## ----setup, include = FALSE---------------------------------------------------
# Global knitr options. Reproducibility is enforced via a seed inside
# every call to run_momst().
knitr::opts_chunk$set(
  collapse = TRUE,
  comment  = "#>",
  fig.align = "center",
  warning   = FALSE,
  message   = FALSE
)

## ----load---------------------------------------------------------------------
library(momst)

## ----shared-setup-------------------------------------------------------------
# Problem size and number of objectives
n_nodes <- 12
n_obj   <- 2

# A single instance reused by all variants
shared_instance <- generate_instance(
  n        = n_nodes,
  num_obj  = n_obj,
  range_a  = c(10, 100),
  range_b  = c(10,  50),
  seed     = 2026
)

# NSGA-II hyper-parameters shared by every run
common_args <- list(
  instance           = shared_instance,
  n                  = n_nodes,
  num_obj            = n_obj,
  iterations         = 3,        # three independent runs per variant
  pop_size           = 40,
  tour_size          = 2,
  cross_rate         = 0.80,
  mut_rate           = 0.10,
  max_generations    = 50,
  convergence_window = 10,
  verbose            = FALSE,
  seed               = 123
)

## ----runner-------------------------------------------------------------------
# Run a given variant with the common arguments.
run_variant <- function(variant) {
  do.call(run_momst, c(common_args, list(variant = variant)))
}

## ----run-all------------------------------------------------------------------
# Pure NSGA-II without local search
res_base <- run_variant("base")

# NSGA-II + Path Relinking
res_PR   <- run_variant("PR")

# NSGA-II + Pareto Local Search
res_PLS  <- run_variant("PLS")

# NSGA-II + Tabu Search
res_TS   <- run_variant("TS")

## ----tidy-fronts--------------------------------------------------------------
# Helper: extract just the objective columns from the global Pareto front
extract_obj <- function(res, label) {
  front <- res$global_pareto
  data.frame(
    variant    = label,
    objective_1 = front$objective_1,
    objective_2 = front$objective_2
  )
}

fronts_all <- rbind(
  extract_obj(res_base, "base"),
  extract_obj(res_PR,   "PR"),
  extract_obj(res_PLS,  "PLS"),
  extract_obj(res_TS,   "TS")
)

# Number of non-dominated solutions returned by each variant
table(fronts_all$variant)

## ----summary-fronts-----------------------------------------------------------
# Best value reached per objective and number of non-dominated points
summary_table <- do.call(rbind, lapply(
  split(fronts_all, fronts_all$variant),
  function(df) {
    data.frame(
      variant     = unique(df$variant),
      n_solutions = nrow(df),
      best_obj1   = round(min(df$objective_1), 2),
      best_obj2   = round(min(df$objective_2), 2),
      mean_obj1   = round(mean(df$objective_1), 2),
      mean_obj2   = round(mean(df$objective_2), 2)
    )
  }
))
rownames(summary_table) <- NULL
summary_table

## ----individual-plots, fig.width = 7, fig.height = 7, fig.cap = "Pareto fronts of the four variants (one panel per variant)."----
op <- par(mfrow = c(2, 2), mar = c(4, 4, 2, 1))
plot_pareto_front(res_base); title(sub = "base")
plot_pareto_front(res_PR);   title(sub = "PR")
plot_pareto_front(res_PLS);  title(sub = "PLS")
plot_pareto_front(res_TS);   title(sub = "TS")
par(op)

## ----combined-plot, fig.cap = "Pareto fronts of the four variants on the same axes."----
# Colour palette: one distinct colour per variant
palette_var <- c(base = "#1f77b4",
                 PR   = "#d62728",
                 PLS  = "#2ca02c",
                 TS   = "#9467bd")

# Set plotting limits from the union of all fronts
xlim <- range(fronts_all$objective_1)
ylim <- range(fronts_all$objective_2)

plot(NA, NA, xlim = xlim, ylim = ylim,
     xlab = "Objective 1", ylab = "Objective 2",
     main = "Pareto fronts: base vs PR vs PLS vs TS")

# Draw each variant in its colour, connecting the points with a dashed line
for (v in names(palette_var)) {
  sub <- fronts_all[fronts_all$variant == v, ]
  sub <- sub[order(sub$objective_1), ]
  lines(sub$objective_1, sub$objective_2,
        col = palette_var[v], lty = 2, lwd = 1.2)
  points(sub$objective_1, sub$objective_2,
         col = palette_var[v], pch = 19)
}

legend("topright", legend = names(palette_var),
       col = palette_var, pch = 19, lty = 2, bty = "n")

## ----combined-front-----------------------------------------------------------
# Pool every chromosome from every variant
all_chr <- rbind(
  res_base$global_pareto[, 1:(n_nodes - 2), drop = FALSE],
  res_PR$global_pareto[,   1:(n_nodes - 2), drop = FALSE],
  res_PLS$global_pareto[,  1:(n_nodes - 2), drop = FALSE],
  res_TS$global_pareto[,   1:(n_nodes - 2), drop = FALSE]
)
all_chr <- unique(as.matrix(all_chr))

# Evaluate the pooled set on the shared instance
ev <- compute_objectives(shared_instance, all_chr, n_obj,
                         lookup = build_weight_lookup(shared_instance, n_nodes, n_obj))

