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BO4Mob: Bayesian Optimization Benchmarks for High-Dimensional Urban Mobility Problem
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Introduces BO4Mob, a benchmark of five SUMO-based San Jose/Bay Area freeway OD-estimation instances (3 to 10,100 dimensions) with PeMS sensor data, and evaluates SPSA, random search, Vanilla BO, SAASBO and TuRBO on it.
Problem
Origin-destination (OD) travel demand estimation from sparse traffic sensor counts is a high-dimensional, stochastic, non-differentiable, expensive black-box inverse problem, and there is no standard benchmark connecting BO methods to realistic urban mobility simulators.
Approach
Builds a reproducible BO benchmark from real road networks and open-source mesoscopic SUMO simulations calibrated to PeMS-BAY detector counts, spanning five network scales up to 10,100 OD variables, and uses NRMSE-based improvement as the evaluation metric.
Key results
- TuRBO achieved the best NRMSE on Simple Ramp (0.001, 99.47% improvement) and Small Region (0.258, 69.54% improvement) among the five methods.
- Vanilla BO achieved the best result on Junction (0.233, 54.15% improvement), while SAASBO was best on One-Way Corridor (0.07, 68.56%).
- On the Full Region (10,100 OD variables, ~40,099 s per simulation), no method improved over the initial solutions under a reduced budget of 5 epochs and 1 run.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use Bayesian optimization rather than random search or SPSA | OD calibration · Simple Ramp, One-Way Corridor, Junction, and Small Region | NRMSE | Helped |
| use TuRBO | OD calibration · Simple Ramp and Small Region | NRMSE | Helped |
| exclude 4 unobservable OD pairs (ablation) | Vanilla BO · One-Way Corridor | NRMSE: 0.187 -> 0.094 | Helped |
| exclude 4 unobservable OD pairs (ablation) | SAASBO · One-Way Corridor | NRMSE: 0.161 -> 0.132 | Helped |
| exclude 4 unobservable OD pairs (ablation) | TuRBO · One-Way Corridor | NRMSE: 0.233 -> 0.032 | Helped |
| exclude 4 unobservable OD pairs (ablation) | SPSA · One-Way Corridor | NRMSE: 0.352 -> 0.410 | Hurt |
| replace Matérn 5/2 with Matérn 3/2 kernel (ablation) | Vanilla BO · Simple Ramp | NRMSE: 0.0033 -> 0.0011 | Helped |
| replace Matérn 5/2 with RBF kernel (ablation) | Vanilla BO · Simple Ramp | NRMSE: 0.0033 -> 0.0074 | Hurt |
| replace Matérn 5/2 with Matérn 3/2 kernel (ablation) | TuRBO · One-Way Corridor | NRMSE: 0.0898 -> 0.0840 | Helped |
| replace Matérn 5/2 with RBF kernel (ablation) | TuRBO · One-Way Corridor | NRMSE: 0.0898 -> 0.0934 | Hurt |
| replace Matérn 5/2 with Matérn 3/2 kernel (ablation) | TuRBO · Junction | NRMSE: 0.2337 -> 0.2376 | Hurt |
| replace Matérn 5/2 with RBF kernel (ablation) | TuRBO · Junction | NRMSE: 0.2337 -> 0.2354 | Hurt |
Surprising findings
- On the Full Region, none of the four optimizers (SPSA, Vanilla BO, SAASBO, TuRBO) improved on the initial candidates under the reduced setting.
- Excluding unobservable OD pairs from the One-Way Corridor improved BO results (e.g., TuRBO best NRMSE dropped from 0.233 to 0.032).
Limitations
- Full Region evaluated only with reduced settings (one run, 5 epochs), so results there are inconclusive.
- Fixed set of predefined subnetworks limits flexibility; high simulation cost restricts experimentation at full scale.
- OD estimation is under-determined and sensor noise/missing data are not modeled in the benchmark objective.
Experimental setup
Datasets: PeMS-BAY traffic counts from Caltrans PeMS SUMO San Francisco Bay Area network model (ETH Zurich supplementary note 2)
Benchmarks: BO4Mob Simple Ramp BO4Mob One-Way Corridor BO4Mob Junction BO4Mob Small Region BO4Mob Full Region
Metrics: NRMSE percentage improvement over initial solution simulation run time
Baselines: Random search SPSA Vanilla BO SAASBO TuRBO
Builds on: SUMO BoTorch SAASBO TuRBO
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