A penalty can be applied to a conservation planning problem() to penalize solutions according to a specific metric. They directly trade-off with the primary objective of a problem (e.g., the primary objective when using add_min_set_objective() is to minimize solution cost).


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 primary problem objective and are mediated by a penalty factor.

The following penalties can be added to a conservation planning problem():


Add penalties to a conservation problem to favor solutions that have planning units clumped together into contiguous areas.


Add penalties to a conservation problem to account for asymmetric connectivity.


Add penalties to a conservation problem to account for symmetric connectivity.


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 asymmetric connectivity data by randomly simulating values
acm <- matrix(runif(ncell(sim_pu_raster) ^ 2), ncol = ncell(sim_pu_raster))
acm[acm < 0.85] <- 0

# create problem with asymmetric connectivity penalties
p4 <- p1 %>% add_asym_connectivity_penalties(1, data = acm)

# create problem with linear penalties,
# here the penalties will be based on random numbers to keep it simple
# \dontrun{
# 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
p5 <- p1 %>% add_linear_penalties(100, data = sim_penalty_raster)

# solve problems
s <- stack(solve(p1), solve(p2), solve(p3), solve(p4), solve(p5))

# plot solutions
plot(s, axes = FALSE, box = FALSE,
     main = c("basic solution", "boundary penalties",
              "connectivity penalties", "asymmetric penalties",
              "linear penalties"))

 # }