Applications of logic constrained equilibria to traffic networks and to power systems with storage
Bibliographic record
Abstract
We study equilibria in traffic networks and in power system networks with storage in the presence of logic constraints. These constraints consist of binary variables that are added to complementarity-based equilibrium models. Although these models have been thoroughly studied, the addition of logic constraints can provide additional benefits for practical applications. The main contribution of this work is to demonstrate, using two specific examples of applications, that logic constraints can render classical equilibrium models more realistic by allowing the inclusion of useful features such as equity in network flows or threshold events. Specifically, for the traffic equilibrium problem, we show how logic constraints can introduce some equity in the assignment of traffic when more than one equilibrium exists. For power system networks, we show that the presence of a storage operator acting as a service provider will not only support the operation of a power grid, but will also help stabilise the price of electricity and avoid the well-documented price-shifting effect. Unlike previous works, our model considers the storage operator as a service provider rather than a competitor to the producers. We also consider the minimum power output of production. We present results illustrating the expanded capabilities and insights provided by these new paradigms.
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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 | 0.002 | 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 | 0.001 | 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".