary_decisions() %>%
  add_default_solver(verbose = FALSE)

# solve problem
s4 <- solve(p4)

# plot solution
plot(s4, main = "solution", axes = FALSE)

# find out which features have their targets met
r4 <- eval_target_coverage_summary(p4, s4)
print(r4, width = Inf)

# plot the example phylogeny and color the represented features in red
plot(
  sim_phylogeny, main = "represented features",
  tip.color = replace(
    rep("black", terra::nlyr(sim_features)), which(r4$met), "red"
  )
)

# we can see here that the third feature ("layer.3", i.e.,
# sim_features[[3]]) is not represented in the solution. Let us pretend
# that it is absolutely critical this feature is adequately conserved
# in the solution. For example, this feature could represent a species
# that plays important role in the ecosystem, or a species that is
# important commercial activities (e.g., eco-tourism). So, to generate
# a solution that conserves the third feature whilst also aiming to
# maximize phylogenetic diversity, we will create a set of weights that
# assign a particularly high weighting to the third feature
w5 <- c(0, 0, 10000, 0, 0)

# we can see that this weighting (i.e., w5[3]) has a much higher value than
# the branch lengths in the phylogeny so solutions that represent this
# feature be much closer to optimality
print(sim_phylogeny$edge.length)

# create problem with high weighting for the third feature and solve it
s5 <- p4 %>% add_feature_weights(w5) %>% solve()

# plot solution
plot(s5, main = "solution", axes = FALSE)

# find which features have their targets met
r5 <- eval_target_coverage_summary(p4, s5)
print(r5, width = Inf)

# plot the example phylogeny and color the represented features in red
# here we can see that this solution only adequately conserves the
# third feature. This means that, given the budget, we are faced with the
# trade-off of conserving either the third feature, or a phylogenetically
# diverse set of three different features.
plot(
  sim_phylogeny, main = "represented features",
  tip.color = replace(
    rep("black", terra::nlyr(sim_features)), which(r5$met), "red"
  )
)

# create multi-zone problem with maximum features objective,
# with 10% representation targets for each feature, and set
# a budget such that the total maximum expenditure in all zones
# cannot exceed 3000
p6 <-
  problem(sim_zones_pu_raster, sim_zones_features) %>%
  add_max_features_objective(3000) %>%
  add_relative_targets(matrix(0.1, ncol = 3, nrow = 5)) %>%
  add_binary_decisions() %>%
  add_default_solver(verbose = FALSE)

# create weights that assign equal weighting for the representation
# of each feature in each zone except that it does not matter if
# feature 1 is represented in zone 1 and it really important
# that feature 3 is really in zone 1
w7 <- matrix(1, ncol = 3, nrow = 5)
w7[1, 1] <- 0
w7[3, 1] <- 100

# create problem with weights
p7 <- p6 %>% add_feature_weights(w7)

# solve problems
s6 <- solve(p6)
s7 <- solve(p7)

# convert solutions to category layers
c6 <- category_layer(s6)
c7 <- category_layer(s7)

# plot solutions
plot(c(c6, c7), main = c("equal weights", "manual weights"), axes = FALSE)

# create minimal problem to show the correct method for setting
# weights for problems with manual targets
p8 <-
  problem(sim_pu_raster, sim_features) %>%
  add_max_features_objective(budget = 3000) %>%
  add_manual_targets(
    data.frame(
    feature = c("feature_1", "feature_4"),
    type = "relative",
    target = 0.1)
  ) %>%
  add_feature_weights(matrix(c(1, 200), ncol = 1)) %>%
  add_binary_decisions() %>%
  add_default_solver(verbose = FALSE)

# solve problem
s8 <- solve(p8)

# plot solution
plot(s8, main = "solution", axes = FALSE)

## End(Not run)

Description

Generate a portfolio of solutions for a conservation planning problem by finding a certain number of solutions that are all within a pre-specified optimality gap. This method is useful for generating multiple solutions that can be used to calculate selection frequencies for moderate and large-sized problems (similar to Marxan).

Usage

add_gap_portfolio(x, number_solutions = 10, pool_gap = 0.1)

Arguments

Details

This strategy for generating a portfolio requires problems to be solved using the Gurobi software suite (i.e., using add_gurobi_solver(). Specifically, version 9.0.0 (or greater) of the gurobi package must be installed. Note that the number of solutions returned may be less than the argument to number_solutions, if the total number of solutions that meet the optimality gap is less than the number of solutions requested. Also, note that this portfolio function only works with problems that have binary decisions (i.e., specified using add_binary_decisions()).

