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COIN · ROSE · PERMUTATION OPTIMIZATION

Parallel-Machine
Tardiness Laboratory

Assign and order jobs on identical parallel machines by encoding exactly m−1 machine separators inside one permutation. Compare total tardiness, maximum tardiness, makespan, completion time and load balance.

One evaluator · equal budgetsEvery algorithm shares the same instance, evaluator, seeds and objective-evaluation budget, making the comparison auditable and reproducible.
StatusReady
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Evaluations
Best primary

Benchmark

Results appear after an experiment.

Current:

Introduction and problem context

Parallel-machine tardiness is more than load balancing because order within each machine changes completion times and job tardiness Tⱼ=max(0,Cⱼ−dⱼ). Minimizing their sum jointly decides assignment and sequencing.

Separator encoding reuses the same permutation engines: separators are learnable nodes with positions and adjacencies. Distinct separator labels are semantically equivalent, however, creating a symmetry that should be reported in research.

Representation

jobs: 0..n−1 · separators: n..n+m−2
π = (J3,J8,J2, |₁, J5,J7,J1, |₂, J6,J4,J9)

The chromosome has n+m−1 unique tokens and always contains m−1 separators, decoding without repair into m machine sequences. Adjacent separators permit an empty machine, penalized naturally through makespan and load variance.

Problem formulation, objectives and fitness calculation

Let pⱼ be processing time, dⱼ due date, Cⱼ completion time on its assigned machine, and Lₖ machine load.

min f₁ = Σⱼ max(0,Cⱼ−dⱼ)
min f₂ = maxⱼ max(0,Cⱼ−dⱼ)
min f₃ = maxₖ Lₖ
min f₄ = Σⱼ Cⱼ
min f₅ = (1/m)Σₖ(Lₖ−L̄)²

The single-objective track follows the classical total-tardiness objective. The MO track exposes conflicts among tardiness, throughput and balance, using nondominated sorting and Flow-Shop-equivalent convergence and Pareto reporting.

Benchmark provenance and literature review

Tanaka and Araki publish identical-parallel-machine benchmarks for 2–10 machines with reported optimum results. The original archive is hosted on Google Drive and is not copied into this deployment; current preload entries are therefore disclosed as controlled fixtures using benchmark dimensions, not published instances. The archive can later replace fixtures without changing the evaluator or API.

References

  1. Tanaka Parallel-Machine Total Tardiness benchmark archive.
  2. Tanaka, S. & Araki, M. A branch-and-bound algorithm with Lagrangian relaxation to minimize total tardiness on identical parallel machines. IJPE 113, 446–458 (2008).
  3. Graham et al. Optimization and approximation in deterministic sequencing and scheduling: a survey. Annals of Discrete Mathematics 5 (1979).