Solve a conservation planning problem().
# S4 method for OptimizationProblem,Solver
solve(a, b, ...)
# S4 method for ProjectProblem,missing
solve(a, b, ...)ProjectProblem or an OptimizationProblem object.
Solver object. Not used if a is an
ProjectProblem object.
arguments passed to compile().
The type of object returned from this function depends on the
argument to a. If the argument to a is an
OptimizationProblem object, then the
solution is returned as a list containing the prioritization and
additional information (e.g. run time, solver status). On the other hand,
if the argument
to a is an ProjectProblem object,
then a tibble::tibble() table object will be returned. In this
table, each row row corresponds to a different solution and each column
describes a different property or result associated with each solution:
"solution"integer solution identifier.
"status"character describing each solution.
For example, is the solution optimal, suboptimal, or was it returned
because the solver ran out of time?
"obj"numeric objective value for each solution.
This is calculated using the objective function defined for the
argument to x.
"cost"numeric total cost associated with each
solution.
x$action_names()numeric column for each action
indicating if they were funded in each solution or not.
x$project_names()numeric column for each
project indicating if it was completely funded (with a value of 1)
or not (with a value of 0).
x$feature_names()numeric column for each
feature indicating the probability that it will persist into
the future given each solution.
# load data
data(sim_projects, sim_features, sim_actions)
# print project data
print(sim_projects)
#> # A tibble: 6 × 13
#> name success F1 F2 F3 F4 F5 F1_action F2_action
#> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <lgl> <lgl>
#> 1 F1_project 0.919 0.791 NA NA NA NA TRUE FALSE
#> 2 F2_project 0.923 NA 0.888 NA NA NA FALSE TRUE
#> 3 F3_project 0.829 NA NA 0.502 NA NA FALSE FALSE
#> 4 F4_project 0.848 NA NA NA 0.690 NA FALSE FALSE
#> 5 F5_project 0.814 NA NA NA NA 0.617 FALSE FALSE
#> 6 baseline_proj… 1 0.298 0.250 0.0865 0.249 0.182 FALSE FALSE
#> # ℹ 4 more variables: F3_action <lgl>, F4_action <lgl>, F5_action <lgl>,
#> # baseline_action <lgl>
# print action data
print(sim_features)
#> # A tibble: 5 × 2
#> name weight
#> <chr> <dbl>
#> 1 F1 0.211
#> 2 F2 0.211
#> 3 F3 0.221
#> 4 F4 0.630
#> 5 F5 1.59
# print feature data
print(sim_actions)
#> # A tibble: 6 × 4
#> name cost locked_in locked_out
#> <chr> <dbl> <lgl> <lgl>
#> 1 F1_action 94.4 FALSE FALSE
#> 2 F2_action 101. FALSE FALSE
#> 3 F3_action 103. TRUE FALSE
#> 4 F4_action 99.2 FALSE FALSE
#> 5 F5_action 99.9 FALSE TRUE
#> 6 baseline_action 0 FALSE FALSE
# build problem
p <- problem(sim_projects, sim_actions, sim_features,
"name", "success", "name", "cost", "name") %>%
add_max_richness_objective(budget = 400) %>%
add_feature_weights("weight") %>%
add_binary_decisions()
# print problem
print(p)
#> Project Prioritization Problem
#> actions F1_action, F2_action, F3_action, ... (6 actions)
#> projects F1_project, F2_project, F3_project, ... (6 projects)
#> features F1, F2, F3, ... (5 features)
#> action costs: min: 0, max: 103.22583
#> project success: min: 0.81379, max: 1
#> objective: Maximum richness objective [budget (400)]
#> targets: none
#> weights: min: 0.21136, max: 1.59167
#> decisions Binary decision
#> constraints: <none>
#> solver: default
# \dontrun{
# solve problem
s <- solve(p)
#> Set parameter Username
#> Set parameter TimeLimit to value 2147483647
#> Set parameter MIPGap to value 0
#> Set parameter NumericFocus to value 3
#> Set parameter Presolve to value 2
#> Set parameter Threads to value 1
#> Set parameter PoolSolutions to value 1
#> Set parameter PoolSearchMode to value 2
#> Academic license - for non-commercial use only - expires 2025-04-21
#> Gurobi Optimizer version 11.0.2 build v11.0.2rc0 (linux64 - "Ubuntu 22.04.4 LTS")
#>
#> CPU model: 11th Gen Intel(R) Core(TM) i7-1185G7 @ 3.00GHz, instruction set [SSE2|AVX|AVX2|AVX512]
#> Thread count: 4 physical cores, 8 logical processors, using up to 1 threads
#>
#> Optimize a model with 47 rows, 47 columns and 102 nonzeros
#> Model fingerprint: 0xa33f6587
#> Variable types: 0 continuous, 42 integer (42 binary)
#> Semi-Variable types: 5 continuous, 0 integer
#> Coefficient statistics:
#> Matrix range [9e-02, 1e+02]
#> Objective range [2e-01, 2e+00]
#> Bounds range [1e+00, 1e+00]
#> RHS range [1e+00, 4e+02]
#> Found heuristic solution: objective 0.6654645
#> Presolve removed 16 rows and 12 columns
#> Presolve time: 0.00s
#> Presolved: 31 rows, 35 columns, 64 nonzeros
#> Variable types: 0 continuous, 35 integer (35 binary)
#> Root relaxation presolved: 31 rows, 35 columns, 64 nonzeros
#>
#>
#> Root relaxation: objective 1.749045e+00, 11 iterations, 0.00 seconds (0.00 work units)
#>
#> Nodes | Current Node | Objective Bounds | Work
#> Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
#>
#> * 0 0 0 1.7490448 1.74904 0.00% - 0s
#>
#> Explored 1 nodes (11 simplex iterations) in 0.00 seconds (0.00 work units)
#> Thread count was 1 (of 8 available processors)
#>
#> Solution count 1: 1.74904
#> No other solutions better than 1.74904
#>
#> Optimal solution found (tolerance 0.00e+00)
#> Best objective 1.749044775334e+00, best bound 1.749044775334e+00, gap 0.0000%
# print output
print(s)
#> # A tibble: 1 × 21
#> solution status obj cost F1_action F2_action F3_action F4_action F5_action
#> <int> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 1 OPTIMAL 1.75 395. 1 1 0 1 1
#> # ℹ 12 more variables: baseline_action <dbl>, F1_project <dbl>,
#> # F2_project <dbl>, F3_project <dbl>, F4_project <dbl>, F5_project <dbl>,
#> # baseline_project <dbl>, F1 <dbl>, F2 <dbl>, F3 <dbl>, F4 <dbl>, F5 <dbl>
# print the solver status
print(s$obj)
#> [1] 1.749045
# print the objective value
print(s$obj)
#> [1] 1.749045
# print the solution cost
print(s$cost)
#> [1] 394.5413
# print which actions are funded in the solution
s[, sim_actions$name, drop = FALSE]
#> # A tibble: 1 × 6
#> F1_action F2_action F3_action F4_action F5_action baseline_action
#> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 1 1 0 1 1 1
# print the expected probability of persistence for each feature
# if the solution were implemented
s[, sim_features$name, drop = FALSE]
#> # A tibble: 1 × 5
#> F1 F2 F3 F4 F5
#> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 0.808 0.865 0.0865 0.688 0.592
# }