Value

An updated problem() object with the portfolio added to it.

See Also

See portfolios for an overview of all functions for adding a portfolio.

Other portfolios: add_cuts_portfolio(), add_default_portfolio(), add_extra_portfolio(), add_shuffle_portfolio(), add_top_portfolio()

Examples

## Not run: 
# set seed for reproducibility
set.seed(600)

# load data
sim_pu_raster <- get_sim_pu_raster()
sim_features <- get_sim_features()
sim_zones_pu_raster <- get_sim_zones_pu_raster()
sim_zones_features <- get_sim_zones_features()

# create minimal problem with a portfolio containing 10 solutions within 20%
# of optimality
p1 <-
  problem(sim_pu_raster, sim_features) %>%
  add_min_set_objective() %>%
  add_relative_targets(0.05) %>%
  add_gap_portfolio(number_solutions = 5, pool_gap = 0.2) %>%
  add_default_solver(gap = 0, verbose = FALSE)

# solve problem and generate portfolio
s1 <- solve(p1)

# convert portfolio into a multi-layer raster
s1 <- terra::rast(s1)

# print number of solutions found
print(terra::nlyr(s1))

# plot solutions
plot(s1, axes = FALSE)

# create multi-zone  problem with a portfolio containing 10 solutions within
# 20% of optimality
p2 <-
  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_gap_portfolio(number_solutions = 5, pool_gap = 0.2) %>%
  add_default_solver(gap = 0, verbose = FALSE)

# solve problem and generate portfolio
s2 <- solve(p2)

# convert portfolio into a multi-layer raster of category layers
s2 <- terra::rast(lapply(s2, category_layer))

# print number of solutions found
print(terra::nlyr(s2))

# plot solutions in portfolio
plot(s2, axes = FALSE)

## End(Not run)

Description

Specify that the Gurobi software should be used to solve a conservation planning problem (Gurobi Optimization LLC 2021). This function can also be used to customize the behavior of the solver. It requires the gurobi package to be installed (see below for installation instructions).

Usage

add_gurobi_solver(
  x,
  gap = 0.1,
  time_limit = .Machine$integer.max,
  presolve = 2,
  threads = 1,
  first_feasible = FALSE,
  numeric_focus = FALSE,
  node_file_start = Inf,
  start_solution = NULL,
  verbose = TRUE
)

Arguments

Details

Gurobi is a state-of-the-art commercial optimization software with an R package interface. It is by far the fastest of the solvers available for generating prioritizations, however, it is not freely available. That said, licenses are available to academics at no cost. The gurobi package is distributed with the Gurobi software suite. This solver uses the gurobi package to solve problems. For information on the performance of different solvers, please see Schuster et al. (2020) for benchmarks comparing the run time and solution quality of different solvers when applied to different sized datasets.

Value

An updated problem() object with the solver added to it.

Installation

Please see the Gurobi Installation Guide vignette for details on installing the Gurobi software and the gurobi package. You can access this vignette online or using the following code:

vignette("gurobi_installation_guide", package = "prioritizr")

Start solution format

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

x has numeric planning units

The argument to start_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 the argument to x. Additionally, any planning units missing cost (NA) values should also have missing (NA) values in the argument to start_solution.

x has matrix planning units

The argument to start_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 the argument to x. Additionally, any planning units missing cost (NA) values for a particular zone should also have a missing (NA) values in the argument to start_solution.

x has terra::rast() planning units

The argument to start_solution be a terra::rast() object where different grid cells (pixels) 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 the argument to x. Additionally, any planning units missing cost (NA) values for a particular zone should also have missing (NA) values in the argument to start_solution.

x has data.frame planning units

The argument to start_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 missing cost (NA) values for a particular zone should also have missing (NA) values in the argument to start_solution.

x has sf::sf() planning units

The argument to start_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, the argument to start_solution must also have the same coordinate reference system as the planning unit data. Furthermore, any planning units missing cost (NA) values for a particular zone should also have missing (NA) values in the argument to start_solution.

References

Gurobi Optimization LLC (2021) Gurobi Optimizer Reference Manual. https://www.gurobi.com.

Schuster R, Hanson JO, Strimas-Mackey M, and Bennett JR (2020). Exact integer linear programming solvers outperform simulated annealing for solving conservation planning problems. PeerJ, 8: e9258.

See Also

See solvers for an overview of all functions for adding a solver.

