add_multiscale_min_set_objective: Add a multiscale minimum-set objective

In MultiscaleSCP: Multiscale Systematic Conservation Planning Across Nested H3 Grids

Add a multiscale minimum-set objective

Description

Sets the objective of a conservation planning problem to minimize cost while meeting feature representation targets across nested H3 resolutions.

Usage

add_multiscale_min_set_objective(x, data)

Arguments

x	A single-zone prioritizr ConservationProblem object.
data	A multiscale_objective_data object returned by build_multiscale_objective_data().

Details

Feature representation is calculated across the planning-unit hierarchy, so selecting a planning unit at one resolution can contribute toward targets for features represented at another resolution. Spatial contributions shared by overlapping parent and descendant planning units are counted once.

This accounting is implemented using non-overlapping spatial units, referred to as atoms, for both cost and feature representation.

The data object and conservation problem must use the same planning-unit row order and matching feature names. The formulation supports single-zone problems with binary planning-unit decisions and the compressed formulation.

Value

An updated ConservationProblem object.

Mathematical formulation

Let x_i indicate whether planning unit i is selected and let z_a indicate whether atom a is activated. If C_a is the set of planning units that cover atom a, atom activation is linked to planning-unit selection by z_a >= x_i for each i in C_a and ⁠z_a <= sum(x_i, i in C_a)⁠.

Planning-unit decisions are binary, with x_i in ⁠{0, 1}⁠, while atom activation variables satisfy ⁠0 <= z_a <= 1⁠.

The objective minimizes sum(c_a * z_a), where c_a is the cost of atom a. Feature representation targets require sum(q_aj * z_a) >= T_j, where q_aj is the amount of feature j assigned to atom a and T_j is its representation target.

See Also

Other objectives: add_multiscale_min_set()

Other multiscale minimum-set: add_multiscale_min_set(), add_multiscale_relative_targets(), build_multiscale_atoms(), build_multiscale_feature_atoms(), build_multiscale_objective_data(), eval_multiscale_atom_solution(), load_multiscale_feature(), multiscale_feature_cols()

Examples

h3_vec <- c("872a1072bffffff","882a1072b1fffff","882a1072b3fffff")
pu <- h3jsr::cell_to_polygon(h3_vec, simple = FALSE)
pu <- pu[match(h3_vec, pu$h3_address), ]

pu$res <- c(7L, 8L, 8L)
pu$area_km2 <- c(14, 2, 2)
pu$A <- c(3, 1, 2)
pu$B <- c(6, 2, 1)

maps <- build_h3_maps(pu)

ms_data <- build_multiscale_objective_data(
  pu, maps, feature_cols = c(A = "A", B = "B"))

p <- prioritizr::problem(
  pu,features = c("A", "B"),cost_column = "area_km2")

p <- add_multiscale_min_set_objective(p, ms_data)
p <- add_multiscale_relative_targets(p, c(A = 2/3, B = 1/2),ms_data)
p <- prioritizr::add_binary_decisions(p)

MultiscaleSCP documentation built on Oct. 14, 2026, 5:07 p.m.