add_connectivity_penalties: Add connectivity penalties
In prioritizr/prioritizrutils: Utilities for prioritizr

Description Usage Arguments Value See Also Examples

Add penalties to a conservation problem to favor solutions that select planning units with high connectivity between them.

1	add_connectivity_penalties(x, penalty, connectivity_data)

`x`	`ConservationProblem-class` object.
`penalty`	`numeric` penalty for missing connections between planning units. This is equivalent to the connectivity strength modifier (CSM; (XXX et al. XXXX). Defaults to one so that penalties are the same as the values in the `data`.
`connectivity_data`	`data.frame`, `matrix`, `Matrix` object that shows the strength of connectivity between consecutive planning units. If `data` is a matrix, then rows and columns represent each planing unit and the cell values represent the connectivity between them. If `data` is a `data.frame` the column names be `"id1"`, `"id2"`, `"boundary"` where each row shows the connectivity between two planning units (following the Marxan format). The data can be describe symmetric or asymmetric connecitivity between planning units.

ConservationProblem-class object.

constraints, penalties.

# load data
data(sim_pu_points, sim_features)

# create a symmetric connectivity matrix where the connectivity between
# two planning units is the inverse distance between them
sc_matrix <- (1 / (as.matrix(dist(sim_pu_points@coords)) + 1))

# remove connections between planning unitswith little connectivity
sc_matrix[sc_matrix < 0.85] <- 0

# create basic problem
p1 <- problem(sim_pu_points, sim_features) %>%
  add_min_set_objective() %>%
  add_relative_targets(0.2)

# create problem with low connectivity penalties
p2 <- p1 %>% add_connectivity_penalties(25, sc_matrix)

# create problem with higher connectivity penalties
p3 <- p1 %>% add_connectivity_penalties(50, sc_matrix)

# create an asymmetric connectivity matrix where links from even numered
# units to odd numbered units have half the connectivity as from odd
# numbered units to even units
even_units <- seq(2, length(sim_pu_points), 2)
odd_units <- seq(1, length(sim_pu_points), 2)
ac_matrix <- sc_matrix
ac_matrix[even_units, odd_units] <- 0.5 * ac_matrix[even_units, odd_units]

# create problem with asymmetric connectivity and high penalties
p4 <- p1 %>% add_connectivity_penalties(50, ac_matrix)


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

# plot solutions
par(mfrow=c(2,2))

plot(s[[1]], pch=19, main="basic solution", cex = 1.5)
points(s[[1]][s[[1]]$solution==1, ], col = "darkgreen", pch = 19, cex = 1.5)

plot(s[[2]], pch=19, main="small penalties", cex = 1.5)
points(s[[2]][s[[2]]$solution==1, ], col = "darkgreen", pch = 19, cex = 1.5)

plot(s[[3]], pch=19, main="high penalties", cex = 1.5)
points(s[[3]][s[[3]]$solution==1, ], col = "darkgreen", pch = 19, cex = 1.5)

plot(s[[4]], pch=19, main="asymmetric connectivity", cex = 1.5)
points(s[[4]][s[[4]]$solution==1, ], col = "darkgreen", pch=19, cex = 1.5)