Other solvers: add_cbc_solver(), add_cplex_solver(), add_default_solver(), add_highs_solver(), add_lsymphony_solver, add_rsymphony_solver()

Examples

## Not run: 
# load data
sim_pu_raster <- get_sim_pu_raster()
sim_features <- get_sim_features()

# create problem
p1 <-
  problem(sim_pu_raster, sim_features) %>%
  add_min_set_objective() %>%
  add_relative_targets(0.1) %>%
  add_binary_decisions() %>%
  add_gurobi_solver(gap = 0, verbose = FALSE)

# generate solution
s1 <- solve(p1)

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

# create a similar problem with boundary length penalties and
# specify the solution from the previous run as a starting solution
p2 <-
  problem(sim_pu_raster, sim_features) %>%
  add_min_set_objective() %>%
  add_relative_targets(0.1) %>%
  add_boundary_penalties(10) %>%
  add_binary_decisions() %>%
  add_gurobi_solver(gap = 0, start_solution = s1, verbose = FALSE)

# generate solution
s2 <- solve(p2)

# plot solution
plot(s2, main = "solution with boundary penalties", axes = FALSE)

## End(Not run)

Description

Specify that the HiGHS software should be used to solve a conservation planning problem (Huangfu and Hall 2018). This function can also be used to customize the behavior of the solver. It requires the highs package to be installed.

Usage

add_highs_solver(
  x,
  gap = 0.1,
  time_limit = .Machine$integer.max,
  presolve = TRUE,
  threads = 1,
  verbose = TRUE
)

Arguments

Details

HiGHS is an open source optimization software. Although this solver can have comparable performance to the CBC solver (i.e., add_cbc_solver()) for particular problems and is generally faster than the SYMPHONY based solvers (i.e., add_rsymphony_solver(), add_lpsymphony_solver()), it can sometimes take much longer than the CBC solver for particular problems. This solver is recommended if the add_gurobi_solver(), add_cplex_solver(), add_cbc_solver() cannot be used.

Value

An updated problem() object with the solver added to it.

References

Huangfu Q and Hall JAJ (2018). Parallelizing the dual revised simplex method. Mathematical Programming Computation, 10: 119-142.

See Also

Other solvers: add_cbc_solver(), add_cplex_solver(), add_default_solver(), add_gurobi_solver(), add_lsymphony_solver, add_rsymphony_solver()

Examples

## Not run: 
# load data
sim_pu_raster <- get_sim_pu_raster()
sim_features <- get_sim_features()

# create problem
p <-
  problem(sim_pu_raster, sim_features) %>%
  add_min_set_objective() %>%
  add_relative_targets(0.1) %>%
  add_binary_decisions() %>%
  add_highs_solver(gap = 0, verbose = FALSE)

# generate solution
s <- solve(p)

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

## End(Not run)

Description

Add constraints to a conservation planning problem to ensure that all selected planning units meet certain criteria.

Usage

## S4 method for signature 'ConservationProblem,ANY,ANY,character'
add_linear_constraints(x, threshold, sense, data)

## S4 method for signature 'ConservationProblem,ANY,ANY,numeric'
add_linear_constraints(x, threshold, sense, data)

## S4 method for signature 'ConservationProblem,ANY,ANY,matrix'
add_linear_constraints(x, threshold, sense, data)

## S4 method for signature 'ConservationProblem,ANY,ANY,Matrix'
add_linear_constraints(x, threshold, sense, data)

## S4 method for signature 'ConservationProblem,ANY,ANY,Raster'
add_linear_constraints(x, threshold, sense, data)

## S4 method for signature 'ConservationProblem,ANY,ANY,SpatRaster'
add_linear_constraints(x, threshold, sense, data)

## S4 method for signature 'ConservationProblem,ANY,ANY,dgCMatrix'
add_linear_constraints(x, threshold, sense, data)

Arguments

Details

This function adds general purpose constraints that can be used to ensure that solutions meet certain criteria (see Examples section below for details). For example, these constraints can be used to add multiple budgets. They can also be used to ensure that the total number of planning units allocated to a certain administrative area (e.g., country) does not exceed a certain threshold (e.g., 30% of its total area). Furthermore, they can also be used to ensure that features have a minimal level of representation (e.g., 30%) when using an objective function that aims to enhance feature representation given a budget (e.g., add_min_shortfall_objective()).

Value

An updated problem() object with the constraints added to it.

