Bicriterion Coevolution for the Multi-objective Travelling Salesperson Problem
Bibliographic record
Abstract
The travelling salesperson problem is an NP-hard combinatorial optimization problem. In this paper, we consider the multi-objective travelling salesperson problem (MTSP), both static and dynamic, with conflicting objectives. NSGA-II and MOEA/D, two popular evolutionary multi-objective optimization algorithms suffer from loss of diversity and poor convergence when applied separately on MTSP. However, both these techniques have their individual strengths. NSGA-II maintains di-versity through non-dominated sorting and crowding distance selection. MOEA/D is good at exploring extreme points on the Pareto front with faster convergence. In this paper, we adopt the bicriterion framework that exploits the strengths of Pareto-Criterion (PC) and Non-Pareto Criterion (NPC) evolutionary populations. In this research, NSGA-II (PC) and MOEA/D (NPC) coevolve to compensate the diversity of each other. We further improve the convergence using local search and a hybrid of order crossover and inver-over operators. To our knowledge, this is the first work that combines NSGA-II and MOEA/D in a bicriterion framework for solving MTSP, both static and dynamic. We perform various experiments on different MTSP bench-mark datasets with and without traffic factors to study static and dynamic MTSP. Our proposed algorithm is compared against standard algorithms such as NSGA-II & III, MOEA/D, and a baseline divide and conquer coevolution technique using performance metrics such as inverted generational distance, hypervolume, and the spacing metric to concurrently quantify the convergence and diversity of our proposed algorithm. We also compare our results to datasets used in the literature and show that our proposed algorithm performs empirically better than compared algorithms.
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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 | 0.003 |
| 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".