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Select a best-compromise Pareto solution by Euclidean distance

Source: R/multiobjective-04-best_compromise_solution.R
best_compromise_solution.Rd

Selects the solution on a Pareto front with the smallest Euclidean distance to the ideal point.

Usage

best_compromise_solution(pareto_solutions, normalize = TRUE)

Arguments

pareto_solutions

matrix/data.frame/tibble. Each row is a solution (objective vector) and each column is an objective; values must be numeric (no NAs) and oriented for minimization.

normalize

logical. Whether to min–max normalize objectives column-wise before distance calculation (default TRUE).

Value

A list with:

  • objectives: numeric vector with the objective values of the selected solution (original, unnormalized scale).

  • index: integer row index of the selected solution in pareto_solutions.

Details

The ideal point is the vector of column minima in the (normalized) objective space. Euclidean distances are computed from each solution to this ideal point; the closest solution is returned. If several solutions have equal minimum distance, the first occurrence (by row order) is returned.

See also

Other Multiobjective calibration: calculate_objectives(), calibrate_swat(), create_calibration_project()

Examples

pareto_solutions <- matrix(
  c(0.1554, 0.0282, 0.30,
    0.1309, 0.0608, 0.28,
    0.1418, 0.0460, 0.25),
  ncol = 3, byrow = TRUE
)
best     <- best_compromise_solution(pareto_solutions)
best_raw <- best_compromise_solution(pareto_solutions, normalize = FALSE)