Add constraints to a conservation planning problem() to ensure that the planning unit values (e.g., proportion, binary) in a solution range between specific lower and upper bounds. This function offers more fine-grained control than the add_manual_locked_constraints() function and is is most useful for problems involving proportion-type or semi-continuous decisions.

add_manual_bounded_constraints(x, data)

# S4 method for ConservationProblem,data.frame
add_manual_bounded_constraints(x, data)

# S4 method for ConservationProblem,tbl_df
add_manual_bounded_constraints(x, data)

Arguments

x

problem() (i.e., ConservationProblem) object.

data

data.frame or tibble::tibble() object. See the Data format section for more information.

Value

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

Data format

The argument to data should be a data.frame with the following fields (columns):

pu

integer planning unit identifier.

zone

character names of zones. Note that this argument is optional for arguments to x that contain a single zone.

lower

numeric values indicating the minimum value that each planning unit can be allocated to in each zone in the solution.

upper

numeric values indicating the maximum value that each planning unit can be allocated to in each zone in the solution.

Examples

# set seed for reproducibility
set.seed(500)

# load data
data(sim_pu_polygons, sim_features, sim_pu_zones_polygons,
     sim_features_zones)

# 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 locked in constraints using add_locked_constraints
p2 <- p1 %>% add_locked_in_constraints("locked_in")

# create identical problem using add_manual_bounded_constraints
bounds_data <- data.frame(pu = which(sim_pu_polygons$locked_in),
                          lower = 1, upper = 1)

p3 <- p1 %>% add_manual_bounded_constraints(bounds_data)
# \dontrun{
# solve problems
s1 <- solve(p1)
s2 <- solve(p2)
s3 <- solve(p3)

# plot solutions
par(mfrow = c(1,3), mar = c(0, 0, 4.1, 0))
plot(s1, main = "none locked in")
plot(s1[s1$solution_1 == 1, ], col = "darkgreen", add = TRUE)

plot(s2, main = "add_locked_in_constraints")
plot(s2[s2$solution_1 == 1, ], col = "darkgreen", add = TRUE)

plot(s3, main = "add_bounds_constraints")
plot(s3[s3$solution_1 == 1, ], col = "darkgreen", add = TRUE)

# }
# create minimal problem with multiple zones
p4 <- problem(sim_pu_zones_polygons, sim_features_zones,
              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)

# create data.frame with the following constraints:
# planning units 1, 2, and 3 must be allocated to zone 1 in the solution
# planning units 4, and 5 must be allocated to zone 2 in the solution
# planning units 8 and 9 must not be allocated to zone 3 in the solution
bounds_data2 <- data.frame(pu = c(1, 2, 3, 4, 5, 8, 9),
                           zone = c(rep("zone_1", 3), rep("zone_2", 2),
                                    rep("zone_3", 2)),
                           lower = c(rep(1, 5), rep(0, 2)),
                           upper = c(rep(1, 5), rep(0, 2)))

# print bounds data
print(bounds_data2)
#>   pu   zone lower upper
#> 1  1 zone_1     1     1
#> 2  2 zone_1     1     1
#> 3  3 zone_1     1     1
#> 4  4 zone_2     1     1
#> 5  5 zone_2     1     1
#> 6  8 zone_3     0     0
#> 7  9 zone_3     0     0

# create problem with added constraints
p5 <- p4 %>% add_manual_bounded_constraints(bounds_data2)
# \dontrun{
# solve problem
s4 <- solve(p4)
s5 <- solve(p5)

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

s4$solution_bounded <- category_vector(s5@data[, c("solution_1_zone_1",
                                                   "solution_1_zone_2",
                                                   "solution_1_zone_3")])
s4$solution_bounded <- factor(s4$solution_bounded)

# plot solutions
spplot(s4, zcol = c("solution", "solution_bounded"), axes = FALSE,
       box = FALSE)

# }