Improving dynamic programming for travelling salesman with precedence constraints: parallel Morin–Marsten bounding
Bibliographic record
Abstract
The precedence constrained traveling salesman (TSP-PC), also known as sequential ordering problem (SOP), consists of finding an optimal tour that satisfies the namesake constraints. Mixed integer-linear programming works well with the ‘lightly constrained’ TSP-PCs, close to asymmetric TSP, as well as the with the ‘heavily constrained’ (Gouveia, Ruthmair, 2015). Dynamic programming (DP) works well with the heavily constrained (Salii, 2019). However, judging by the open TSPLIB SOP instances, the worst for any method are the ‘medium’.We implement a parallel Morin–Marsten branch-and-bound scheme for DP (DPBB). We show how the lower bound heuristic parameterizes DPBB's worst-case complexity and DPBB ‘inherits’ the abstract travel cost aggregation feature of the DP, permitting its direct use with both the conventional and bottleneck TSP-PC.The scheme was tested on TSPLIB instances, with best known upper bounds (TSP-PC), or those found by restricted DP (Bottleneck TSP-PC), and lower bounds from a greedy-type heuristic. Our OPENMP-based parallel implementation achieved 20-fold speedup for larger instances. We close the long-standing kro124p.4.sop (conventional TSP-PC) and both kro124p.4.sop and ry48p.2.sop (Bottleneck TSP-PC).
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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) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.009 | 0.002 |
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".