Mixed Discrete and Continuous Variable Optimization Based on Constraint Aggregation and Relative Sensitivity
Bibliographic record
Abstract
This work presents a new approach for solving nonlinear mixed discrete-continuous variable problems with constraints. The proposed method falls under the category of direct search methods for discrete variables. Different from the traditional direct search methods that determine the search direction based on decreasing objective function within the feasible space, a relative sensitivity that jointly considers change in objective and constraint functions is introduced in this work to help determining the search direction. For feasible discrete points, the coordinate direction with the maximum relative sensitivity is taken as the search direction, so that the objective function value decreases the fastest with minimum increase in constraint values. For infeasible points, the search direction is determined by the minimum relative sensitivity, so that the points can be dragged into the feasible region with constraints decreasing the fastest and minimum increase of the objective. In addition, in order to reduce the number of constraints and calculate the relative sensitivity, a constraint aggregation technique with Kreisselmeier-Steinhauser function is applied to transform all constraints into an equivalent differentiable inequality constraint. The efficacy and accuracy of the proposed approach is demonstrated with different types of test problems and application to a design problem. The proposed method has advantages in solving nonlinear mixed discrete-continuous variable problems with constraints compared to other existing methods.
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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 | 0.002 | 0.003 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| 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".