View source: R/add_max_utility_objective.R
add_max_utility_objective  R Documentation 
Set the objective of a conservation planning problem to secure as much of the features as possible without exceeding a budget. This objective does not use targets, and feature weights should be used instead to increase the representation of certain features by a solution. Note that this objective does not aim to maximize as much of each feature as possible, and so often results in solutions that are heavily biased towards just a few features.
add_max_utility_objective(x, budget)
x 

budget 

The maximum utility objective seeks to maximize the overall level of
representation across a suite of conservation features, while keeping cost
within a fixed budget.
Additionally, weights can be used to favor the
representation of certain features over other features (see
add_feature_weights()
). It is essentially calculated as a weighted
sum of the feature data inside the selected planning units.
An updated problem()
object with the objective added to it.
This objective can be expressed mathematically for a set of planning units
(I
indexed by i
) and a set of features (J
indexed
by j
) as:
\mathit{Maximize} \space \sum_{i = 1}^{I} s \space c_i \space x_i +
\sum_{j = 1}^{J} a_j w_j \\
\mathit{subject \space to} \\ a_j = \sum_{i = 1}^{I} x_i r_{ij} \space
\forall j \in J \\ \sum_{i = 1}^{I} x_i c_i \leq B
Here, x_i
is the decisions variable (e.g.,
specifying whether planning unit i
has been selected (1) or not
(0)), r_{ij}
is the amount of feature j
in planning
unit i
, A_j
is the amount of feature j
represented in in the solution, and w_j
is the weight for
feature j
(defaults to 1 for all features; see
add_feature_weights()
to specify weights). Additionally, B
is the budget allocated for
the solution, c_i
is the cost of planning unit i
, and
s
is a scaling factor used to shrink the costs so that the problem
will return a cheapest solution when there are multiple solutions that
represent the same amount of all features within the budget.
In early versions (< 3.0.0.0), this function was named as
the add_max_cover_objective
function. It was renamed to avoid
confusion with existing terminology.
See objectives for an overview of all functions for adding objectives.
Also, see add_feature_weights()
to specify weights for different features.
Other objectives:
add_max_cover_objective()
,
add_max_features_objective()
,
add_max_phylo_div_objective()
,
add_max_phylo_end_objective()
,
add_min_largest_shortfall_objective()
,
add_min_set_objective()
,
add_min_shortfall_objective()
## Not run:
# load data
sim_pu_raster < get_sim_pu_raster()
sim_features < get_sim_features()
sim_zones_pu_raster < get_sim_zones_pu_raster()
sim_zones_features < get_sim_zones_features()
# create problem with maximum utility objective
p1 <
problem(sim_pu_raster, sim_features) %>%
add_max_utility_objective(5000) %>%
add_binary_decisions() %>%
add_default_solver(gap = 0, verbose = FALSE)
# solve problem
s1 < solve(p1)
# plot solution
plot(s1, main = "solution", axes = FALSE)
# create multizone problem with maximum utility objective that
# has a single budget for all zones
p2 <
problem(sim_zones_pu_raster, sim_zones_features) %>%
add_max_utility_objective(5000) %>%
add_binary_decisions() %>%
add_default_solver(gap = 0, verbose = FALSE)
# solve problem
s2 < solve(p2)
# plot solution
plot(category_layer(s2), main = "solution", axes = FALSE)
# create multizone problem with maximum utility objective that
# has separate budgets for each zone
p3 <
problem(sim_zones_pu_raster, sim_zones_features) %>%
add_max_utility_objective(c(1000, 2000, 3000)) %>%
add_binary_decisions() %>%
add_default_solver(gap = 0, verbose = FALSE)
# solve problem
s3 < solve(p3)
# plot solution
plot(category_layer(s3), main = "solution", axes = FALSE)
## End(Not run)
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