Provides the connectivity penalty value for all actions and planning units in a solution.
getConnectivityPenalty(x)The connectivity penalty among is calculated as the sum of all connectivity penalties by each action and planning unit in the solution. This can be expressed mathematically for a set of planning units \(I\) indexed by \(i\) and \(j\), and a set of threats \(K\) indexed by \(k\) as:
$$ \sum_{k \in K}\sum_{i \in I_k}\sum_{j \in I_k} x_{ik} (1 - x_{jk})cv_{ij} $$
Where, \(x_{ik}\) is the decisions variable that specify whether an action has been selected to abate threat \(k\) in planning unit \(i\) (1) or not (0), \(cv_{ij}\) is the connectivity penalty that applies when a solution contains planning unit \(i\) but not \(j\) o viceversa.
Note that there is an action per threat, so it is assumed that the index of the threat coincides with the index of the action used to abate it.
# \donttest{
# set seed for reproducibility
set.seed(14)
## Load data
data(sim_pu_data, sim_features_data, sim_dist_features_data,
sim_threats_data, sim_dist_threats_data, sim_sensitivity_data,
sim_boundary_data)
## Create data instance
problem_data <- inputData(
pu = sim_pu_data, features = sim_features_data, dist_features = sim_dist_features_data,
threats = sim_threats_data, dist_threats = sim_dist_threats_data,
sensitivity = sim_sensitivity_data, boundary = sim_boundary_data
)
## Create optimization model
problem_model <- problem(x = problem_data, blm = 0.03)
#> Warning: Some blm_actions argument were set to 0, so the boundary data has no effect for these cases
## Solve the optimization model
s <- solve(a = problem_model, time_limit = 2, output_file = FALSE, cores = 2)
#> Rcplex: num variables=10296 num constraints=29984
# get connectivity penalty values
getConnectivityPenalty(s)
#> solution_name units threat_1 threat_2
#> 1 sol 0 2890.835 1518.804
# }