Expected Length of the Shortest Path of the Traveling Salesman Problem in 3D Space
Bibliographic record
Abstract
Finding the shortest path of the traveling salesman problem (TSP) is a typical NP-hard problem and one of the basic optimization problems. TSP in three-dimensional space (3D-TSP) is an extension of TSP. It plays an important role in the fields of 3D path planning and UAV inspection, such as forest fire patrol path planning. Many existing studies have focused on the expected length of the shortest path of TSP in 2D space. The expected length of the shortest path in 3D space has not yet been studied. To fill this gap, this research focuses on developing models to estimate the expected length of the shortest path of 3D-TSP. First, different experimental scenarios are designed by combining different service areas and the number of demand points. Under each scenario, the specified number of demand points is randomly generated, and an improved genetic algorithm and Gurobi are used to find the shortest path. A total of 500 experiments are performed for each scenario, and the average length of the shortest path is calculated. The models to estimate the expected length of the shortest path are proposed. Model parameters are estimated and k-fold cross-validation is used to evaluate the goodness of fit. Results show that all the models fit the data well and the best model is selected. The developed models can be used to estimate the expected length of the shortest path of 3D-TSP and provide important references for many applications.
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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 | 0.002 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.001 |
| 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 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".