Efficient Traveling Salesman Problem Solvers using the Ising Model with Simulated Bifurcation
Bibliographic record
Abstract
An Ising model-based solver has shown efficiency in obtaining suboptimal solutions for combinatorial optimization problems. As an NP-hard problem, the traveling salesman problem (TSP) plays an important role in various routing and scheduling applications. However, the execution speed and solution quality significantly deteriorate using a solver with simulated annealing (SA) due to the quadratically increasing number of spins and strong constraints placed on the spins. The ballistic simulated bifurcation (bSB) algorithm utilizes the signs of Kerr-nonlinear parametric oscillators' positions as the spins' states. It can update the states in parallel to alleviate the time explosion problem. In this paper, we propose an efficient method for solving TSPs by using the Ising model with bSB. Firstly, the TSP is mapped to an Ising model without external magnetic fields by introducing a redundant spin. Secondly, various evolution strategies for the introduced position and different dynamic configurations of the time step are considered to improve the efficiency in solving TSPs. The effectiveness is specifically discussed and evaluated by comparing the solution quality to SA. Experiments on benchmark datasets show that the proposed bSB-based TSP solvers offer superior performance in solution quality and achieve a significant speed up in runtime than recent SA-based ones.
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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 | 0.000 |
| 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".