An Extension of DIRECT Algorithm Using Kriging Metamodel for Global Optimization
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Bibliographic record
Abstract
As a very well-known non-gradient global optimization method, DIviding RECTangles (DIRECT) algorithm has been proven to be an effective and efficient search method for many global optimization problems. However, computation of the algorithm could be costly and slow in solving problems involving computation intensive, Expensive Black Box (EBB) function due to the high number of objective function evolution required. This work proposes a new strategy which integrates meta-modeling techniques with DIRECT for solving EBB problems. The principal idea of the new approach is to use meta-modeling techniques, such as Kriging, to assist DIRECT to identify the optimum with less number of function evolutions. Specifically, the new approach starts with DIRECT search with a number of iterations and then uses the resulting points in Kriging to construct the meta-model. The best point predicted by Kriging search will then be used by DIRECT as new initial point. As a result, the entire search domain will gradually shrink to the region enclosing the possible optimum. Several runs are carried out to avoid high number of function evaluations to obtain the approximation solution at each stage. The newly proposed method has been tested using ten commonly used benchmark functions. All these tests showed significant improvements over the original DIRECT for EBB design problems.
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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 | 0.000 | 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 | 0.002 |
| 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 it