Add manually specified bounds constraints

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 Details section for more information.

Value

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

Details

The argument to data must contain 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()

# 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)
#> Gurobi Optimizer version 9.0.2 build v9.0.2rc0 (linux64)
#> Optimize a model with 5 rows, 90 columns and 450 nonzeros
#> Model fingerprint: 0x8a299781
#> Variable types: 0 continuous, 90 integer (90 binary)
#> Coefficient statistics:
#>   Matrix range     [2e-01, 9e-01]
#>   Objective range  [2e+02, 2e+02]
#>   Bounds range     [1e+00, 1e+00]
#>   RHS range        [6e+00, 1e+01]
#> Found heuristic solution: objective 3934.6218396
#> Presolve time: 0.00s
#> Presolved: 5 rows, 90 columns, 450 nonzeros
#> Variable types: 0 continuous, 90 integer (90 binary)
#> Presolved: 5 rows, 90 columns, 450 nonzeros
#> 
#> 
#> Root relaxation: objective 3.496032e+03, 16 iterations, 0.00 seconds
#> 
#>     Nodes    |    Current Node    |     Objective Bounds      |     Work
#>  Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time
#> 
#>      0     0 3496.03193    0    4 3934.62184 3496.03193  11.1%     -    0s
#> H    0     0                    3585.9601335 3496.03193  2.51%     -    0s
#> 
#> Explored 1 nodes (16 simplex iterations) in 0.00 seconds
#> Thread count was 1 (of 4 available processors)
#> 
#> Solution count 2: 3585.96 3934.62 
#> 
#> Optimal solution found (tolerance 1.00e-01)
#> Best objective 3.585960133519e+03, best bound 3.496031931890e+03, gap 2.5078%
s2 <- solve(p2)
#> Gurobi Optimizer version 9.0.2 build v9.0.2rc0 (linux64)
#> Optimize a model with 5 rows, 90 columns and 450 nonzeros
#> Model fingerprint: 0x532eb6d6
#> Variable types: 0 continuous, 90 integer (90 binary)
#> Coefficient statistics:
#>   Matrix range     [2e-01, 9e-01]
#>   Objective range  [2e+02, 2e+02]
#>   Bounds range     [1e+00, 1e+00]
#>   RHS range        [6e+00, 1e+01]
#> Found heuristic solution: objective 4017.6427161
#> Presolve removed 0 rows and 10 columns
#> Presolve time: 0.00s
#> Presolved: 5 rows, 80 columns, 400 nonzeros
#> Variable types: 0 continuous, 80 integer (80 binary)
#> Presolved: 5 rows, 80 columns, 400 nonzeros
#> 
#> 
#> Root relaxation: objective 3.610717e+03, 15 iterations, 0.00 seconds
#> 
#>     Nodes    |    Current Node    |     Objective Bounds      |     Work
#>  Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time
#> 
#>      0     0 3610.71743    0    4 4017.64272 3610.71743  10.1%     -    0s
#> H    0     0                    3655.0632348 3610.71743  1.21%     -    0s
#> 
#> Explored 1 nodes (15 simplex iterations) in 0.00 seconds
#> Thread count was 1 (of 4 available processors)
#> 
#> Solution count 2: 3655.06 4017.64 
#> 
#> Optimal solution found (tolerance 1.00e-01)
#> Best objective 3.655063234840e+03, best bound 3.610717428789e+03, gap 1.2133%
s3 <- solve(p3)
#> Gurobi Optimizer version 9.0.2 build v9.0.2rc0 (linux64)
#> Optimize a model with 5 rows, 90 columns and 450 nonzeros
#> Model fingerprint: 0x532eb6d6
#> Variable types: 0 continuous, 90 integer (90 binary)
#> Coefficient statistics:
#>   Matrix range     [2e-01, 9e-01]
#>   Objective range  [2e+02, 2e+02]
#>   Bounds range     [1e+00, 1e+00]
#>   RHS range        [6e+00, 1e+01]
#> Found heuristic solution: objective 4017.6427161
#> Presolve removed 0 rows and 10 columns
#> Presolve time: 0.00s
#> Presolved: 5 rows, 80 columns, 400 nonzeros
#> Variable types: 0 continuous, 80 integer (80 binary)
#> Presolved: 5 rows, 80 columns, 400 nonzeros
#> 
#> 
#> Root relaxation: objective 3.610717e+03, 15 iterations, 0.00 seconds
#> 
#>     Nodes    |    Current Node    |     Objective Bounds      |     Work
#>  Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time
#> 
#>      0     0 3610.71743    0    4 4017.64272 3610.71743  10.1%     -    0s
#> H    0     0                    3655.0632348 3610.71743  1.21%     -    0s
#> 
#> Explored 1 nodes (15 simplex iterations) in 0.00 seconds
#> Thread count was 1 (of 4 available processors)
#> 
#> Solution count 2: 3655.06 4017.64 
#> 
#> Optimal solution found (tolerance 1.00e-01)
#> Best objective 3.655063234840e+03, best bound 3.610717428789e+03, gap 1.2133%

