Conservation planning problems involve making decisions on
how different planning units will be managed. These decisions might involve
turning an entire planning unit into a protected area, turning part
of a planning unit into a protected area, or allocating a planning
unit to a specific management zone. If no decision is explicitly added to a
problem(), then binary decisions will be used by default.
Details
Only a single type of decision can be added to a conservation
planning problem(). Note that if multiple decisions are added
to a problem, then the last one added will be used.
The following decisions can be added to a conservation planning
problem():
add_binary_decisions()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 object
then this decision class will be used by default.
add_proportion_decisions()Add a proportion decision to
a conservation planning problem. This is a relaxed decision
where a part of a planning unit can be prioritized, as opposed to the
default of the entire planning unit. Typically, this decision
has the assumed action of buying a fraction of a planning unit to
include in a protected area network.
add_semicontinuous_decisions()Add a semi-continuous
decision to a conservation planning problem. This decision is
similar to add_proportion_decision except that it has an upper
bound parameter. By default, the decision can range from prioritizing
none (0%) to all (100%) of a planning unit. However, a upper
bound can be specified to ensure that at most only a fraction
(e.g. 80%) of a planning unit can be preserved. This type of
decision may be useful when it is not practical to conserve the
entire area encompassed by any single planning unit.
See also
Examples
# load data data(sim_pu_raster, sim_features) # create basic problem and using the default decision types (binary) p1 <- problem(sim_pu_raster, sim_features) %>% add_min_set_objective() %>% add_relative_targets(0.1) # create problem with manually specified binary decisions p2 <- p1 %>% add_binary_decisions() # create problem with proportion decisions p3 <- p1 %>% add_proportion_decisions() # create problem with semicontinuous decisions p4 <- p1 %>% add_semicontinuous_decisions(upper_limit = 0.5) # \dontrun{ # solve problem s <- stack(solve(p1), solve(p2), solve(p3), solve(p4))#> Gurobi Optimizer version 9.0.2 build v9.0.2rc0 (linux64) #> Optimize a model with 5 rows, 90 columns and 450 nonzeros #> Model fingerprint: 0x6442bf6e #> 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 [3e+00, 8e+00] #> Found heuristic solution: objective 2337.9617505 #> 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 1.931582e+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 1931.58191 0 4 2337.96175 1931.58191 17.4% - 0s #> H 0 0 1987.3985265 1931.58191 2.81% - 0s #> #> Explored 1 nodes (12 simplex iterations) in 0.00 seconds #> Thread count was 1 (of 4 available processors) #> #> Solution count 2: 1987.4 2337.96 #> #> Optimal solution found (tolerance 1.00e-01) #> Best objective 1.987398526526e+03, best bound 1.931581908865e+03, gap 2.8085% #> Gurobi Optimizer version 9.0.2 build v9.0.2rc0 (linux64) #> Optimize a model with 5 rows, 90 columns and 450 nonzeros #> Model fingerprint: 0x6442bf6e #> 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 [3e+00, 8e+00] #> Found heuristic solution: objective 2337.9617505 #> 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 1.931582e+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 1931.58191 0 4 2337.96175 1931.58191 17.4% - 0s #> H 0 0 1987.3985265 1931.58191 2.81% - 0s #> #> Explored 1 nodes (12 simplex iterations) in 0.00 seconds #> Thread count was 1 (of 4 available processors) #> #> Solution count 2: 1987.4 2337.96 #> #> Optimal solution found (tolerance 1.00e-01) #> Best objective 1.987398526526e+03, best bound 1.931581908865e+03, gap 2.8085% #> Gurobi Optimizer version 9.0.2 build v9.0.2rc0 (linux64) #> Optimize a model with 5 rows, 90 columns and 450 nonzeros #> Model fingerprint: 0xb1a01a19 #> Coefficient statistics: #> Matrix range [2e-01, 9e-01] #> Objective range [2e+02, 2e+02] #> Bounds range [1e+00, 1e+00] #> RHS range [3e+00, 8e+00] #> Presolve time: 0.00s #> Presolved: 5 rows, 90 columns, 450 nonzeros #> #> Iteration Objective Primal Inf. Dual Inf. Time #> 0 0.0000000e+00 3.170407e+01 0.000000e+00 0s #> 12 1.9315819e+03 0.000000e+00 0.000000e+00 0s #> #> Solved in 12 iterations and 0.00 seconds #> Optimal objective 1.931581909e+03 #> Gurobi Optimizer version 9.0.2 build v9.0.2rc0 (linux64) #> Optimize a model with 5 rows, 90 columns and 450 nonzeros #> Model fingerprint: 0xa17b0799 #> Coefficient statistics: #> Matrix range [2e-01, 9e-01] #> Objective range [2e+02, 2e+02] #> Bounds range [5e-01, 5e-01] #> RHS range [3e+00, 8e+00] #> Presolve time: 0.00s #> Presolved: 5 rows, 90 columns, 450 nonzeros #> #> Iteration Objective Primal Inf. Dual Inf. Time #> 0 0.0000000e+00 3.170407e+01 0.000000e+00 0s #> 12 1.9495280e+03 0.000000e+00 0.000000e+00 0s #> #> Solved in 12 iterations and 0.00 seconds #> Optimal objective 1.949528006e+03# plot solutions plot(s, main = c("default (binary)", "binary", "proportion", "semicontinuous (upper = 0.5)"))# }