Mathematical formulation

The linear constraints are implemented using the following equation. Let $I$ denote the set of planning units (indexed by $i$), $Z$ the set of management zones (indexed by $z$), and $X_{iz}$ the decision variable for allocating planning unit $i$ to zone $z$ (e.g., with binary values indicating if each planning unit is allocated or not). Also, let $D_{iz}$ denote the constraint data associated with planning units $i \in I$ for zones $z \in Z$ (argument to data, if supplied as a matrix object), $\theta$ denote the constraint sense (argument to sense, e.g., $<=$), and $t$ denote the constraint threshold (argument to threshold).

$\sum_{i}^{I} \sum_{z}^{Z} (D_{iz} \times X_{iz}) \space \theta \space t$

Data format

The argument to data can be specified using the following formats.

data as character vector

containing column name(s) that contain penalty values for planning units. This format is only compatible if the planning units in the argument to x are a sf::sf() or data.frame object. The column(s) must have numeric values, and must not contain any missing (NA) values. For problems that contain a single zone, the argument to data must contain a single column name. Otherwise, for problems that contain multiple zones, the argument to data must contain a column name for each zone.

data as a numeric vector

containing values for planning units. These values must not contain any missing (NA) values. Note that this format is only available for planning units that contain a single zone.

data as a matrix/Matrix object

containing numeric values that specify data for each planning unit. Each row corresponds to a planning unit, each column corresponds to a zone, and each cell indicates the data for penalizing a planning unit when it is allocated to a given zone.

data as a terra::rast() object

containing values for planning units. This format is only compatible if the planning units in the argument to x are sf::sf(), or terra::rast() objects. If the planning unit data are a sf::sf() object, then the values are calculated by overlaying the planning units with the argument to data and calculating the sum of the values associated with each planning unit. If the planning unit data are a terra::rast() object, then the values are calculated by extracting the cell values (note that the planning unit data and the argument to data must have exactly the same dimensionality, extent, and missingness). For problems involving multiple zones, the argument to data must contain a layer for each zone.

See Also

See constraints for an overview of all functions for adding constraints.

Other constraints: add_contiguity_constraints(), add_feature_contiguity_constraints(), add_locked_in_constraints(), add_locked_out_constraints(), add_mandatory_allocation_constraints(), add_manual_bounded_constraints(), add_manual_locked_constraints(), add_neighbor_constraints()

Examples

## Not run: 
# load data
sim_pu_raster <- get_sim_pu_raster()
sim_features <- get_sim_features()

# create a baseline problem with minimum shortfall objective
p0 <-
  problem(sim_pu_raster, sim_features) %>%
  add_min_shortfall_objective(1800) %>%
  add_relative_targets(0.2) %>%
  add_binary_decisions() %>%
  add_default_solver(verbose = FALSE)

# solve problem
s0 <- solve(p0)

# plot solution
plot(s0, main = "solution", axes = FALSE)

# now let's create some modified versions of this baseline problem by
# adding additional criteria using linear constraints

# first, let's create a modified version of p0 that contains
# an additional budget for a secondary cost dataset

# create a secondary cost dataset by simulating values
sim_pu_raster2 <- simulate_cost(sim_pu_raster)

# plot the primary cost dataset (sim_pu_raster) and
# the secondary cost dataset (sim_pu_raster2)
plot(
  c(sim_pu_raster, sim_pu_raster2),
  main = c("sim_pu_raster", "sim_pu_raster2"),
  axes = FALSE
)

# create a modified version of p0 with linear constraints that
# specify that the planning units in the solution must not have
# values in sim_pu_raster2 that sum to a total greater than 500
p1 <-
  p0 %>%
  add_linear_constraints(
    threshold = 500, sense = "<=", data = sim_pu_raster2
  )

# solve problem
s1 <- solve(p1)

# plot solutions s1 and s2 to compare them
plot(c(s0, s1), main = c("s0", "s1"), axes = FALSE)

# second, let's create a modified version of p0 that contains
# additional constraints to ensure that each feature definitely has
# at least 8% of its overall distribution represented by the solution
# (in addition to the 20% targets which specify how much we would
# ideally want to conserve for each feature) 

# to achieve this, we need to calculate the total amount of each feature
# within the planning units so we can, in turn, set the constraint thresholds
feat_abund <- feature_abundances(p0)$absolute_abundance

# create a modified version of p0 with additional constraints for each
# feature to specify that the planning units in the solution must
# secure at least 8% of the total abundance for each feature
p2 <- p0
for (i in seq_len(terra::nlyr(sim_features))) {
  p2 <-
    p2 %>%
    add_linear_constraints(
      threshold = feat_abund[i] * 0.08,
      sense = ">=",
      data = sim_features[[i]]
    )
}

