Overnight technician routing and scheduling problem with time windows and balanced workloads: a bi-objective zebra optimization algorithm
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Bibliographic record
Abstract
In this paper, we develop a mathematical model of a technician routeing and scheduling problem with time windows (TRSPTW) and overnight shifts, which we title the ‘overnight TRSPTW’. This problem is motivated by a real application in the telecommunications industry in Saskatchewan, Canada. A mixed-integer nonlinear programming (MINLP) model is employed to achieve two key objectives: (1) minimising the total costs associated with technicians and subcontractors, including travel costs, accommodation costs and penalty costs caused by late starts and (2) minimising imbalanced workloads. Furthermore, the present work aims to determine the daily assignment of technicians to communities, depots and routes; find a high-quality schedule for technicians’ start times in communities and lunch breaks and determine the daily assignment of tasks to the subcontractor. The bi-objective MINLP model used to solve the overnight TRSPTW is a typical NP-hard problem in combinatorial optimisation. As such, we introduce a new hybrid category of TRSPTW that combines centroid-based clustering, which is an unsupervised machine learning (ML) approach, with a bi-objective zebra optimisation algorithm (BOZOA). The resultant algorithm blends the advantages of the ZOA and ML to strike a balance between the exploration and exploitation of the solution region. Finally, we compare our results with those obtained using an exact solver for small-, medium-, and large-sized instances. The performance evaluation and validation results revealed that the proposed ML-based BOZOA provides very good performance in solving TRSPTWs at a variety of scales with respect to the optimality criteria, including, number of taken iterations, infeasibility, optimality error and complementarity compared with both an exact solver and two inspired algorithms from ZOA. <b>Highlights</b>An ML-based bi-objective zebra optimisation algorithm to treat large-scale TRSPsCentroid-based clustering on the population of zebras to avoid bias towards a specific search spaceMaking a trade-off between exploration and exploitation of the feasible region in the developed algorithmA new MINLP model of a weighted bi-objective TRSP with limited capacity depotsWorkload function, penalty function for lateness, subcontracts, time windows for tasks and breaksExperiments using real data to show the performance of the model and solution method An ML-based bi-objective zebra optimisation algorithm to treat large-scale TRSPs Centroid-based clustering on the population of zebras to avoid bias towards a specific search space Making a trade-off between exploration and exploitation of the feasible region in the developed algorithm A new MINLP model of a weighted bi-objective TRSP with limited capacity depots Workload function, penalty function for lateness, subcontracts, time windows for tasks and breaks Experiments using real data to show the performance of the model and solution method
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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