library(ggplot2)
library(dplyr)
library(ggridges)

Context

The OLA-26 paper computes workload energy by subtracting a per-combination trimmed-mean baseline from each raw workload measurement — but the subtraction is presented only as a summary table. It is impossible to see, run-by-run, how far individual workload readings sit from their respective baseline average, or whether the spread differs between parameter combinations.

This document fills that gap. The three views below all come from the same pair of data files:

The four parameter combinations tested are chromosome dimension × population size: Dim 3 | Pop 200, Dim 3 | Pop 400, Dim 5 | Pop 200, Dim 5 | Pop 400.

Data preparation

null_cols <- c("alpha", "max_gens", "different_seeds",
               "diff_fitness", "generations", "evaluations")

# ── Baseline (100 ms sampling) ───────────────────────────────────────────────
baseline <- read.csv("data/ola-base-ola-baseline-14-Dec-12-06-42.csv")
baseline[null_cols] <- NULL

# Per-combination trimmed mean (20 % trimming) — this is the value subtracted
baseline_summary <- baseline %>%
  group_by(dimension, population_size) %>%
  summarise(
    n_baseline       = n(),
    trimmed_mean_PKG = mean(PKG, trim = 0.2),
    sd_PKG           = sd(PKG),
    .groups = "drop"
  ) %>%
  mutate(param_combo = paste0("Dim ", dimension, " | Pop ", population_size))

# ── Workload ─────────────────────────────────────────────────────────────────
workload <- read.csv("data/ola-1.11.7-ola-14-Dec-13-02-30.csv")
workload$param_combo <- paste0("Dim ", workload$dimension,
                                " | Pop ", workload$population_size)

# Join the per-combination trimmed mean onto every workload row
workload <- workload %>%
  left_join(
    baseline_summary %>% select(dimension, population_size, trimmed_mean_PKG, sd_PKG),
    by = c("dimension", "population_size")
  ) %>%
  mutate(
    delta_PKG = PKG - trimmed_mean_PKG,
    run_index = ave(seq_along(PKG), param_combo, FUN = seq_along)
  )

The trimmed means that will be subtracted are:

baseline_summary %>%
  select(param_combo, n_baseline, trimmed_mean_PKG, sd_PKG) %>%
  mutate(across(where(is.numeric), ~ round(.x, 2)))

View 1 — Every run plotted against its own baseline

Each workload run as a dot. The dashed line is the trimmed-mean baseline for that combination — the exact value that will be subtracted.

Vertical segments connect each run to its baseline: green segments reach upward (Δ PKG > 0), pink segments reach downward (Δ PKG < 0). The shaded band is ±1 SD of the baseline energy, giving a sense of how variable the idle system itself was.

pal_sign <- c("TRUE" = "#3D9970", "FALSE" = "#E07A5F")

ggplot(workload, aes(x = as.numeric(run_index), y = PKG)) +
  # ±1 SD baseline band
  geom_rect(
    data = baseline_summary,
    aes(xmin = -Inf, xmax = Inf,
        ymin = trimmed_mean_PKG - sd_PKG,
        ymax = trimmed_mean_PKG + sd_PKG),
    fill = "#F28E2B", alpha = 0.10, inherit.aes = FALSE
  ) +
  # sign-coded vertical segments
  geom_segment(
    aes(xend = as.numeric(run_index),
        yend = trimmed_mean_PKG,
        colour = delta_PKG >= 0),
    alpha = 0.40, linewidth = 0.6
  ) +
  # workload points
  geom_point(colour = "grey20", size = 2.2, alpha = 0.80) +
  # baseline average line
  geom_hline(
    data = baseline_summary,
    aes(yintercept = trimmed_mean_PKG),
    linetype = "dashed", colour = "#F28E2B", linewidth = 1.0
  ) +
  scale_colour_manual(
    values = pal_sign,
    labels = c("TRUE" = "Above baseline (Δ PKG > 0)",
               "FALSE" = "Below baseline (Δ PKG < 0)"),
    name = NULL
  ) +
  facet_wrap(~ param_combo, ncol = 2) +
  theme_minimal(base_size = 14) +
  theme(
    legend.position  = "bottom",
    strip.text       = element_text(face = "bold"),
    panel.grid.minor = element_blank(),
    plot.title       = element_text(face = "bold"),
    plot.subtitle    = element_text(colour = "grey40")
  ) +
  labs(
    title    = "Workload runs vs. their per-combination baseline average",
    subtitle = "Dashed line = trimmed mean of baseline (the subtracted value) · Shaded band = ±1 SD",
    x        = "Run index within parameter combination",
    y        = "PKG energy (Joules)"
  )
**Fig. 1** — Workload PKG energy per run (dark points) with per-combination trimmed-mean baseline overlaid (dashed orange line). Green segments indicate runs above the baseline; pink segments indicate runs below. Shaded band = ±1 SD of baseline energy.

