docs(examples): add bi-objective TSP, 3-objective JSS, and bi-objective knapsack benchmarks
Three harder Pareto-front demos: - btsp_kroab.rs — Lust-Teghem bi-objective TSP (KroAB-25 subset of TSPLIB KroA100/KroB100). NSGA-II with EdgeRecombinationCrossover + InversionMutation. Reports hypervolume vs a fixed reference. - mo_jss_la01.rs — 3-objective JSS on Lawrence LA01 (10x5 instance). Objectives: makespan, total flow time, total tardiness (with synthetic due dates dj = 1.3 * sum_processing_times(j)). NSGA-III with reference_divisions = 12 (91 Das-Dennis points). - mo_knapsack.rs — bi-objective 0/1 knapsack a la Zitzler-Thiele. 30 items, two profit vectors, one capacity. NSGA-II with a local one-point binary crossover + BitFlipMutation; weight overruns penalized in both objectives.
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//! 3-objective Job-Shop Scheduling on Lawrence's LA01 instance, solved with
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//! NSGA-III (the many-objective successor to NSGA-II).
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//!
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//! - **Benchmark**: Lawrence LA01 (1984), 10 jobs × 5 machines, 50 operations
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//! total. Each operation has a fixed machine and processing time;
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//! operations within a job run in order. Data taken from the OR-Library /
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//! JSPLIB la01 instance file.
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//! - **Three objectives** (this example):
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//! - f₁ = makespan
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//! - f₂ = total flow time Σⱼ Cⱼ
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//! - f₃ = total tardiness Σⱼ max(0, Cⱼ − dⱼ), with synthetic due dates
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//! dⱼ = 1.3 × (sum of processing times of job j)
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//! - **Algorithm**: [`Nsga3`] — designed for ≥ 3 objectives (NSGA-II's
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//! crowding distance degrades in higher dim).
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//! - **Encoding**: operation-based string of length 50.
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//! - **Variation**: a local POX (multiset-preserving) crossover piped through
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//! a small randomly-chosen mutation that alternates between
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//! [`InsertionMutation`] and [`ScrambleMutation`]. Strict-permutation
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//! crossovers cannot be used on multiset encodings.
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//! - **Initializer**: [`ShuffledMultisetPermutation`].
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//!
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//! Sources:
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//! - Lawrence (1984), thesis benchmark instances.
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//! - OR-Library / JSPLIB LA01 instance file.
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//! - Deb & Jain (2014), "An evolutionary many-objective optimization
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//! algorithm using reference-point based non-dominated sorting approach,
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//! Part I" — NSGA-III.
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//!
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//! Run with:
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//!
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//! ```bash
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//! cargo run --release --example mo_jss_la01
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//! ```
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use heuropt::prelude::*;
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use rand::Rng as _;
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const N_JOBS: usize = 10;
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const N_MACHINES: usize = 5;
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/// LA01 routing — machine id for the k-th operation of job j.
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const LA01_MACHINE: [[usize; N_MACHINES]; N_JOBS] = [
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[1, 0, 4, 3, 2],
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[0, 3, 4, 2, 1],
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[3, 4, 1, 2, 0],
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[1, 0, 4, 2, 3],
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[0, 3, 2, 1, 4],
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[1, 2, 4, 0, 3],
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[3, 4, 1, 2, 0],
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[2, 0, 1, 3, 4],
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[3, 1, 4, 0, 2],
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[4, 3, 1, 2, 0],
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];
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/// LA01 processing times — duration of the k-th operation of job j.
