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.
add_locked_in_constraints(x, locked_in) # S4 method for ConservationProblem,numeric add_locked_in_constraints(x, locked_in) # S4 method for ConservationProblem,logical add_locked_in_constraints(x, locked_in) # S4 method for ConservationProblem,matrix add_locked_in_constraints(x, locked_in) # S4 method for ConservationProblem,character add_locked_in_constraints(x, locked_in) # S4 method for ConservationProblem,Spatial add_locked_in_constraints(x, locked_in) # S4 method for ConservationProblem,sf add_locked_in_constraints(x, locked_in) # S4 method for ConservationProblem,Raster add_locked_in_constraints(x, locked_in)
Arguments
| x |
|
|---|---|
| locked_in | Object that determines which planning units that should be locked in. See the Details section for more information. |
Value
ConservationProblem-class object with the constraints
added to it.
Details
The locked planning units can be specified in several different
ways. Generally, the locked data should correspond to the planning units
in the argument to x. To help make working with
Raster-class planning unit data easier,
the locked data should correspond to cell indices in the
Raster-class 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.
integervector of indices pertaining to which
planning units should be locked for the solution. This argument is only
compatible with problems that contain a single zone.
logicalvector 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.
matrixcontaining 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.
characterfield (column) name(s) that indicate if planning
units should be locked for the solution. This type of argument is only
compatible if the planning units in the argument to x are a
Spatial-class, sf, or
data.frame object. The fields
(columns) must have logical (i.e. TRUE or FALSE)
values indicating if the planning unit is to be locked for the solution.
For problems containing multiple zones, this argument should contain
a field (column) name for each management zone.
Spatial-class or sfplanning units in x that spatially intersect with the
argument to y (according to intersecting_units
are locked for to the solution. Note that this option is only available
for problems that contain a single management zone.
Raster-classplanning units in x
that intersect with non-zero and non-NA raster cells are locked
for the solution. For problems that contain multiple zones, the
Raster-class 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 Raster-class 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
Examples
# set seed for reproducibility set.seed(500) # load data data(sim_pu_polygons, sim_features, sim_locked_in_raster) # 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 added locked in constraints using integers p2 <- p1 %>% add_locked_in_constraints(which(sim_pu_polygons$locked_in)) # create problem with added locked in constraints using a field name p3 <- p1 %>% add_locked_in_constraints("locked_in") # create problem with added locked in constraints using raster data p4 <- p1 %>% add_locked_in_constraints(sim_locked_in_raster) # create problem with added locked in constraints using spatial polygon data locked_in <- sim_pu_polygons[sim_pu_polygons$locked_in == 1, ] p5 <- p1 %>% add_locked_in_constraints(locked_in) # \donttest{ # solve problems s1 <- solve(p1)#> Gurobi Optimizer version 9.0.1 build v9.0.1rc0 (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%#> Gurobi Optimizer version 9.0.1 build v9.0.1rc0 (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%#> Gurobi Optimizer version 9.0.1 build v9.0.1rc0 (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%#> Gurobi Optimizer version 9.0.1 build v9.0.1rc0 (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%#> Gurobi Optimizer version 9.0.1 build v9.0.1rc0 (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(3,2), mar = c(0, 0, 4.1, 0)) plot(s1, main = "none locked in") plot(s1[s1$solution_1 == 1, ], col = "darkgreen", add = TRUE) plot(s2, main = "locked in (integer input)") plot(s2[s2$solution_1 == 1, ], col = "darkgreen", add = TRUE) plot(s3, main = "locked in (character input)") plot(s3[s3$solution_1 == 1, ], col = "darkgreen", add = TRUE) plot(s4, main = "locked in (raster input)") plot(s4[s4$solution_1 == 1, ], col = "darkgreen", add = TRUE) plot(s5, main = "locked in (polygon input)") plot(s5[s5$solution_1 == 1, ], col = "darkgreen", add = TRUE) # } # create minimal multi-zone problem with spatial data p6 <- problem(sim_pu_zones_polygons, sim_features_zones, cost_column = c("cost_1", "cost_2", "cost_3")) %>% add_min_set_objective() %>% add_absolute_targets(matrix(rpois(15, 1), nrow = 5, ncol = 3)) %>% add_binary_decisions() # create multi-zone problem with locked in constraints using matrix data locked_matrix <- sim_pu_zones_polygons@data[, c("locked_1", "locked_2", "locked_3")] locked_matrix <- as.matrix(locked_matrix) p7 <- p6 %>% add_locked_in_constraints(locked_matrix) # \donttest{ # solve problem