Add a penalty
A penalty can be applied to a conservation planning problem() to
penalize solutions according to a specific metric. Penalties—unlike
constraints—act as an explicit trade-off with the objective
being minimized or maximized (e.g. solution cost when used with
add_min_set_objective()).
Both penalties and constraints can be used to modify a problem and identify solutions that exhibit specific characteristics. Constraints work by invalidating solutions that do not exhibit specific characteristics. On the other hand, penalties work by specifying trade-offs against the main problem objective and are mediated by a penalty factor.
The following penalties can be added to a conservation planning
problem():
add_boundary_penalties()Add penalties to a conservation problem to favor solutions that have planning units clumped together into contiguous areas.
add_connectivity_penalties()Add penalties to a conservation problem to favor solutions that select planning units with high connectivity between them.
add_linear_penalties()Add penalties to a conservation problem to favor solutions that avoid selecting planning units based on a certain variable (e.g. anthropogenic pressure).
# load data
data(sim_pu_raster, sim_features)
# create basic problem
p1 <- problem(sim_pu_raster, sim_features) %>%
add_min_set_objective() %>%
add_relative_targets(0.2) %>%
add_default_solver(verbose = FALSE)
# create problem with boundary penalties
p2 <- p1 %>% add_boundary_penalties(5, 1)
# create connectivity matrix based on spatial proximity
scm <- as.data.frame(sim_pu_raster, xy = TRUE, na.rm = FALSE)
scm <- 1 / (as.matrix(dist(scm)) + 1)
# remove weak and moderate connections between planning units to reduce
# run time
scm[scm < 0.85] <- 0
# create problem with connectivity penalties
p3 <- p1 %>% add_connectivity_penalties(25, data = scm)
# create problem with linear penalties,
# here the penalties will be based on random numbers to keep it simple
# simulate penalty data
sim_penalty_raster <- simulate_cost(sim_pu_raster)
# plot penalty data
plot(sim_penalty_raster, main = "penalty data", axes = FALSE, box = FALSE)
# create problem with linear penalties, with a penalty scaling factor of 100
p4 <- p1 %>% add_linear_penalties(100, data = sim_penalty_raster)
## Not run:
# solve problems
s <- stack(solve(p1), solve(p2), solve(p3), solve(p4))
# plot solutions
plot(s, axes = FALSE, box = FALSE,
main = c("basic solution", "boundary penalties",
"connectivity penalties", "linear penalties"))
## End(Not run)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.