Plot trade-offs from a multi-objective solution set

Plot pairwise trade-offs among objective values stored in a SolutionSet.

This function is intended for multi-objective workflows in which the solution set contains one row per run and one or more objective value columns of the form value_*.

If exactly two objectives are selected, the function returns a single scatterplot. If three or more objectives are selected, all pairwise combinations are plotted using facets.

Usage

plot_tradeoff(
  x,
  objectives = NULL,
  color_by = NULL,
  all_pairs = NULL,
  connect = FALSE,
  label_runs = FALSE,
  point_size = 3,
  line_alpha = 0.5,
  text_size = 3,
  ...
)

Arguments

x: A SolutionSet object.
objectives: Optional character vector of objective aliases to display. These must match the suffixes of the value_* columns in x$solution$runs. If NULL, all available objective columns are used.
color_by: Optional character scalar used to colour points. This may be either one of the selected objective aliases or one of the run-level columns "run_id", "status", "runtime", or "gap".
all_pairs: Logical. If TRUE, allow plotting all pairwise combinations even when more than four objectives are selected. If NULL, it is treated as FALSE.
connect: Logical. If TRUE, connect points by run order within each panel.
label_runs: Logical. If TRUE, add run labels to points.
point_size: Numeric point size.
line_alpha: Numeric alpha value for connecting lines.
text_size: Numeric size for run labels.
...: Reserved for future extensions.

Value

Invisibly returns a ggplot object.

Details

This function reads the run-level table stored in x$solution$runs. It expects objective values to be stored in columns whose names begin with "value_".

If the available objective columns are, for example, value_cost, value_benefit, and value_frag, then the corresponding objective aliases are "cost", "benefit", and "frag".

Let $f_k(r)$ denote the value of objective $k$ in run $r$. This function visualizes pairwise projections of the run table of the form: $$ \left(f_k(r), f_\ell(r)\right) $$ for selected pairs of objectives $k,\ell$.

If exactly two objectives are selected, a single panel is produced.

If three or more objectives are selected, all pairwise combinations are generated: $$ \{(k,\ell): k < \ell,\; k,\ell \in \mathcal{O}\}, $$ where $\mathcal{O}$ is the selected set of objective aliases.

By default, plotting more than four objectives is not allowed unless all_pairs = TRUE, because the number of panels grows quadratically in the number of objectives.

Colouring

If color_by is supplied, points are coloured by either:

one of the selected objective aliases, in which case the corresponding value_* column is used,
or one of the run-level columns run_id, status, runtime, or gap.

Connecting runs

If connect = TRUE, runs are connected in their current table order within each panel. This can be useful when runs correspond to an ordered scan of weights, $\epsilon$-levels, or frontier points, but it should be used with care when run order has no substantive meaning.

Run labels

If label_runs = TRUE, each point is labelled by its run_id. If the ggrepel package is available, repelled labels are used.

Examples

if (requireNamespace("ggplot2", quietly = TRUE)) {
  solset <- structure(
    list(
      solution = list(
        runs = data.frame(
          run_id = 1:5,
          status = rep("optimal", 5),
          runtime = c(1.2, 1.1, 1.4, 1.3, 1.5),
          gap = c(0, 0, 0, 0, 0),
          value_cost = c(10, 12, 14, 16, 18),
          value_benefit = c(5, 7, 8, 9, 10),
          value_loss = c(4, 3, 3, 2, 2)
        )
      )
    ),
    class = "SolutionSet"
  )

  # Plot all pairwise trade-offs
  plot_tradeoff(solset)

  # Plot two selected objectives
  plot_tradeoff(solset, objectives = c("cost", "benefit"))

  # Colour points by one objective and label runs
  plot_tradeoff(solset, color_by = "loss", label_runs = TRUE)
}