prioritizr (version 8.0.6)

solve: Solve

Description

Solve a conservation planning problem.

Usage

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

Value

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

objective

numeric mathematical objective value for the solution used to evaluate the prioritization during optimization.

runtime

numeric total amount of time elapsed while during the optimization process (reported in seconds). Note that this measure of time does not include any data pre-processing or post-processing steps.

status

character status of the optimization process. This status typically describes the reason why the optimization process terminated. For example, it might indicate that the optimization process terminated because an optimal solution was found, or because a pre-specified time limit was reached. These status values are (mostly) obtained directly from the solver software, and so we recommend consulting the solver's documentation for further information on what particular status values mean. Note that some solvers (e.g., Gurobi and HiGHS) will return an "OPTIMAL" status when the solver has found a solution within the pre-specified optimality gap (e.g., it has found a solution within 10% of optimality), even though the solution itself may not be strictly optimal.

gap

numeric optimality of the solution. This gap value provides an upper bound of how far the solution is from optimality. For example, you might specify a 10% optimality gap for the optimization process (e.g., using add_highs_solver(gap = 0.1)), and this might produce a solution that is actually 5% from optimality. As such, the solution might have a gap value of 0.05 (corresponding to 5%). Because this value represents an upper bound, it is also possible that the solution in this example -- even though it is actually 5% from optimality -- might have a gap value of 7% (i.e., 0.07). Note that only some solvers are able to provide this information (i.e., the Gurobi and HiGHS solvers), and the gap value for other solvers will contain missing (NA) values.

Arguments

a

problem() object.

b

missing.

...

arguments passed to compile().

run_checks

logical flag indicating whether presolve checks should be run prior solving the problem. These checks are performed using the presolve_check() function. Defaults to TRUE. Skipping these checks may reduce run time for large problems.

force

logical flag indicating if an attempt to should be made to solve the problem even if potential issues were detected during the presolve checks. Defaults to FALSE.

Output format

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

a has numeric planning units

The solution will be returned as a numeric vector. Here, each element in the vector corresponds to a different planning unit. Note that if a portfolio is used to generate multiple solutions, then a list of such numeric vectors will be returned.

a has matrix planning units

The solution will be returned as a matrix object. Here, rows correspond to different planning units, and columns correspond to different management zones. Note that if a portfolio is used to generate multiple solutions, then a list of such matrix objects will be returned.

a has terra::rast() planning units

The solution will be returned as a terra::rast() object. If the argument to x contains multiple zones, then the object will have a different layer for each management zone. Note that if a portfolio is used to generate multiple solutions, then a list of terra::rast() objects will be returned.

a has sf::sf(), or data.frame planning units

The solution will be returned in the same data format as the planning units. Here, each row corresponds to a different planning unit, and columns contain solutions. If the argument to a contains a single zone, then the solution object will contain columns named by solution. Specifically, the column names containing the solution values be will named as "solution_XXX" where "XXX" corresponds to a solution identifier (e.g., "solution_1"). If the argument to a contains multiple zones, then the columns containing solutions will be named as "solution_XXX_YYY" where "XXX" corresponds to the solution identifier and "YYY" is the name of the management zone (e.g., "solution_1_zone1").

Details

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

See Also

See problem() to create conservation planning problems, and presolve_check() to check problems for potential issues. Also, see the category_layer() and category_vector() function to reformat solutions that contain multiple zones.

Examples

if (FALSE) {
# set seed for reproducibility
set.seed(500)

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

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

# solve the problem
s1 <- solve(p1)

# print solution
print(s1)

# print attributes describing the optimization process and the solution
print(attr(s1, "objective"))
print(attr(s1, "runtime"))
print(attr(s1, "status"))
print(attr(s1, "gap"))

# calculate feature representation in the solution
r1 <- eval_feature_representation_summary(p1, s1)
print(r1)

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

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

# solve the problem
s2 <- solve(p2)

# print solution
print(s2)

# calculate feature representation in the solution
r2 <- eval_feature_representation_summary(p2, s2[, "solution_1"])
print(r2)

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

# build multi-zone conservation problem with raster data
p3 <-
  problem(sim_zones_pu_raster, sim_zones_features) %>%
  add_min_set_objective() %>%
  add_relative_targets(matrix(runif(15, 0.1, 0.2), nrow = 5, ncol = 3)) %>%
  add_binary_decisions() %>%
  add_default_solver(verbose = FALSE)

# solve the problem
s3 <- solve(p3)

# print solution
print(s3)

# calculate feature representation in the solution
r3 <- eval_feature_representation_summary(p3, s3)
print(r3)

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

# build multi-zone conservation problem with polygon data
p4 <-
  problem(
    sim_zones_pu_polygons, sim_zones_features,
    cost_column = c("cost_1", "cost_2", "cost_3")
  ) %>%
  add_min_set_objective() %>%
  add_relative_targets(matrix(runif(15, 0.1, 0.2), nrow = 5, ncol = 3)) %>%
  add_binary_decisions() %>%
  add_default_solver(verbose = FALSE)

# solve the problem
s4 <- solve(p4)

# print solution
print(s4)

# calculate feature representation in the solution
r4 <- eval_feature_representation_summary(
  p4, s4[, c("solution_1_zone_1", "solution_1_zone_2", "solution_1_zone_3")]
)
print(r4)

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

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