An efficient hierarchical parallel genetic algorithm for graph coloring problem
Bibliographic record
Abstract
Graph coloring problems (GCPs) are constraint optimization problems with various applications including scheduling, time tabling, and frequency allocation. The GCP consists in finding the minimum number of colors for coloring the graph vertices such that adjacent vertices have distinct colors. We propose a parallel approach based on Hierarchical Parallel Genetic Algorithms (HPGAs) to solve the GCP. We also propose a new extension to PGA, that is Genetic Modification (GM) operator designed for solving constraint optimization problems by taking advantage of the properties between variables and their relations. Our proposed GM for solving the GCP is based on a novel Variable Ordering Algorithm (VOA). In order to evaluate the performance of our new approach, we have conducted several experiments on GCP instances taken from the well known DIMACS website. The results show that the proposed approach has a high performance in time and quality of the solution returned in solving graph coloring instances taken from DIMACS website. The quality of the solution is measured here by comparing the returned solution with the optimal one.
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".