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const LA01_TIME: [[f64; N_MACHINES]; N_JOBS] = [
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[21.0, 53.0, 95.0, 55.0, 34.0],
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[21.0, 52.0, 16.0, 26.0, 71.0],
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[39.0, 98.0, 42.0, 31.0, 12.0],
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[77.0, 55.0, 79.0, 66.0, 77.0],
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[83.0, 34.0, 64.0, 19.0, 37.0],
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[54.0, 43.0, 79.0, 92.0, 62.0],
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[69.0, 77.0, 87.0, 87.0, 93.0],
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[38.0, 60.0, 41.0, 24.0, 66.0],
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[17.0, 49.0, 25.0, 44.0, 98.0],
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[77.0, 79.0, 43.0, 75.0, 96.0],
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];
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/// Synthetic due dates: 1.3 × total processing time of each job.
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fn due_dates() -> [f64; N_JOBS] {
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let mut d = [0.0_f64; N_JOBS];
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for (j, row) in LA01_TIME.iter().enumerate() {
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d[j] = 1.3 * row.iter().sum::<f64>();
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}
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d
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}
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struct La01ThreeObjective {
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due: [f64; N_JOBS],
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}
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impl Problem for La01ThreeObjective {
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type Decision = Vec<usize>;
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fn objectives(&self) -> ObjectiveSpace {
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ObjectiveSpace::new(vec![
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Objective::minimize("makespan"),
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Objective::minimize("total_flow_time"),
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Objective::minimize("total_tardiness"),
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])
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}
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fn evaluate(&self, schedule: &Vec<usize>) -> Evaluation {
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let mut job_next = [0_usize; N_JOBS];
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let mut job_clock = [0.0_f64; N_JOBS];
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let mut machine_clock = [0.0_f64; N_MACHINES];
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for &job in schedule {
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let k = job_next[job];
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let m = LA01_MACHINE[job][k];
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let t = LA01_TIME[job][k];
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let start = job_clock[job].max(machine_clock[m]);
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let end = start + t;
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job_clock[job] = end;
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machine_clock[m] = end;
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job_next[job] = k + 1;
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}
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let makespan = machine_clock.iter().cloned().fold(0.0_f64, f64::max);
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let flow_time: f64 = job_clock.iter().sum();
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let tardiness: f64 = job_clock
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.iter()
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.zip(self.due.iter())
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.map(|(&c, &d)| (c - d).max(0.0))
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.sum();
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Evaluation::new(vec![makespan, flow_time, tardiness])
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}
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fn decision_schema(&self) -> Vec<DecisionVariable> {
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(0..N_JOBS * N_MACHINES)
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.map(|k| DecisionVariable::new(format!("op_slot_{k}")))
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.collect()
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}
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}
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/// POX — multiset-preserving crossover for operation-string encodings.
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/// (Identical in spirit to the one in `jss_ft06_bi.rs`; copied locally so
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/// each example stays self-contained.)
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#[derive(Debug, Clone, Copy, Default)]
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struct PrecedenceOrderCrossover;
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impl Variation<Vec<usize>> for PrecedenceOrderCrossover {
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fn vary(&mut self, parents: &[Vec<usize>], rng: &mut Rng) -> Vec<Vec<usize>> {
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assert!(parents.len() >= 2, "POX requires 2 parents");
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let p1 = &parents[0];
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let p2 = &parents[1];
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let mut in_j1 = [false; N_JOBS];
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loop {
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for slot in &mut in_j1 {
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*slot = rng.random_bool(0.5);
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}
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let n_in_j1 = in_j1.iter().filter(|&&b| b).count();
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if n_in_j1 > 0 && n_in_j1 < N_JOBS {
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break;
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}
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}
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vec![pox_child(p1, p2, &in_j1), pox_child(p2, p1, &in_j1)]
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}
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}
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fn pox_child(donor: &[usize], filler: &[usize], in_donor_set: &[bool]) -> Vec<usize> {
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let n = donor.len();
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let mut child = vec![usize::MAX; n];
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for k in 0..n {
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if in_donor_set[donor[k]] {
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child[k] = donor[k];
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}
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}
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let mut fill_idx = 0;
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for &v in filler {
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if !in_donor_set[v] {
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while fill_idx < n && child[fill_idx] != usize::MAX {
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fill_idx += 1;
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}
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child[fill_idx] = v;
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fill_idx += 1;
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}
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}
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child
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}
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/// Per-call random choice between Insertion and Scramble. Both preserve the
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/// multiset; flipping a coin gives the schedule access to two complementary
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/// neighborhood moves.