# overall, p2 could be described as an optimization problem
# that maximizes feature representation as much as possible
# towards securing 20% of the total amount of each feature,
# whilst ensuring that (i) the total cost of the solution does
# not exceed 1800 (per cost values in sim_pu_raster) and (ii)
# the solution secures at least 8% of the total amount of each feature
# (if 20% is not possible due to the budget)

# solve problem
s2 <- solve(p2)

# plot solutions s0 and s2 to compare them
plot(c(s0, s2), main = c("s1", "s2"), axes = FALSE)

# third, let's create a modified version of p0 that contains
# additional constraints to ensure that the solution equitably
# distributes conservation effort across different administrative areas
# (e.g., countries) within the study region

# to begin with, we will simulate a dataset describing the spatial extent of
# four different administrative areas across the study region
sim_admin <- sim_pu_raster
sim_admin <- terra::aggregate(sim_admin, fact = 5)
sim_admin <- terra::setValues(sim_admin, seq_len(terra::ncell(sim_admin)))
sim_admin <- terra::resample(sim_admin, sim_pu_raster, method = "near")
sim_admin <- terra::mask(sim_admin, sim_pu_raster)

# plot administrative areas layer,
# we can see that the administrative areas subdivide
# the study region into four quadrants, and the sim_admin object is a
# SpatRaster with integer values denoting ids for the administrative areas
plot(sim_admin, axes = FALSE)

# next we will convert the sim_admin SpatRaster object into a SpatRaster
# object (with a layer for each administrative area) indicating which
# planning units belong to each administrative area using binary
# (presence/absence) values
sim_admin2 <- binary_stack(sim_admin)

# plot binary stack of administrative areas
plot(sim_admin2, axes = FALSE)

# we will now calculate the total amount of planning units associated
# with each administrative area, so that we can set the constraint threshold

# since we are using raster data, we won't bother explicitly
# accounting for the total area of each planning unit (because all
# planning units have the same area in raster formats) -- but if we were
# using vector data then we would need to account for the area of each unit
admin_total <- Matrix::rowSums(rij_matrix(sim_pu_raster, sim_admin2))

# create a modified version of p0 with additional constraints for each
# administrative area to specify that the planning units in the solution must
# not encompass more than 10% of the total extent of the administrative
# area
p3 <- p0
for (i in seq_len(terra::nlyr(sim_admin2))) {
  p3 <-
    p3 %>%
    add_linear_constraints(
      threshold = admin_total[i] * 0.1,
      sense = "<=",
      data = sim_admin2[[i]]
    )
}

# solve problem
s3 <- solve(p3)

# plot solutions s0 and s3 to compare them
plot(c(s0, s3), main = c("s0", "s3"), axes = FALSE)

## End(Not run)

Description

Add penalties to a conservation planning problem to penalize solutions that select planning units with higher values from a specific data source (e.g., anthropogenic impact). These penalties assume a linear trade-off between the penalty values and the primary objective of the conservation planning problem (e.g., solution cost for minimum set problems; add_min_set_objective().

Usage

## S4 method for signature 'ConservationProblem,ANY,character'
add_linear_penalties(x, penalty, data)

## S4 method for signature 'ConservationProblem,ANY,numeric'
add_linear_penalties(x, penalty, data)

## S4 method for signature 'ConservationProblem,ANY,matrix'
add_linear_penalties(x, penalty, data)

## S4 method for signature 'ConservationProblem,ANY,Matrix'
add_linear_penalties(x, penalty, data)

## S4 method for signature 'ConservationProblem,ANY,Raster'
add_linear_penalties(x, penalty, data)

## S4 method for signature 'ConservationProblem,ANY,SpatRaster'
add_linear_penalties(x, penalty, data)

## S4 method for signature 'ConservationProblem,ANY,dgCMatrix'
add_linear_penalties(x, penalty, data)

Arguments

Details

This function penalizes solutions that have higher values according to the sum of the penalty values associated with each planning unit, weighted by status of each planning unit in the solution.

Value

An updated problem() object with the penalties added to it.

