The Non-Walking Triangle Optimization Representation: Enabling Monte Carlo Tree Search-like Methods for Real Parameter Optimization Problems
Bibliographic record
Abstract
Real parameter estimation is typically performed by an algorithm that operates directly on vectors of real parameters. This study presents an extension of a representation for real parameter optimization that is discrete and based on the iterated partition of simplices, known as the Walking Triangle Representation (WTR), and pairs it with Monte Carlo Tree Search (MCTS)-like algorithms. The number of moves allowed to the WTR is reduced to only its centering move, where a vertex of the simplex is replaced by its center of mass. This representation converts a real parameter optimization to a discrete form, which can then be paired with MCTS-like algorithms. The tree structure of MCTS allows one to keep track of and exploit information from previous attempts (tree extensions) when choosing the next set of moves to try. Six real parameter optimization problems were used to test the algorithm. Four parameters in the algorithm were studied, including: minimum gene length, maximum gene length, number of tree extensions, and probability of exploration (chance). The algorithm regularly performed consistently well, even with a low number of fitness evaluations (typical number of fitness evaluations is up to 3750 per run). This paper focuses on the ability of the Non-Walking Triangle Representation to convert real parameter optimization problems into discrete representations. This concept is demonstrated through the evaluation of the Non-Walking Triangle Monte Carlo Tree Search (MCNon-Walk) algorithm's ability to find optima in a variety of real parameter optimization problems, using differential evolution as a baseline for comparison.
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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 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 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".