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#[derive(Debug, Clone, Copy, Default)]
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struct InsertionOrScramble;
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impl Variation<Vec<usize>> for InsertionOrScramble {
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fn vary(&mut self, parents: &[Vec<usize>], rng: &mut Rng) -> Vec<Vec<usize>> {
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if rng.random_bool(0.5) {
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InsertionMutation.vary(parents, rng)
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} else {
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ScrambleMutation.vary(parents, rng)
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}
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}
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}
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fn main() {
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let problem = La01ThreeObjective { due: due_dates() };
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let mut optimizer = Nsga3::new(
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Nsga3Config {
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population_size: 120,
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generations: 600,
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reference_divisions: 12,
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seed: 9,
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},
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ShuffledMultisetPermutation::new(vec![N_MACHINES; N_JOBS]),
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CompositeVariation {
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crossover: PrecedenceOrderCrossover,
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mutation: InsertionOrScramble,
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},
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);
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let result = optimizer.run(&problem);
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println!("LA01 — 3-objective JSS via NSGA-III");
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println!("Source: Lawrence (1984), OR-Library la01 instance");
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println!();
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println!("Objectives: f1 = makespan, f2 = total flow time, f3 = total tardiness");
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println!("Due dates: dⱼ = 1.3 × Σ(processing times of job j)");
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println!();
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println!("Total evaluations: {}", result.evaluations);
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println!("Pareto-front size: {}", result.pareto_front.len());
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println!();
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// Sort by makespan and print up to 12 well-spaced rows.
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let mut front: Vec<&Candidate<Vec<usize>>> = result.pareto_front.iter().collect();
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front.sort_by(|a, b| {
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a.evaluation.objectives[0]
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.partial_cmp(&b.evaluation.objectives[0])
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.unwrap_or(std::cmp::Ordering::Equal)
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});
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let stride = (front.len() / 12).max(1);
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println!(" f1 makespan f2 flow time f3 tardiness");
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let mut printed = 0_usize;
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for (i, c) in front.iter().enumerate() {
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if i % stride == 0 || i + 1 == front.len() {
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let o = &c.evaluation.objectives;
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println!(" {:>11.0} {:>12.0} {:>11.0}", o[0], o[1], o[2]);
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printed += 1;
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if printed >= 12 {
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break;
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}
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}
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}
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println!();
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if let (Some(corner_ms), Some(corner_ft), Some(corner_td)) = (
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front.first(),
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front.iter().min_by(|a, b| {
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a.evaluation.objectives[1]
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.partial_cmp(&b.evaluation.objectives[1])
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.unwrap_or(std::cmp::Ordering::Equal)
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}),
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front.iter().min_by(|a, b| {
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a.evaluation.objectives[2]
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.partial_cmp(&b.evaluation.objectives[2])
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.unwrap_or(std::cmp::Ordering::Equal)
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}),
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) {
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println!(
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"Makespan corner: f1={:.0}, f2={:.0}, f3={:.0}",
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corner_ms.evaluation.objectives[0],
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corner_ms.evaluation.objectives[1],
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corner_ms.evaluation.objectives[2],
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);
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println!(
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"Flow-time corner: f1={:.0}, f2={:.0}, f3={:.0}",
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corner_ft.evaluation.objectives[0],
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corner_ft.evaluation.objectives[1],
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corner_ft.evaluation.objectives[2],
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);
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println!(
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"Tardiness corner: f1={:.0}, f2={:.0}, f3={:.0}",
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corner_td.evaluation.objectives[0],
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corner_td.evaluation.objectives[1],
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corner_td.evaluation.objectives[2],
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);
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}
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}
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