Data format

The argument to data can be specified using the following formats.

data as character vector

containing column name(s) that contain penalty values for planning units. This format is only compatible if the planning units in the argument to x are a sf::sf() or data.frame object. The column(s) must have numeric values, and must not contain any missing (NA) values. For problems that contain a single zone, the argument to data must contain a single column name. Otherwise, for problems that contain multiple zones, the argument to data must contain a column name for each zone.

data as a numeric vector

containing values for planning units. These values must not contain any missing (NA) values. Note that this format is only available for planning units that contain a single zone.

data as a matrix/Matrix object

containing numeric values that specify data for each planning unit. Each row corresponds to a planning unit, each column corresponds to a zone, and each cell indicates the data for penalizing a planning unit when it is allocated to a given zone.

data as a terra::rast() object

containing values for planning units. This format is only compatible if the planning units in the argument to x are sf::sf(), or terra::rast() objects. If the planning unit data are a sf::sf() object, then the values are calculated by overlaying the planning units with the argument to data and calculating the sum of the values associated with each planning unit. If the planning unit data are a terra::rast() object, then the values are calculated by extracting the cell values (note that the planning unit data and the argument to data must have exactly the same dimensionality, extent, and missingness). For problems involving multiple zones, the argument to data must contain a layer for each zone.

Mathematical formulation

The linear penalties are implemented using the following equations. Let $I$ denote the set of planning units (indexed by $i$), $Z$ the set of management zones (indexed by $z$), and $X_{iz}$ the decision variable for allocating planning unit $i$ to zone $z$ (e.g., with binary values indicating if each planning unit is allocated or not). Also, let $P_z$ represent the penalty scaling value for zones $z \in Z$ (argument to penalty), and $D_{iz}$ the penalty data for allocating planning unit $i \in I$ to zones $z \in Z$ (argument to data, if supplied as a matrix object).

$\sum_{i}^{I} \sum_{z}^{Z} P_z \times D_{iz} \times X_{iz}$

Note that when the problem objective is to maximize some measure of benefit and not minimize some measure of cost, the term $P_z$ is replaced with $-P_z$.

See Also

See penalties for an overview of all functions for adding penalties.

Other penalties: add_asym_connectivity_penalties(), add_boundary_penalties(), add_connectivity_penalties(), add_feature_weights()

Examples

## Not run: 
# set seed for reproducibility
set.seed(600)

# load data
sim_pu_polygons <- get_sim_pu_polygons()
sim_features <- get_sim_features()
sim_zones_pu_raster <- get_sim_zones_pu_raster()
sim_zones_features <- get_sim_zones_features()

# add a column to contain the penalty data for each planning unit
# e.g., these values could indicate the level of habitat
sim_pu_polygons$penalty_data <- runif(nrow(sim_pu_polygons))

# plot the penalty data to visualise its spatial distribution
plot(sim_pu_polygons[, "penalty_data"], axes = FALSE)

# create minimal problem with minimum set objective,
# this does not use the penalty data
p1 <-
  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)

# print problem
print(p1)

# create an updated version of the previous problem,
# with the penalties added to it
p2 <- p1 %>% add_linear_penalties(100, data = "penalty_data")

# print problem
print(p2)

# solve the two problems
s1 <- solve(p1)
s2 <- solve(p2)

# create a new object with both solutions
s3 <- sf::st_sf(
  tibble::tibble(
    s1 = s1$solution_1,
    s2 = s2$solution_1
  ),
  geometry = sf::st_geometry(s1)
)


# plot the solutions and compare them,
# since we supplied a very high penalty value (i.e., 100), relative
# to the range of values in the penalty data and the objective function,
# the solution in s2 is very sensitive to values in the penalty data
plot(s3, axes = FALSE)

# for real conservation planning exercises,
# it would be worth exploring a range of penalty values (e.g., ranging
# from 1 to 100 increments of 5) to explore the trade-offs

# now, let's examine a conservation planning exercise involving multiple
# management zones

# create targets for each feature within each zone,
# these targets indicate that each zone needs to represent 10% of the
# spatial distribution of each feature
targ <- matrix(
  0.1, ncol = number_of_zones(sim_zones_features),
  nrow = number_of_features(sim_zones_features)
)

# create penalty data for allocating each planning unit to each zone,
# these data will be generated by simulating values
penalty_raster <- simulate_cost(
  sim_zones_pu_raster[[1]],
  n = number_of_zones(sim_zones_features)
)

# plot the penalty data, each layer corresponds to a different zone
plot(penalty_raster, main = "penalty data", axes = FALSE)

