View source: R/add_min_shortfall_objective.R
add_min_shortfall_objective  R Documentation 
Set the objective of a conservation planning problem to minimize the overall shortfall for as many targets as possible while ensuring that the cost of the solution does not exceed a budget.
add_min_shortfall_objective(x, budget)
x 

budget 

The minimum shortfall objective aims to
find the set of planning units that minimize the overall
(weighted sum) shortfall for the
representation targets—that is, the fraction of each target that
remains unmet—for as many features as possible while staying within a
fixed budget (inspired by Table 1, equation IV, Arponen et al.
2005). Additionally, weights can be used
to favor the representation of certain features over other features (see
add_feature_weights()
.
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{Minimize} \space \sum_{j = 1}^{J} w_j \frac{y_j}{t_j} \\
\mathit{subject \space to} \\
\sum_{i = 1}^{I} x_i r_{ij} + y_j \geq t_j \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
, t_j
is the representation target for feature
j
, y_j
denotes the representation shortfall for
the target t_j
for feature j
, 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
. Note that y_j
is a continuous
variable bounded between zero and infinity, and denotes the shortfall
for target j
.
Arponen A, Heikkinen RK, Thomas CD, and Moilanen A (2005) The value of biodiversity in reserve selection: representation, species weighting, and benefit functions. Conservation Biology, 19: 2009–2014.
See objectives for an overview of all functions for adding objectives.
Also, see targets for an overview of all functions for adding targets, and
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_max_utility_objective()
,
add_min_largest_shortfall_objective()
,
add_min_set_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 minimum shortfall objective
p1 <
problem(sim_pu_raster, sim_features) %>%
add_min_shortfall_objective(1800) %>%
add_relative_targets(0.1) %>%
add_binary_decisions() %>%
add_default_solver(verbose = FALSE)
# solve problem
s1 < solve(p1)
# plot solution
plot(s1, main = "solution", axes = FALSE)
# create multizone problem with minimum shortfall objective,
# with 10% representation targets for each feature, and set
# a budget such that the total maximum expenditure in all zones
# cannot exceed 3000
p2 <
problem(sim_zones_pu_raster, sim_zones_features) %>%
add_min_shortfall_objective(3000) %>%
add_relative_targets(matrix(0.1, ncol = 3, nrow = 5)) %>%
add_binary_decisions() %>%
add_default_solver(verbose = FALSE)
# solve problem
s2 < solve(p2)
# plot solution
plot(category_layer(s2), main = "solution", axes = FALSE)
# create multizone problem with minimum shortfall objective,
# with 10% representation targets for each feature, and set
# separate budgets for each management zone
p3 <
problem(sim_zones_pu_raster, sim_zones_features) %>%
add_min_shortfall_objective(c(3000, 3000, 3000)) %>%
add_relative_targets(matrix(0.1, ncol = 3, nrow = 5)) %>%
add_binary_decisions() %>%
add_default_solver(verbose = FALSE)
# solve problem
s3 < solve(p3)
# plot solution
plot(category_layer(s3), main = "solution", axes = FALSE)
## End(Not run)
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