# Keep only the non-dominated solutions of the pooled set
ev <- non_dominated_crowding(ev, n_obj)
combined_front <- as.data.frame(ev[ev[, "rankingIndex"] == 1, , drop = FALSE])

# How many trees define the combined Pareto front
nrow(combined_front)

## ----contribution-------------------------------------------------------------
# Build a key for each tree on the combined front
key_combined <- apply(combined_front[, 1:(n_nodes - 2)], 1,
                      function(r) paste(as.integer(r), collapse = "_"))

# Same key for the front of every variant
key_of <- function(res) {
  apply(res$global_pareto[, 1:(n_nodes - 2), drop = FALSE], 1,
        function(r) paste(as.integer(r), collapse = "_"))
}

# Number of solutions of each variant that survive on the combined front
contribution <- data.frame(
  variant      = c("base", "PR", "PLS", "TS"),
  contribution = c(
    sum(key_of(res_base) %in% key_combined),
    sum(key_of(res_PR)   %in% key_combined),
    sum(key_of(res_PLS)  %in% key_combined),
    sum(key_of(res_TS)   %in% key_combined)
  )
)
contribution

## ----combined-plot-final, fig.cap = "Combined Pareto front (black) on top of each variant front."----
plot(NA, NA, xlim = xlim, ylim = ylim,
     xlab = "Objective 1", ylab = "Objective 2",
     main = "Variants vs combined Pareto front")

for (v in names(palette_var)) {
  sub <- fronts_all[fronts_all$variant == v, ]
  sub <- sub[order(sub$objective_1), ]
  points(sub$objective_1, sub$objective_2,
         col = palette_var[v], pch = 1)
}

cf <- combined_front[order(combined_front$objective_1), ]
points(cf$objective_1, cf$objective_2,
       col = "black", pch = 19, cex = 1.1)
lines(cf$objective_1, cf$objective_2, col = "black", lwd = 1.4)

legend("topright",
       legend = c("base", "PR", "PLS", "TS", "Combined"),
       col    = c(palette_var, "black"),
       pch    = c(rep(1, 4), 19),
       lty    = c(rep(NA, 4), 1),
       bty    = "n")

## ----elapsed------------------------------------------------------------------
data.frame(
  variant         = c("base", "PR", "PLS", "TS"),
  elapsed_seconds = round(c(res_base$elapsed,
                            res_PR$elapsed,
                            res_PLS$elapsed,
                            res_TS$elapsed), 2)
)

## ----best-trees, fig.width = 7, fig.height = 7, fig.cap = "Best-compromise spanning tree of each variant."----
if (requireNamespace("igraph", quietly = TRUE)) {
  op <- par(mfrow = c(2, 2), mar = c(2, 2, 3, 2))
  plot_best_tree(res_base, n = n_nodes); title(sub = "base")
  plot_best_tree(res_PR,   n = n_nodes); title(sub = "PR")
  plot_best_tree(res_PLS,  n = n_nodes); title(sub = "PLS")
  plot_best_tree(res_TS,   n = n_nodes); title(sub = "TS")
  par(op)
} else {
  message("Install 'igraph' to plot the best-compromise trees.")
}

## ----three-obj----------------------------------------------------------------
common_3 <- list(
  n                  = 9,
  num_obj            = 3,
  iterations         = 2,
  pop_size           = 30,
  max_generations    = 30,
  range_a            = c(10, 100),
  range_b            = c(10,  50),
  range_c            = c(30, 200),
  convergence_window = 8,
  verbose            = FALSE,
  seed               = 555
)

run_variant_3 <- function(variant) {
  do.call(run_momst, c(common_3, list(variant = variant)))
}

res3_base <- run_variant_3("base")
res3_PR   <- run_variant_3("PR")
res3_PLS  <- run_variant_3("PLS")
res3_TS   <- run_variant_3("TS")

## ----three-obj-summary--------------------------------------------------------
# Numerical summary across the three objectives
summary_3 <- do.call(rbind, lapply(
  list(base = res3_base, PR = res3_PR, PLS = res3_PLS, TS = res3_TS),
  function(res) {
    f <- res$global_pareto
    c(n = nrow(f),
      best_o1 = round(min(f$objective_1), 2),
      best_o2 = round(min(f$objective_2), 2),
      best_o3 = round(min(f$objective_3), 2))
  }
))
summary_3

## ----three-obj-pairs, fig.width = 7, fig.height = 7, fig.cap = "Pairwise projection of the three-objective fronts across variants."----
# Combine the three-objective fronts and project them pairwise
df3 <- rbind(
  data.frame(variant = "base", res3_base$global_pareto[, c("objective_1","objective_2","objective_3")]),
  data.frame(variant = "PR",   res3_PR$global_pareto[,   c("objective_1","objective_2","objective_3")]),
  data.frame(variant = "PLS",  res3_PLS$global_pareto[,  c("objective_1","objective_2","objective_3")]),
  data.frame(variant = "TS",   res3_TS$global_pareto[,   c("objective_1","objective_2","objective_3")])
)

# Colour by variant
col_v <- palette_var[df3$variant]
pairs(df3[, c("objective_1", "objective_2", "objective_3")],
      col = col_v, pch = 19,
      main = "Three-objective Pareto fronts (colour by variant)")