# create a multi-zone problem with the minimum set objective
# and penalties for allocating planning units to each zone,
# with a penalty scaling factor of 1 for each zone
p4 <-
  problem(sim_zones_pu_raster, sim_zones_features) %>%
  add_min_set_objective() %>%
  add_relative_targets(targ) %>%
  add_linear_penalties(c(1, 1, 1), penalty_raster) %>%
  add_binary_decisions() %>%
  add_default_solver(verbose = FALSE)

# print problem
print(p4)

# solve problem
s4 <- solve(p4)

# plot solution
plot(category_layer(s4), main = "multi-zone solution", axes = FALSE)

## End(Not run)

Description

Add constraints to a conservation planning problem to ensure that specific planning units are selected (or allocated to a specific zone) in the solution. For example, it may be desirable to lock in planning units that are inside existing protected areas so that the solution fills in the gaps in the existing reserve network. If specific planning units should be locked out of a solution, use add_locked_out_constraints(). For problems with non-binary planning unit allocations (e.g., proportions), the add_manual_locked_constraints() function can be used to lock planning unit allocations to a specific value.

Usage

add_locked_in_constraints(x, locked_in)

## S4 method for signature 'ConservationProblem,numeric'
add_locked_in_constraints(x, locked_in)

## S4 method for signature 'ConservationProblem,logical'
add_locked_in_constraints(x, locked_in)

## S4 method for signature 'ConservationProblem,matrix'
add_locked_in_constraints(x, locked_in)

## S4 method for signature 'ConservationProblem,character'
add_locked_in_constraints(x, locked_in)

## S4 method for signature 'ConservationProblem,Spatial'
add_locked_in_constraints(x, locked_in)

## S4 method for signature 'ConservationProblem,sf'
add_locked_in_constraints(x, locked_in)

## S4 method for signature 'ConservationProblem,Raster'
add_locked_in_constraints(x, locked_in)

## S4 method for signature 'ConservationProblem,SpatRaster'
add_locked_in_constraints(x, locked_in)

Arguments

Value

An updated problem() object with the constraints added to it.

Data format

The locked planning units can be specified using the following formats. Generally, the locked data should correspond to the planning units in the argument to x. To help make working with terra::rast() planning unit data easier, the locked data should correspond to cell indices in the terra::rast() data. For example, integer arguments should correspond to cell indices and logical arguments should have a value for each cell—regardless of which planning unit cells contain NA values.

data as an integer vector

containing indices that indicate which planning units should be locked for the solution. This argument is only compatible with problems that contain a single zone.

data as a logical vector

containing TRUE and/or FALSE values that indicate which planning units should be locked in the solution. This argument is only compatible with problems that contain a single zone.

data as a matrix object

containing logical TRUE and/or FALSE values which indicate if certain planning units are should be locked to a specific zone in the solution. Each row corresponds to a planning unit, each column corresponds to a zone, and each cell indicates if the planning unit should be locked to a given zone. Thus each row should only contain at most a single TRUE value.

data as a character vector

containing column name(s) that indicates if planning units should be locked for the solution. This format is only compatible if the planning units in the argument to x are a sf::sf() or data.frame object. The columns must have logical (i.e., TRUE or FALSE) values indicating if the planning unit is to be locked for the solution. For problems that contain a single zone, the argument to data must contain a single column name. Otherwise, for problems that contain multiple zones, the argument to data must contain a column name for each zone.

data as a sf::sf() object

containing geometries that will be used to lock planning units for the solution. Specifically, planning units in x that spatially intersect with y will be locked (per intersecting_units()). Note that this option is only available for problems that contain a single management zone.

data as a terra::rast() object

containing cells used to lock planning units for the solution. Specifically, planning units in x that intersect with cells that have non-zero and non-NA values are locked. For problems that contain multiple zones, the data object must contain a layer for each zone. Note that for multi-band arguments, each pixel must only contain a non-zero value in a single band. Additionally, if the cost data in x is a terra::rast() object, we recommend standardizing NA values in this dataset with the cost data. In other words, the pixels in x that have NA values should also have NA values in the locked data.

See Also

See constraints for an overview of all functions for adding constraints.

