Effects of crossover operator combined with mutation operator in genetic algorithms for the generalized travelling salesman problem
Bibliographic record
Abstract
Here, we consider the generalized travelling salesman problem (GTSP), which is a generalization of the travelling salesman problem (TSP). This problem has several real-life applications. Since the problem is complex and NP-hard, solving this problem by exact methods is very difficult. Therefore, researchers have applied several heuristic algorithms to solve this problem. We propose the application of genetic algorithms (GAs) to obtain a solution. In the GA, three operators—selection, crossover, and mutation—are successively applied to a group of chromosomes to obtain a solution to an optimization problem. The crossover operator is applied to create better offspring and thus to converge the population, and the mutation operator is applied to explore the areas that cannot be explored by the crossover operator and thus to diversify the search space. All the crossover and mutation operators developed for the TSP can be used for the GTSP with some modifications. A better combination of these two operators can create a very good GA to obtain optimal solutions to the GTSP instances. Therefore, four crossover and three mutation operators are used here to develop GAs for solving the GTSP. Then, GAs is compared on several benchmark GTSPLIB instances. Our experiment shows the effectiveness of the sequential constructive crossover operator combined with the insertion mutation operator for this problem.
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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 | 0.005 |
| 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) | 0.001 | 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".