Fig. 1 — Workload PKG energy per run (dark points) with per-combination trimmed-mean baseline overlaid (dashed orange line). Green segments indicate runs above the baseline; pink segments indicate runs below. Shaded band = ±1 SD of baseline energy.

What to take away: The baseline average does not sit at the centre of the workload distribution — individual runs land 100–200 J above or below it. Theoretically, it should be very similar, since different combinations of problem size and population size shouldn’t affect it too much. Because only a constant is subtracted, the spread of Δ PKG is essentially the same as the spread of the raw workload PKG. Runs that fall below their own baseline line produce negative Δ PKG values, visible here as pink segments.

View 2 — Δ PKG distributions per combination

What does the subtracted delta look like for each parameter combination?

combo_pal <- c(
  "Dim 3 | Pop 200" = "#4E79A7",
  "Dim 3 | Pop 400" = "#76B7B2",
  "Dim 5 | Pop 200" = "#F28E2B",
  "Dim 5 | Pop 400" = "#E15759"
)

ggplot(workload,
       aes(x = param_combo, y = delta_PKG,
           fill = param_combo, colour = param_combo)) +
  geom_violin(alpha = 0.35, linewidth = 0.4, width = 0.85) +
  geom_boxplot(
    width = 0.18, notch = TRUE,
    outlier.size = 1.8, outlier.alpha = 0.5,
    fill = "white", colour = "grey30", alpha = 0.9
  ) +
  geom_hline(yintercept = 0, linetype = "dotted",
             colour = "red", linewidth = 0.8) +
  scale_fill_manual(values = combo_pal) +
  scale_colour_manual(values = combo_pal) +
  theme_minimal(base_size = 14) +
  theme(
    legend.position  = "none",
    axis.text.x      = element_text(angle = 15, hjust = 1),
    panel.grid.minor = element_blank(),
    plot.title       = element_text(face = "bold"),
    plot.subtitle    = element_text(colour = "grey40")
  ) +
  labs(
    title    = "Distribution of Δ PKG per parameter combination",
    subtitle = "Δ PKG = workload PKG − per-combination trimmed-mean baseline · Red line at zero",
    x        = NULL,
    y        = "Δ PKG energy (Joules)"
  )
**Fig. 2** — Violin + notched box-plot of Δ PKG for each parameter combination. The red dotted line marks zero; values below it are negative deltas. Notch = 95 % CI for the median.

Fig. 2 — Violin + notched box-plot of Δ PKG for each parameter combination. The red dotted line marks zero; values below it are negative deltas. Notch = 95 % CI for the median. 

ggsave("preso/img/baseline-workload-comparison.png", height=4.5, width=8)

View 3 — Ridgeline density of Δ PKG

An overlapping density view makes it easier to compare the shape of each combination’s distribution.

ggplot(workload,
       aes(x = delta_PKG, y = param_combo, fill = param_combo)) +
  geom_density_ridges(
    alpha          = 0.55,
    scale          = 0.85,
    quantile_lines = TRUE,
    quantiles      = c(0.25, 0.5, 0.75),
    linewidth      = 0.4
  ) +
  geom_vline(xintercept = 0, linetype = "dashed",
             colour = "red", linewidth = 0.8) +
  scale_fill_manual(values = combo_pal) +
  theme_ridges(font_size = 14) +
  theme(
    legend.position = "none",
    plot.title      = element_text(face = "bold"),
    plot.subtitle   = element_text(colour = "grey40")
  ) +
  labs(
    title    = "Ridgeline density of Δ PKG per parameter combination",
    subtitle = "Quantile lines at Q1, median, Q3 · Red dashed line at zero",
    x        = "Δ PKG energy (Joules)",
    y        = NULL
  )
**Fig. 3** — Ridgeline density of Δ PKG. Vertical lines mark Q1, median (solid) and Q3. The red dashed line is at zero.

Fig. 3 — Ridgeline density of Δ PKG. Vertical lines mark Q1, median (solid) and Q3. The red dashed line is at zero.

What to take away: The distributions are roughly similar across combinations, but their centres (medians) and tails differ. The fraction of runs producing a negative Δ PKG varies between combinations — a direct consequence of how variable the idle system was during the (separately recorded) baseline campaign. This motivates the sequential mixed approach described in the paper, where each workload run is paired with the baseline run that immediately preceded it.

About

This document is a companion to the OLA-26 paper “Best practices in measuring energy consumption in population-based metaheuristics” by Merelo & Merelo-Molina. All data and code are available at https://github.com/JJ/brave-new-green-algorithm.

Research supported by the Ministerio español de Economía y Competitividad under project PID2023-147409NB-C21.

Source: JJ Merelo, Cecilia Merelo Molina Best practices in measuring energy consumption in population-based metaheuristics, in Proceedings OLA’26 International Conference on Optimization and Learning, pp 183-194, available online. Please check references.bib for the BibTeX entry.