Mathematical Program with Vanishing Constraints for Optimal Pressure Control in Water Distribution Systems
Bibliographic record
Abstract
Optimizing pressure management to reduce water leakage in water distribution systems (WDSs) is one of the major tasks for water utilities. By regulating the operation of pressure reducing valves (PRVs) installed in WDSs, the pressure in WDSs can be kept under control and thus the water leakage amount can be decreased. Mathematically, the problem of pressure management to water leakage reduction can be formulated as a nonlinear optimization program. To make the optimization model proper for practice, the model of PRVs should be accurate and can describe all its operation modes in practice: active, fully opened, and check valve modes. In the literature, the model can be represented either by a non-smooth equation with low accuracy or by several complicated constraints. This research developed a highly accurate PRV model based on vanishing constraints. The idea comes from the fact that the model equation representing operations of PRVs in active mode will be vanished as PRVs operate in the check valve mode. The formulated mathematical program with vanishing constraints (MPVCs) can be solved efficiently by using the regularization approach. Several WDSs have evaluated the new PRV model which shows that accurate solutions are obtained with less computation time.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| 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".