Add absolute targets

Source: R/add_absolute_targets.R

Set targets for a project prioritization problem() by specifying exactly what probability of persistence is required for each feature. For instance, setting an absolute target of 10% (i.e. 0.1) corresponds to a threshold 10% probability of persisting.

add_absolute_targets(x, targets)

# S4 method for ProjectProblem,numeric
add_absolute_targets(x, targets)

# S4 method for ProjectProblem,character
add_absolute_targets(x, targets)

Arguments

x

ProjectProblem object.

targets

Object that specifies the targets for each feature. See the Details section for more information.

Details

Targets are used to specify the minimum probability of persistence for each feature in solutions. For minimum set objectives (i.e. add_min_set_objective(), these targets specify the minimum probability of persistence required for each species in the solution. And for budget constrained objectives that use targets (i.e.add_max_targets_met_objective()), these targets specify the minimum threshold probability of persistence that needs to be achieved to count the benefits for conserving these species. Please note that attempting to solve problems with objectives that require targets without specifying targets will throw an error.

The targets for a problem can be specified in several different ways:

numeric

vector of target values for each feature. The order of the target values should correspond to the order of the features in the data used to create the argument to x. Additionally, for convenience, this type of argument can be a single value to assign the same target to each feature.

character

specifying the name of column in the feature data (i.e. the argument to features in the problem() function) that contains the persistence targets.

See also

targets.

Examples

# load data
data(sim_projects, sim_features, sim_actions)

# build problem with minimum set objective and targets that require each
# feature to have a 30% chance of persisting into the future
p1 <- problem(sim_projects, sim_actions, sim_features,
             "name", "success", "name", "cost", "name") %>%
      add_min_set_objective() %>%
      add_absolute_targets(0.3) %>%
      add_binary_decisions()

# print problem
print(p1)
#> 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:       Minimum set objective 
#>   targets:         Absolute targets [targets (min: 0.3, max: 0.3)]
#>   weights:         default
#>   decisions        Binary decision 
#>   constraints:     <none>
#>   solver:          default

# build problem with minimum set objective and specify targets that require
# different levels of persistence for each feature
p2 <- problem(sim_projects, sim_actions, sim_features,
             "name", "success", "name", "cost", "name") %>%
      add_min_set_objective() %>%
      add_absolute_targets(c(0.1, 0.2, 0.3, 0.4, 0.5)) %>%
      add_binary_decisions()

# print problem
print(p2)
#> 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:       Minimum set objective 
#>   targets:         Absolute targets [targets (min: 0.1, max: 0.5)]
#>   weights:         default
#>   decisions        Binary decision 
#>   constraints:     <none>
#>   solver:          default

# add a column name to the feature data with targets
sim_features$target <- c(0.1, 0.2, 0.3, 0.4, 0.5)

# build problem with minimum set objective and specify targets using
# column name in the feature data
p3 <- problem(sim_projects, sim_actions, sim_features,
             "name", "success", "name", "cost", "name") %>%
      add_min_set_objective() %>%
      add_absolute_targets("target") %>%
      add_binary_decisions()

# print problem
print(p3)
#> 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:       Minimum set objective 
#>   targets:         Absolute targets [targets (min: 0.1, max: 0.5)]
#>   weights:         default
#>   decisions        Binary decision 
#>   constraints:     <none>
#>   solver:          default