# 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()

# 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)
#> Gurobi Optimizer version 9.0.2 build v9.0.2rc0 (linux64)
#> Optimize a model with 105 rows, 270 columns and 1620 nonzeros
#> Model fingerprint: 0xf54fe7c9
#> Variable types: 0 continuous, 270 integer (270 binary)
#> Coefficient statistics:
#>   Matrix range     [2e-01, 1e+00]
#>   Objective range  [2e+02, 2e+02]
#>   Bounds range     [1e+00, 1e+00]
#>   RHS range        [1e+00, 1e+01]
#> Found heuristic solution: objective 11123.160980
#> Presolve removed 3 rows and 0 columns
#> Presolve time: 0.00s
#> Presolved: 102 rows, 270 columns, 1350 nonzeros
#> Variable types: 0 continuous, 270 integer (270 binary)
#> Presolved: 102 rows, 270 columns, 1350 nonzeros
#> 
#> 
#> Root relaxation: objective 9.843159e+03, 91 iterations, 0.00 seconds
#> 
#>     Nodes    |    Current Node    |     Objective Bounds      |     Work
#>  Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time
#> 
#>      0     0 9843.15923    0   14 11123.1610 9843.15923  11.5%     -    0s
#> H    0     0                    10160.156963 9843.15923  3.12%     -    0s
#> 
#> Explored 1 nodes (91 simplex iterations) in 0.01 seconds
#> Thread count was 1 (of 4 available processors)
#> 
#> Solution count 2: 10160.2 11123.2 
#> 
#> Optimal solution found (tolerance 1.00e-01)
#> Best objective 1.016015696337e+04, best bound 9.843159228876e+03, gap 3.1200%
s5 <- solve(p5)
#> Gurobi Optimizer version 9.0.2 build v9.0.2rc0 (linux64)
#> Optimize a model with 105 rows, 270 columns and 1620 nonzeros
#> Model fingerprint: 0x0cf976a6
#> Variable types: 0 continuous, 270 integer (270 binary)
#> Coefficient statistics:
#>   Matrix range     [2e-01, 1e+00]
#>   Objective range  [2e+02, 2e+02]
#>   Bounds range     [1e+00, 1e+00]
#>   RHS range        [1e+00, 1e+01]
#> Found heuristic solution: objective 10775.471081
#> Presolve removed 9 rows and 17 columns
#> Presolve time: 0.00s
#> Presolved: 96 rows, 253 columns, 1182 nonzeros
#> Variable types: 0 continuous, 253 integer (253 binary)
#> Presolved: 96 rows, 253 columns, 1182 nonzeros
#> 
#> 
#> Root relaxation: objective 9.914683e+03, 71 iterations, 0.00 seconds
#> 
#>     Nodes    |    Current Node    |     Objective Bounds      |     Work
#>  Expl Unexpl |  Obj  Depth IntInf | Incumbent    BestBd   Gap | It/Node Time
#> 
#>      0     0 9914.68289    0   13 10775.4711 9914.68289  7.99%     -    0s
#> 
#> Explored 0 nodes (71 simplex iterations) in 0.01 seconds
#> Thread count was 1 (of 4 available processors)
#> 
#> Solution count 1: 10775.5 
#> 
#> Optimal solution found (tolerance 1.00e-01)
#> Best objective 1.077547108111e+04, best bound 9.914682890311e+03, gap 7.9884%

# 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)
# }

Arguments

Value

Details

See also

Examples