Add objective: minimize loss

Define an objective that minimizes the total negative effects generated by selected actions on selected features.

This objective is based on the canonical effects table and uses only the non-negative loss component.

Usage

add_objective_min_loss(x, actions = NULL, features = NULL, alias = NULL)

Arguments

x

A Problem object.

actions

Optional subset of actions to include in the objective. Values may match x$data$actions$id and, if present, x$data$actions$action_set. If NULL, all actions are included.

features

Optional subset of features to include in the objective. Values may match x$data$features$id and, if present, x$data$features$name. If NULL, all features are included.

alias

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

Value

An updated Problem object.

Details

Use this function when harmful ecological effects should be minimized explicitly, without offsetting them against beneficial effects.

Let \(\ell_{iaf} \ge 0\) denote the stored loss associated with planning unit \(i\), action \(a\), and feature \(f\).

If no subsets are supplied, the objective can be written as:

$$ \min \sum_{(i,a,f) \in \mathcal{R}} \ell_{iaf} \, x_{ia}. $$

where \(\mathcal{R}\) denotes the set of stored loss rows and \(x_{ia} \in \{0,1\}\) indicates whether action \(a\) is selected in planning unit \(i\).

If actions is provided, only rows whose action belongs to the selected subset contribute to the objective.

If features is provided, only rows whose feature belongs to the selected subset contribute to the objective.

More generally, letting \(\mathcal{R}^{\star}\) be the subset induced by the selected actions and features, the objective is:

$$ \min \sum_{(i,a,f) \in \mathcal{R}^{\star}} \ell_{iaf} \, x_{ia}. $$

This objective minimizes harmful effects only. It does not offset losses against benefits unless benefits are handled elsewhere through additional objectives or constraints.

See also

add_objective_max_benefit, add_effects

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")
)
effects_df <- data.frame(
  pu = c(1, 2, 3, 4, 1, 2, 3, 4),
  action = c("conservation", "conservation", "conservation", "conservation",
             "restoration", "restoration", "restoration", "restoration"),
  feature = c(1, 1, 1, 1, 2, 2, 2, 2),
  benefit = c(2, 1, 0, 1, 3, 0, 1, 2),
  loss = c(0, 0, 1, 0, 0, 1, 0, 0)
)

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)) |>
  add_effects(effects_df)

p1 <- add_objective_min_loss(p)
p1$data$model_args
#> $model_type
#> [1] "minimizeLosses"
#> 
#> $objective_id
#> [1] "min_loss"
#> 
#> $objective_args
#> $objective_args$actions
#> NULL
#> 
#> $objective_args$features
#> NULL
#> 
#> 

p2 <- add_objective_min_loss(
  p,
  actions = "restoration"
)
p2$data$model_args
#> $model_type
#> [1] "minimizeLosses"
#> 
#> $objective_id
#> [1] "min_loss"
#> 
#> $objective_args
#> $objective_args$actions
#> [1] 2
#> 
#> $objective_args$features
#> NULL
#> 
#> 

p3 <- add_objective_min_loss(
  p,
  features = 1
)
p3$data$model_args
#> $model_type
#> [1] "minimizeLosses"
#> 
#> $objective_id
#> [1] "min_loss"
#> 
#> $objective_args
#> $objective_args$actions
#> NULL
#> 
#> $objective_args$features
#> [1] 1
#> 
#>