# Mixed-Integer Optimal Control via Reinforcement Learning: A Case Study on Hybrid Electric Vehicle Energy Management

arXiv: https://arxiv.org/abs/2305.01461 · HTML: https://mlsanity.com/paper/2305.01461/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 48 references that are in the map.
- First posted on arXiv 2 May 2023.

## Builds on (most cited first, 14 of 14)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Continuous control with deep reinforcement learning](https://mlsanity.com/paper/1509.02971/) (2015)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Addressing Function Approximation Error in Actor-Critic Methods](https://mlsanity.com/paper/1802.09477/) (2018)
- [Rainbow: Combining Improvements in Deep Reinforcement Learning](https://mlsanity.com/paper/1710.02298/) (2017)
- [Deep Reinforcement Learning in Parameterized Action Space](https://mlsanity.com/paper/1511.04143/) (2015)
- [Reinforcement Learning with Parameterized Actions](https://mlsanity.com/paper/1509.01644/) (2015)
- [Parametrized Deep Q-Networks Learning: Reinforcement Learning with Discrete-Continuous Hybrid Action Space](https://mlsanity.com/paper/1810.06394/) (2018)
- [Hybrid Actor-Critic Reinforcement Learning in Parameterized Action Space](https://mlsanity.com/paper/1903.01344/) (2019)
- [Continuous-Discrete Reinforcement Learning for Hybrid Control in Robotics](https://mlsanity.com/paper/2001.00449/) (2020)
- [HyAR: Addressing Discrete-Continuous Action Reinforcement Learning via Hybrid Action Representation](https://mlsanity.com/paper/2109.05490/) (2021)
- [Multi-Pass Q-Networks for Deep Reinforcement Learning with Parameterised Action Spaces](https://mlsanity.com/paper/1905.04388/) (2019)
- [Homotopy Continuation Enhanced Branch and Bound Algorithms for Strongly Nonconvex Mixed-Integer Nonlinear Programming Problems](https://mlsanity.com/paper/2109.07379/) (2021)
- [Tailored Presolve Techniques in Branch-and-Bound Method for Fast Mixed-Integer Optimal Control Applications](https://mlsanity.com/paper/2211.12700/) (2022)

## Abstract (arXiv)

Many optimal control problems require the simultaneous output of discrete and continuous control variables. These problems are usually 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 paper proposes a novel hybrid-action reinforcement learning (HARL) algorithm, twin delayed deep deterministic actor-Q (TD3AQ), for MIOC problems. TD3AQ combines the advantages of both actor-critic and Q-learning methods, and can handle the 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 outcomes demonstrate that TD3AQ achieves control results close to optimality when compared with dynamic programming (DP), with just 4.69% difference. Furthermore, it surpasses the performance of baseline reinforcement learning algorithms.