Mixed‐Integer Optimal Control via Reinforcement Learning: A Case Study on Hybrid Electric Vehicle Energy Management
Bibliographic record
Abstract
ABSTRACT Many optimal control problems require the simultaneous output of discrete and continuous control variables. These problems are typically formulated as mixed‐integer optimal control (MIOC) problems, which are challenging to solve due to the complexity of the solution space. Numerical methods such as branch‐and‐bound are computationally expensive and undesirable for real‐time control. This article proposes a novel hybrid‐action reinforcement learning (HARL) algorithm, twin delayed deep deterministic actor‐Q (TD3AQ), for MIOC problems. TD3AQ leverages actor‐critic and Q‐learning methods to manage discrete and continuous action spaces simultaneously. The proposed algorithm is evaluated on a plug‐in hybrid electric vehicle (PHEV) energy management problem, where real‐time control of the discrete variables, clutch engagement/disengagement and gear shift, and continuous variable, engine torque, is essential to maximize fuel economy while satisfying driving constraints. Simulation results show that TD3AQ achieves near‐optimal control, with only a 4.69% difference from dynamic programming (DP), and outperforms baseline reinforcement learning algorithms for hybrid action spaces. The sub‐millisecond execution time indicates potential applicability in other time‐critical scenarios, such as autonomous driving or robotic control.
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| 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".