Mathematical modelling and a meta-heuristic for flexible job shop scheduling
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Bibliographic record
Abstract
AbstractThis study develops new solution methodologies for the flexible job shop scheduling problem (F-JSSP). As a first step towards dealing with this complex problem, mathematical modellings have been used; two novel effective position- and sequence-based mixed integer linear programming (MILP) models have been developed to fully characterise operations of the shop floor. The developed MILP models are capable of solving both partially and totally F-JSSPs. Size complexities, solution effectiveness and computational efficiencies of the developed MILPs are numerically explored and comprehensively compared vis-à-vis the makespan optimisation criterion. The acquired results demonstrate that the proposed MILPs, by virtue of its structural efficiencies, outperform the state-of-the-art MILPs in literature. The F-JSSP is strongly NP-hard; hence, it renders even the developed enhanced MILPs inefficient in generating schedules with the desired quality for industrial scale problems. Thus, a meta-heuristic that is a hybrid of Artificial Immune and Simulated Annealing (AISA) Algorithms has been proposed and developed for larger instances of the F-JSSP. Optimality gap is measured through comparison of AISA’s suboptimal solutions with its MILP exact optimal counterparts obtained for small- to medium-size benchmarks of F-JSSP. The AISA’s results were examined further by comparing them with seven of the best-performing meta-heuristics applied to the same benchmark. The performed comparative analysis demonstrated the superiority of the developed AISA algorithm. An industrial problem in a mould- and die-making shop was used for verification.Keywords: schedulingflexible job shopmixed integer linear programminghybrid artificial immune algorithmssimulated annealingsize complexityoptimality gap AcknowledgementsThis research was conducted in the Intelligent Manufacturing Systems Center at the University of Windsor, Canada. Research funding from the Canada Research Chairs program and the Natural Sciences and Engineering Council (NSERC) of Canada are gratefully acknowledged.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it