Solving Traveling Salesman Problems Using Ising Models with Simulated Bifurcation
Bibliographic record
Abstract
Many combinatorial optimization problems can be solved by numerically simulating classical nonlinear Hamiltonian systems based on the Ising model. Solving the traveling salesman problem (TSP) using the Ising model requires a quadratically increasing number of spins with strict constraints. Unlike classical simulated annealing, simulated bifurcation (SB) can update the states of spins in parallel. This feature can potentially accelerate the convergence of Hamiltonian in the Ising model by taking advantage of modern multi-core processors. As an improved SB algorithm, the ballistic SB (bSB) algorithm is considered for solving the TSP in this paper. The TSP is converted to an Ising problem with external magnetic fields. bSB is then expanded by introducing a time-dependent factor. Experiments on benchmark datasets show that the bSB-based Ising solver offers superior performance in solution quality and convergence speed.
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How this classification was reachedexpand
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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".