Multi-Objective Identical Parallel Flow Shop Scheduling Using NSGA-II and MOPSO with a Novel Load Balancing Procedure
Bibliographic record
Abstract
Although flow shop scheduling has been widely investigated, the Identical Parallel Flow Shop Scheduling Problem (IPFSSP) remains largely overlooked, particularly in multiobjective optimization contexts.This study addresses this gap by formulating a biobjective mathematical model that minimizes makespan and earliness-tardiness under strict waiting time constraints.To solve it, a dynamic Load Balancing Procedure (LBP) is embedded within two established metaheuristics: NSGA-II and MOPSO.The proposed algorithms are evaluated across six benchmark instance scales with varying job-machine configurations.Results show that NSGA-II-LBP and MOPSO-LBP achieve average reductions of 13.7%-19.2% in makespan and 18.4%-22.8%in earliness-tardiness compared to their baseline counterparts.Statistical analyses using ANOVA and paired ttests confirm the significance of these improvements.NSGA-II-LBP delivers superior convergence, solution diversity, and scalability, while MOPSO-LBP offers higher computational efficiency, making it particularly well-suited for real-time scheduling in complex manufacturing systems.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".