Pareto Frontier Approximation Network (PA-Net) to Solve Bi-objective TSP
Why this work is in the frame
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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 website <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> .
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it