Generate a survey scheme by selecting the set of sites with the greatest overall weight value, a maximum budget for the survey scheme.
weighted_survey_scheme(
site_data,
cost_column,
survey_budget,
weight_column,
locked_in_column = NULL,
locked_out_column = NULL,
solver = "auto",
verbose = FALSE
)
sf::sf()
object containing the candidate survey
sites.
character
name of the column in the argument to
the argument to site_data
that contains the cost for surveying each
site. No missing (NA
) values are permitted.
numeric
vector of maximum budgets for the survey
schemes. No missing (NA
) values are permitted.
character
name of the column in the argument
to site_data
with the weights for each site.
character
(optional) name of the column in
the argument to site_data
that contains logical
(TRUE
/ FALSE
) values indicating if certain sites should be
locked into the survey scheme.
No missing (NA
) values are permitted.
Defaults to NULL
such that no sites are locked in.
character
(optional) name of the column in
the argument to site_data
that contains logical
(TRUE
/ FALSE
) values indicating if certain sites should be
locked out of the survey scheme.
No missing (NA
) values are permitted.
Defaults to NULL
such that no sites are locked out.
character
name of the optimization solver to use
for generating survey schemes.
Available options include: "Rsymphony"
, "gurobi"
and "auto"
.
The "auto"
method will use the Gurobi optimization software if
it is available; otherwise, it will use the SYMPHONY software
via the Rsymphony package.
Defaults to "auto"
.
logical
indicating if information should be
printed while generating survey scheme(s). Defaults to FALSE
.
A matrix
of logical
(TRUE
/ FALSE
)
values indicating if a site is selected in a scheme or not. Columns
correspond to sites, and rows correspond to different schemes.
Let \(J\) denote the set of sites (indexed by \(j\)), and let \(b\) denote the maximum budget available for surveying the sites. Next, let \(c_j\) represent the cost of surveying each site \(j \in J\), and \(w_j\) denote the relative value (weight) for surveying each site \(j \in J\). The set of sites with the greatest overall weight values, subject to a given budget can the be identified by solving the following integer programming problem. Here, \(x_j\) is the binary decision variable indicating each if site is selected in the survey scheme or not.
$$\mathit{Maximize} \space \sum_{j \in J} x_j w_i \\ \mathit{subject \space to} \\ \sum_{j \in J} x_j c_j \leq b$$
This function can use the Rsymphony package and the Gurobi optimization software to generate survey schemes. Although the Rsymphony package is easier to install because it is freely available on the The Comprehensive R Archive Network (CRAN), it is strongly recommended to install the Gurobi optimization software and the gurobi R package because it can generate survey schemes much faster. Note that special academic licenses are available at no cost. Installation instructions are available online for Linux, Windows, and Mac OS operating systems.
# set seed for reproducibility
set.seed(123)
# simulate data
x <- sf::st_as_sf(
tibble::tibble(x = rnorm(4), y = rnorm(4),
w = c(0.01, 10, 8, 1),
cost = c(1, 1, 1, 1)),
coords = c("x", "y"))
# plot site' locations and color by weight values
plot(x[, "w"], pch = 16, cex = 3)
# generate scheme without any sites locked in
s <- weighted_survey_scheme(x, cost_column = "cost", survey_budget = 2,
weight_column = "w")
# print solution
print(s)
#> [,1] [,2] [,3] [,4]
#> [1,] FALSE TRUE TRUE FALSE
# plot solution
x$s <- c(s)
plot(x[, "s"], pch = 16, cex = 3)