Efficient Simulation-Based Toll Optimization for Large-Scale Networks
Bibliographic record
Abstract
This paper proposes a simulation-based optimization technique for high-dimensional toll optimization problems of large-scale road networks. We formulate a novel analytical network model. The latter is embedded within a metamodel simulation-based optimization (SO) algorithm. It provides analytical and differentiable structural information of the underlying problem to the SO algorithm. Hence, the algorithm no longer treats the simulator as a black box. The analytical model is formulated as a system of nonlinear equations that can be efficiently evaluated with standard solvers. The dimension of the system of equations scales linearly with network size. It scales independently of the dimension of the route choice set and of link attributes such as link length. Hence, it is a scalable formulation suitable for the optimization of large-scale networks. For instance, the model is used in the case study of the paper for toll optimization of a Singapore network with more than 4,050 OD (origin-destination) pairs and 18,200 feasible routes. The corresponding analytical model is implemented as a system of 860 nonlinear equations. The analytical network model is validated based on one-dimensional toy network problems. It captures the main trends of the simulation-based objective function and, more importantly, accurately locates the global optimum for all experiments. The proposed SO approach is then used to optimize a set of 16 tolls for the network of expressways and major arterials of Singapore. The proposed method is compared with a general-purpose algorithm. The proposed method identifies good quality solutions at the very first iteration. The benchmark method identifies solutions with similar performance after 2 days of computation or similarly after more than 30 points have been simulated. The case study indicates that the analytical structural information provided to the algorithm by the analytical network model enables it to (i) identify good quality solutions fast and (ii) become robust to both the quality of the initial points and to the stochasticity of the simulator. The final solutions identified by the proposed algorithm outperform those of the benchmark method by an average of 18%.
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| 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".