Identify Pareto Optimal Solutions

Identifies parcels that are Pareto optimal (non-dominated) across multiple objectives. A parcel is Pareto optimal if no other parcel performs better on all objectives simultaneously. This function supports both maximization and minimization objectives.

Usage

identify_pareto_optimal(
  data,
  objectives,
  maximize = rep(TRUE, length(objectives))
)

Arguments

data

An sf object or data.frame containing the parcels to analyze

objectives

Character vector of column names representing the objectives to optimize (e.g., c("family_C", "family_B", "family_P"))

maximize

Logical vector of same length as objectives, indicating whether each objective should be maximized (TRUE) or minimized (FALSE). Default is to maximize all objectives.

Value

The input data with an additional is_optimal logical column indicating whether each parcel is Pareto optimal. If input is sf object, output preserves the sf class and geometry.

Details

## Pareto Dominance

For maximization objectives: - Parcel A dominates parcel B if A ≥ B on all objectives AND A > B on at least one objective

For minimization objectives: - Parcel A dominates parcel B if A ≤ B on all objectives AND A < B on at least one objective

A parcel is **Pareto optimal** if it is not dominated by any other parcel.

## Applications

Pareto analysis is useful for: - Multi-criteria decision making (e.g., balancing production vs conservation) - Identifying trade-off frontiers between ecosystem services - Selecting parcels for diverse management objectives - Benchmarking parcel performance across multiple dimensions

Examples

if (FALSE) { # \dontrun{
# Load demo dataset
data("massif_demo_units")

# Find parcels that are optimal for carbon, biodiversity, and production
result <- identify_pareto_optimal(
  massif_demo_units,
  objectives = c("family_C", "family_B", "family_P"),
  maximize = c(TRUE, TRUE, TRUE)
)

# How many are Pareto optimal?
sum(result$is_optimal)

# Mixed objectives: maximize carbon and biodiversity, minimize fire risk
result_mixed <- identify_pareto_optimal(
  massif_demo_units,
  objectives = c("family_C", "family_B", "family_R"),
  maximize = c(TRUE, TRUE, FALSE)
)

# Visualize optimal parcels
library(ggplot2)
ggplot(result, aes(x = family_C, y = family_B, color = is_optimal)) +
  geom_point(size = 3) +
  scale_color_manual(values = c("gray", "red")) +
  labs(
    title = "Pareto Optimal Parcels",
    x = "Carbon Storage", y = "Biodiversity"
  )
} # }