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)
#> Gurobi Optimizer version 10.0.0 build v10.0.0rc2 (linux64)
#>
#> CPU model: 12th Gen Intel(R) Core(TM) i5-1240P, instruction set [SSE2|AVX|AVX2]
#> Thread count: 16 physical cores, 16 logical processors, using up to 2 threads
#>
#> Optimize a model with 29984 rows, 10296 columns and 70085 nonzeros
#> Model fingerprint: 0x197c5e8d
#> Variable types: 176 continuous, 10120 integer (10120 binary)
#> Coefficient statistics:
#> Matrix range [5e-01, 2e+00]
#> Objective range [3e-02, 3e+01]
#> Bounds range [1e+00, 1e+00]
#> RHS range [1e+00, 5e+01]
#> Found heuristic solution: objective 964.0000000
#> Presolve removed 19990 rows and 5131 columns
#> Presolve time: 0.14s
#> Presolved: 9994 rows, 5165 columns, 20209 nonzeros
#> Variable types: 0 continuous, 5165 integer (5160 binary)
#> Found heuristic solution: objective 868.0000000
#>
#> Root relaxation: objective 8.477969e+02, 6685 iterations, 0.42 seconds (0.96 work units)
#>
#> Nodes | Current Node | Objective Bounds | Work
#> Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
#>
#> 0 0 847.79688 0 5133 868.00000 847.79688 2.33% - 0s
#> H 0 0 867.0000000 847.79688 2.21% - 0s
#> 0 0 852.59894 0 5154 867.00000 852.59894 1.66% - 0s
#> H 0 0 865.0000000 852.59894 1.43% - 0s
#> 0 0 852.71808 0 5153 865.00000 852.71808 1.42% - 1s
#> 0 0 852.71808 0 5153 865.00000 852.71808 1.42% - 1s
#> H 0 0 863.0000000 852.71808 1.19% - 1s
#>
#> Cutting planes:
#> Gomory: 2
#> Cover: 24
#> Zero half: 1
#>
#> Explored 1 nodes (7888 simplex iterations) in 2.00 seconds (4.53 work units)
#> Thread count was 2 (of 16 available processors)
#>
#> Solution count 5: 863 865 867 ... 964
#>
#> Time limit reached
#> Best objective 8.630000000000e+02, best bound 8.527180805001e+02, gap 1.1914%
# get connectivity penalty values
getConnectivityPenalty(s)
#> solution_name units threat_1 threat_2
#> 1 sol 0 2861.172 1319.892
# }