Other constraints: add_contiguity_constraints(), add_feature_contiguity_constraints(), add_linear_constraints(), add_locked_out_constraints(), add_mandatory_allocation_constraints(), add_manual_bounded_constraints(), add_manual_locked_constraints(), add_neighbor_constraints()

Examples

## Not run: 
# set seed for reproducibility
set.seed(500)

# load data
sim_pu_polygons <- get_sim_pu_polygons()
sim_features <- get_sim_features()
sim_locked_in_raster <- get_sim_locked_in_raster()
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()

# create minimal problem
p1 <-
  problem(sim_pu_polygons, sim_features, "cost") %>%
  add_min_set_objective() %>%
  add_relative_targets(0.2) %>%
  add_binary_decisions() %>%
  add_default_solver(verbose = FALSE)

# create problem with added locked in constraints using integers
p2 <- p1 %>% add_locked_in_constraints(which(sim_pu_polygons$locked_in))

# create problem with added locked in constraints using a column name
p3 <- p1 %>% add_locked_in_constraints("locked_in")

# create problem with added locked in constraints using raster data
p4 <- p1 %>% add_locked_in_constraints(sim_locked_in_raster)

# create problem with added locked in constraints using spatial polygon data
locked_in <- sim_pu_polygons[sim_pu_polygons$locked_in == 1, ]
p5 <- p1 %>% add_locked_in_constraints(locked_in)

# solve problems
s1 <- solve(p1)
s2 <- solve(p2)
s3 <- solve(p3)
s4 <- solve(p4)
s5 <- solve(p5)

# create single object with all solutions
s6 <- sf::st_sf(
  tibble::tibble(
    s1 = s1$solution_1,
    s2 = s2$solution_1,
    s3 = s3$solution_1,
    s4 = s4$solution_1,
    s5 = s5$solution_1
  ),
  geometry = sf::st_geometry(s1)
)

# plot solutions
plot(
  s6,
  main = c(
    "none locked in", "locked in (integer input)",
    "locked in (character input)", "locked in (raster input)",
    "locked in (polygon input)"
  )
)

# create minimal multi-zone problem with spatial data
p7 <-
  problem(
    sim_zones_pu_polygons, sim_zones_features,
    cost_column = c("cost_1", "cost_2", "cost_3")
  ) %>%
  add_min_set_objective() %>%
  add_absolute_targets(matrix(rpois(15, 1), nrow = 5, ncol = 3)) %>%
  add_binary_decisions() %>%
  add_default_solver(verbose = FALSE)

# create multi-zone problem with locked in constraints using matrix data
locked_matrix <- as.matrix(sf::st_drop_geometry(
  sim_zones_pu_polygons[, c("locked_1", "locked_2", "locked_3")]
))

p8 <- p7 %>% add_locked_in_constraints(locked_matrix)

# solve problem
s8 <- solve(p8)

# create new column representing the zone id that each planning unit
# was allocated to in the solution
s8$solution <- category_vector(sf::st_drop_geometry(
  s8[, c("solution_1_zone_1", "solution_1_zone_2", "solution_1_zone_3")]
))
s8$solution <- factor(s8$solution)

# plot solution
plot(s8[ "solution"], axes = FALSE)

# create multi-zone problem with locked in constraints using column names
p9 <- p7 %>% add_locked_in_constraints(c("locked_1", "locked_2", "locked_3"))

# solve problem
s9 <- solve(p9)

# create new column representing the zone id that each planning unit
# was allocated to in the solution
s9$solution <- category_vector(sf::st_drop_geometry(
  s9[, c("solution_1_zone_1", "solution_1_zone_2", "solution_1_zone_3")]
))
s9$solution[s9$solution == 1 & s9$solution_1_zone_1 == 0] <- 0
s9$solution <- factor(s9$solution)

# plot solution
plot(s9[, "solution"], axes = FALSE)

# create multi-zone problem with raster planning units
p10 <-
  problem(sim_zones_pu_raster, sim_zones_features) %>%
  add_min_set_objective() %>%
  add_absolute_targets(matrix(rpois(15, 1), nrow = 5, ncol = 3)) %>%
  add_binary_decisions() %>%
  add_default_solver(verbose = FALSE)

# create multi-layer raster with locked in units
locked_in_raster <- sim_zones_pu_raster[[1]]
locked_in_raster[!is.na(locked_in_raster)] <- 0
locked_in_raster <- locked_in_raster[[c(1, 1, 1)]]
names(locked_in_raster) <- c("zone_1", "zone_2", "zone_3")
locked_in_raster[[1]][1] <- 1
locked_in_raster[[2]][2] <- 1
locked_in_raster[[3]][3] <- 1

# plot locked in raster
plot(locked_in_raster)

# add locked in raster units to problem
p10 <- p10 %>% add_locked_in_constraints(locked_in_raster)

# solve problem
s10 <- solve(p10)

# plot solution
plot(category_layer(s10), main = "solution", axes = FALSE)

## End(Not run)