# \dontrun{
# solve problems
s1 <- solve(p1)
#> Gurobi Optimizer version 9.5.2 build v9.5.2rc0 (linux64)
#> Thread count: 4 physical cores, 8 logical processors, using up to 1 threads
#> Optimize a model with 46 rows, 42 columns and 92 nonzeros
#> Model fingerprint: 0xde05e947
#> Variable types: 0 continuous, 42 integer (42 binary)
#> Coefficient statistics:
#>   Matrix range     [9e-02, 1e+00]
#>   Objective range  [9e+01, 1e+02]
#>   Bounds range     [1e+00, 1e+00]
#>   RHS range        [3e-01, 1e+00]
#> Found heuristic solution: objective 497.7671458
#> Presolve removed 45 rows and 20 columns
#> Presolve time: 0.00s
#> Presolved: 1 rows, 22 columns, 2 nonzeros
#> Variable types: 0 continuous, 22 integer (22 binary)
#> 
#> Explored 0 nodes (0 simplex iterations) in 0.00 seconds (0.00 work units)
#> Thread count was 1 (of 8 available processors)
#> 
#> Solution count 1: 497.767 
#> 
#> Optimal solution found (tolerance 0.00e+00)
#> Best objective 4.977671458279e+02, best bound 4.977671458279e+02, gap 0.0000%
s2 <- solve(p2)
#> Gurobi Optimizer version 9.5.2 build v9.5.2rc0 (linux64)
#> Thread count: 4 physical cores, 8 logical processors, using up to 1 threads
#> Optimize a model with 46 rows, 42 columns and 92 nonzeros
#> Model fingerprint: 0x4e7d2c3e
#> Variable types: 0 continuous, 42 integer (42 binary)
#> Coefficient statistics:
#>   Matrix range     [9e-02, 1e+00]
#>   Objective range  [9e+01, 1e+02]
#>   Bounds range     [1e+00, 1e+00]
#>   RHS range        [1e-01, 1e+00]
#> Found heuristic solution: objective 403.3678534
#> Presolve removed 31 rows and 14 columns
#> Presolve time: 0.00s
#> Presolved: 15 rows, 28 columns, 30 nonzeros
#> Variable types: 0 continuous, 28 integer (28 binary)
#> Root relaxation presolved: 15 rows, 28 columns, 30 nonzeros
#> 
#> 
#> Root relaxation: objective 3.023765e+02, 4 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     302.3764827  302.37648  0.00%     -    0s
#> 
#> Explored 1 nodes (4 simplex iterations) in 0.00 seconds (0.00 work units)
#> Thread count was 1 (of 8 available processors)
#> 
#> Solution count 1: 302.376 
#> 
#> Optimal solution found (tolerance 0.00e+00)
#> Best objective 3.023764827378e+02, best bound 3.023764827378e+02, gap 0.0000%
s3 <- solve(p3)
#> Gurobi Optimizer version 9.5.2 build v9.5.2rc0 (linux64)
#> Thread count: 4 physical cores, 8 logical processors, using up to 1 threads
#> Optimize a model with 46 rows, 42 columns and 92 nonzeros
#> Model fingerprint: 0x4e7d2c3e
#> Variable types: 0 continuous, 42 integer (42 binary)
#> Coefficient statistics:
#>   Matrix range     [9e-02, 1e+00]
#>   Objective range  [9e+01, 1e+02]
#>   Bounds range     [1e+00, 1e+00]
#>   RHS range        [1e-01, 1e+00]
#> Found heuristic solution: objective 403.3678534
#> Presolve removed 31 rows and 14 columns
#> Presolve time: 0.00s
#> Presolved: 15 rows, 28 columns, 30 nonzeros
#> Variable types: 0 continuous, 28 integer (28 binary)
#> Root relaxation presolved: 15 rows, 28 columns, 30 nonzeros
#> 
#> 
#> Root relaxation: objective 3.023765e+02, 4 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     302.3764827  302.37648  0.00%     -    0s
#> 
#> Explored 1 nodes (4 simplex iterations) in 0.00 seconds (0.00 work units)
#> Thread count was 1 (of 8 available processors)
#> 
#> Solution count 1: 302.376 
#> 
#> Optimal solution found (tolerance 0.00e+00)
#> Best objective 3.023764827378e+02, best bound 3.023764827378e+02, gap 0.0000%

# print solutions
print(s1)
#> # A tibble: 1 × 21
#>   solution status    obj  cost F1_action F2_ac…¹ F3_ac…² F4_ac…³ F5_ac…⁴ basel…⁵
#>      <int> <chr>   <dbl> <dbl>     <dbl>   <dbl>   <dbl>   <dbl>   <dbl>   <dbl>
#> 1        1 OPTIMAL  498.  498.         1       1       1       1       1       1
#> # … with 11 more variables: 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>,
#> #   and abbreviated variable names ¹​F2_action, ²​F3_action, ³​F4_action,
#> #   ⁴​F5_action, ⁵​baseline_action
print(s2)
#> # A tibble: 1 × 21
#>   solution status    obj  cost F1_action F2_ac…¹ F3_ac…² F4_ac…³ F5_ac…⁴ basel…⁵
#>      <int> <chr>   <dbl> <dbl>     <dbl>   <dbl>   <dbl>   <dbl>   <dbl>   <dbl>
#> 1        1 OPTIMAL  302.  302.         0       0       1       1       1       1
#> # … with 11 more variables: 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>,
#> #   and abbreviated variable names ¹​F2_action, ²​F3_action, ³​F4_action,
#> #   ⁴​F5_action, ⁵​baseline_action
print(s3)
#> # A tibble: 1 × 21
#>   solution status    obj  cost F1_action F2_ac…¹ F3_ac…² F4_ac…³ F5_ac…⁴ basel…⁵
#>      <int> <chr>   <dbl> <dbl>     <dbl>   <dbl>   <dbl>   <dbl>   <dbl>   <dbl>
#> 1        1 OPTIMAL  302.  302.         0       0       1       1       1       1
#> # … with 11 more variables: 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>,
#> #   and abbreviated variable names ¹​F2_action, ²​F3_action, ³​F4_action,
#> #   ⁴​F5_action, ⁵​baseline_action

# plot solutions
plot(p1, s1)

plot(p2, s2)

plot(p3, s3)

# }