Route optimization for open-close multiple travelling salesman problem with load-balancing constraint: A multi-chromosome based genetic algorithm
Why this work is in the frame
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Bibliographic record
Abstract
The Multiple Travelling Salesman Problem (MTSP) is one of the prominent combinatorial optimization problems with both theoretical interest and practical applications. However, its less-explored variants, such as the Open-Close Multiple Travelling Salesman Problem (OCMTSP), have received comparatively limited attention. In the OCMTSP, all salesmen commence their routes from a central depot, but unlike the classical MTSP, not all are required to return to the starting point upon completing their deliveries. Additionally, allowing any salesman to visit the maximum number of cities can lead to an imbalanced workload distribution among the salesmen. To address this imbalance, the current study incorporates a load balancing constraint into the OCMTSP framework, ensuring a fair distribution of cities among all salesmen. This extended problem variant is termed as Open-Close Multiple Travelling Salesman Problem with Load Balancing (OCMTSPLB). The primary objective of the OCMTSPLB is to minimize the total travel distance or cost incurred by the combined open and closed tours while maintaining balanced workloads. To solve this variant, the study proposes two distinct crossover based multi-chromosome Genetic Algorithm (GA) frameworks. Given the novelty of this problem, the algorithms are assessed using standardized benchmark instances from the TSPLIB. Experimental findings indicate that one of the proposed GA variants consistently achieves superior solution quality, a result further validated through non-parametric statistical tests.
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 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 | 0.000 | 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