s6 <- solve(p6)#> Gurobi Optimizer version 9.0.1 build v9.0.1rc0 (linux64) #> Optimize a model with 105 rows, 270 columns and 1620 nonzeros #> Model fingerprint: 0x1bde86be #> Variable types: 0 continuous, 270 integer (270 binary) #> Coefficient statistics: #> Matrix range [2e-01, 1e+00] #> Objective range [2e+02, 2e+02] #> Bounds range [1e+00, 1e+00] #> RHS range [1e+00, 3e+00] #> Found heuristic solution: objective 3524.7950998 #> Presolve removed 7 rows and 0 columns #> Presolve time: 0.01s #> Presolved: 98 rows, 270 columns, 990 nonzeros #> Variable types: 0 continuous, 270 integer (270 binary) #> Presolved: 98 rows, 270 columns, 990 nonzeros #> #> #> Root relaxation: objective 2.642776e+03, 9 iterations, 0.00 seconds #> #> Nodes | Current Node | Objective Bounds | Work #> Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time #> #> 0 0 2642.77567 0 5 3524.79510 2642.77567 25.0% - 0s #> H 0 0 2875.8073247 2642.77567 8.10% - 0s #> #> Explored 1 nodes (9 simplex iterations) in 0.01 seconds #> Thread count was 1 (of 4 available processors) #> #> Solution count 2: 2875.81 3524.8 #> #> Optimal solution found (tolerance 1.00e-01) #> Best objective 2.875807324677e+03, best bound 2.642775673413e+03, gap 8.1032%# create new column representing the zone id that each planning unit # was allocated to in the solution s6$solution <- category_vector(s6@data[, c("solution_1_zone_1", "solution_1_zone_2", "solution_1_zone_3")]) s6$solution <- factor(s6$solution) # plot solution spplot(s6, zcol = "solution", main = "solution", axes = FALSE, box = FALSE) # } # create multi-zone problem with locked in constraints using field names p8 <- p6 %>% add_locked_in_constraints(c("locked_1", "locked_2", "locked_3")) # \donttest{ # solve problem s8 <- solve(p8)#> Gurobi Optimizer version 9.0.1 build v9.0.1rc0 (linux64) #> Optimize a model with 105 rows, 270 columns and 1620 nonzeros #> Model fingerprint: 0x617a8fe5 #> 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, 3e+00] #> Found heuristic solution: objective 3335.9942703 #> Presolve removed 27 rows and 118 columns #> Presolve time: 0.00s #> Presolved: 78 rows, 152 columns, 304 nonzeros #> Variable types: 0 continuous, 152 integer (152 binary) #> Presolved: 78 rows, 152 columns, 304 nonzeros #> #> #> Root relaxation: objective 3.324542e+03, 2 iterations, 0.00 seconds #> #> Nodes | Current Node | Objective Bounds | Work #> Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time #> #> * 0 0 0 3324.5423913 3324.54239 0.00% - 0s #> #> Explored 0 nodes (2 simplex iterations) in 0.00 seconds #> Thread count was 1 (of 4 available processors) #> #> Solution count 2: 3324.54 3335.99 #> #> Optimal solution found (tolerance 1.00e-01) #> Best objective 3.324542391321e+03, best bound 3.324542391321e+03, gap 0.0000%# create new column representing the zone id that each planning unit # was allocated to in the solution s8$solution <- category_vector(s8@data[, c("solution_1_zone_1", "solution_1_zone_2", "solution_1_zone_3")]) s8$solution[s8$solution == 1 & s8$solution_1_zone_1 == 0] <- 0 s8$solution <- factor(s8$solution) # plot solution spplot(s8, zcol = "solution", main = "solution", axes = FALSE, box = FALSE) # } # create multi-zone problem with raster planning units p9 <- problem(sim_pu_zones_stack, sim_features_zones) %>% add_min_set_objective() %>% add_absolute_targets(matrix(rpois(15, 1), nrow = 5, ncol = 3)) %>% add_binary_decisions() # create raster stack with locked in units locked_in_stack <- sim_pu_zones_stack[[1]] locked_in_stack[!is.na(locked_in_stack)] <- 0 locked_in_stack <- locked_in_stack[[c(1, 1, 1)]] locked_in_stack[[1]][1] <- 1 locked_in_stack[[2]][2] <- 1 locked_in_stack[[3]][3] <- 1 # plot locked in stack # \donttest{ plot(locked_in_stack)# } # add locked in raster units to problem p9 <- p9 %>% add_locked_in_constraints(locked_in_stack) # \donttest{ # solve problem s9 <- solve(p9)#> Gurobi Optimizer version 9.0.1 build v9.0.1rc0 (linux64) #> Optimize a model with 105 rows, 270 columns and 1620 nonzeros #> Model fingerprint: 0x56303b56 #> 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, 2e+00] #> Found heuristic solution: objective 2881.4469505 #> Presolve removed 12 rows and 9 columns #> Presolve time: 0.00s #> Presolved: 93 rows, 261 columns, 783 nonzeros #> Variable types: 0 continuous, 261 integer (261 binary) #> Presolved: 93 rows, 261 columns, 783 nonzeros #> #> #> Root relaxation: objective 2.289262e+03, 12 iterations, 0.00 seconds #> #> Nodes | Current Node | Objective Bounds | Work #> Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time #> #> 0 0 2289.26159 0 6 2881.44695 2289.26159 20.6% - 0s #> H 0 0 2666.3302066 2289.26159 14.1% - 0s #> H 0 0 2463.5687146 2289.26159 7.08% - 0s #> #> Explored 1 nodes (12 simplex iterations) in 0.01 seconds #> Thread count was 1 (of 4 available processors) #> #> Solution count 3: 2463.57 2666.33 2881.45 #> #> Optimal solution found (tolerance 1.00e-01) #> Best objective 2.463568714567e+03, best bound 2.289261594758e+03, gap 7.0754%
