Pareto Frontier Approximation Network (PA-Net) to Solve Bi-objective TSP
Bibliographic record
Abstract
The travelling salesperson problem (TSP) is a classic resource allocation problem used to find an optimal order of doing a set of tasks while minimizing (or maximizing) an associated objective function. It is widely used in robotics for applications such as planning and scheduling. In this work, we solve TSP for two objectives using reinforcement learning (RL). Often in multi-objective optimization problems, the associated objective functions can be conflicting in nature. In such cases, the optimality is defined in terms of Pareto optimality. A set of these Pareto optimal solutions in the objective space form a Pareto front (or frontier). Each solution has its tradeoff. We present the Pareto frontier approximation network (PA-Net), a network that generates good approximations of the Pareto front for the bi-objective travelling salesperson problem (BTSP). Firstly, BTSP is converted into a constrained optimization problem. We then train our network to solve this constrained problem using the Lagrangian relaxation and policy gradient. With PA-Net we improve the performance over an existing deep RL-based method. The average improvement in the hypervolume metric, which is used to measure the optimality of the Pareto front, is 2.3%. At the same time, PANet has 4.5× faster inference time. Finally, we present the application of PA-Net to find optimal visiting order in a robotic navigation task/coverage planning. Our code is available on the project website1.
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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 | 0.001 |
| 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 | 0.002 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
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".