Add objective: minimize intervention impact

Define an objective that minimizes the impact associated with selecting planning units for intervention.

This objective uses planning-unit selection variables rather than summing the same impact repeatedly over multiple actions. As a result, each planning unit contributes at most once to the objective, regardless of how many feasible actions exist in that unit.

Usage

add_objective_min_intervention_impact(
  x,
  impact_col = "amount",
  features = NULL,
  actions = NULL,
  alias = NULL
)

Arguments

x

A Problem object.

impact_col

Character string giving the column in the feature-distribution table that contains the per-(pu, feature) impact amount. The default is "amount".

features

Optional subset of features to include. Values may match x$data$features$id and, if present, x$data$features$name.

actions

Optional subset of actions used to define the intervention context. Values may match x$data$actions$id and, if present, x$data$actions$action_set.

alias

Optional identifier used to register this objective for multi-objective workflows.

Value

An updated Problem object.

Details

Use this function when intervention itself has a baseline ecological, social, or operational burden that should be minimized independently of the detailed effects of particular actions.

Let \(w_i \in \{0,1\}\) denote whether planning unit \(i\) is selected for intervention. Let \(q_{if}\) denote the impact amount associated with planning unit \(i\) and feature \(f\), taken from column impact_col in the feature-distribution table.

If all selected features are included, the objective can be interpreted as:

$$ \min \sum_{i \in \mathcal{I}} \left( \sum_{f \in \mathcal{F}^{\star}} q_{if} \right) w_i, $$

where \(\mathcal{F}^{\star}\) denotes the selected subset of features.

Thus, the coefficient attached to \(w_i\) is the aggregated impact of the selected features in planning unit \(i\).

The role of actions in this objective is not to make impact additive over actions, but to restrict the notion of intervention to planning units that are relevant for the selected subset of actions in downstream model construction. Even when multiple feasible actions exist in a planning unit, the planning unit contributes at most once through \(w_i\).

This objective is useful when intervention itself has a baseline ecological, social, or operational impact that should be minimized independently of the detailed gain or loss generated by particular actions.

See also

add_objective_max_benefit, add_objective_min_loss

Examples

pu_tbl <- data.frame(
  id = 1:4,
  cost = c(1, 2, 3, 4)
)
feat_tbl <- data.frame(
  id = 1:2,
  name = c("feature_1", "feature_2")
)
dist_feat_tbl <- data.frame(
  pu = c(1, 1, 2, 3, 4),
  feature = c(1, 2, 2, 1, 2),
  amount = c(5, 2, 3, 4, 1)
)
actions_df <- data.frame(
  id = c("conservation", "restoration"),
  name = c("conservation", "restoration")
)

p <- create_problem(
  pu = pu_tbl,
  features = feat_tbl,
  dist_features = dist_feat_tbl,
  cost = "cost"
) |>
  add_actions(actions_df, cost = c(conservation = 1, restoration = 2))

p1 <- add_objective_min_intervention_impact(p)
p1$data$model_args
#> $model_type
#> [1] "minimizeInterventionImpact"
#> 
#> $objective_id
#> [1] "min_intervention_impact"
#> 
#> $objective_args
#> $objective_args$impact_col
#> [1] "amount"
#> 
#> $objective_args$features
#> [1] 1 2
#> 
#> $objective_args$actions
#> [1] "conservation" "restoration" 
#> 
#> 

p2 <- add_objective_min_intervention_impact(
  p,
  features = 1
)
p2$data$model_args
#> $model_type
#> [1] "minimizeInterventionImpact"
#> 
#> $objective_id
#> [1] "min_intervention_impact"
#> 
#> $objective_args
#> $objective_args$impact_col
#> [1] "amount"
#> 
#> $objective_args$features
#> [1] 1
#> 
#> $objective_args$actions
#> [1] "conservation" "restoration" 
#> 
#> 

p3 <- add_objective_min_intervention_impact(
  p,
  actions = "restoration"
)
p3$data$model_args
#> $model_type
#> [1] "minimizeInterventionImpact"
#> 
#> $objective_id
#> [1] "min_intervention_impact"
#> 
#> $objective_args
#> $objective_args$impact_col
#> [1] "amount"
#> 
#> $objective_args$features
#> [1] 1 2
#> 
#> $objective_args$actions
#> [1] "restoration"
#> 
#>