A Practicable Robust Counterpart Formulation for Decomposable Functions: A Network Congestion Case Study
Bibliographic record
Abstract
Robust optimization is a powerful means to handle optimization problems where there is a set of parameters that are uncertain. The effectiveness of the method is especially noticeable when these parameters are only known to lie inside some uncertainty region. Unfortunately, there are important computational considerations that have prevented the methodology from being fully adopted in fields of practice where the cost function that needs to be robustified is nonlinear with respect to such parameters. In this paper, we propose a new robust optimization formulation that circumvent the computational burden in problems where the cost decomposes as the sum of costs that each involve a single decision variable. This is done by exploiting the fact that in this formulation the worst-case cost function can be expressed as a convex combination between a nominal and an upper-bounding cost function. One can still control the conservatism of the robust solution by adjusting how many terms of this total cost can simultaneously reach their respective most pessimistic value. To demonstrate the potential of this “practicable robust counterpart” formulation, we present how it can be employed for the robust optimization of packet routing on a telecommunication network with congestion. In such problems, an important source of uncertainty stems from the queueing delay, which is usually approximated by a nonlinear convex function using the theory of M/M/1 queues. Computational results on a large number of problem instances of realistic size confirm that it is possible to identify robust solutions that significantly outperform a deterministic approach in terms of both the amount of congestion and the risks of excessive congestion. Moreover, our proposed method also improves significantly the quality of solutions that are obtained using two other natural approximation schemes.
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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 | 0.011 | 0.005 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.002 |
| Science and technology studies | 0.003 | 0.000 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.001 |
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".