Optimizing Electric Bus Charging Scheduling with Uncertainties Using Hierarchical Deep Reinforcement Learning

The growing adoption of Electric Buses (EBs) represents a significant step toward sustainable development. By utilizing Internet of Things (IoT) systems, charging stations can autonomously determine charging schedules based on real-time data. However, optimizing EB charging schedules remains a critical challenge due to uncertainties in travel time, energy consumption, and fluctuating electricity prices. Moreover, to address real-world complexities, charging policies must make decisions efficiently across multiple time scales and remain scalable for large EB fleets. In this paper, we propose a Hierarchical Deep Reinforcement Learning (HDRL) approach that reformulates the original Markov Decision Process (MDP) into two augmented MDPs. To solve these MDPs and enable multi-timescale decision-making, we introduce a novel HDRL algorithm, namely Double Actor-Critic Multi-Agent Proximal Policy Optimization Enhancement (DAC-MAPPO-E). Scalability challenges of the Double Actor-Critic (DAC) algorithm for large-scale EB fleets are addressed through enhancements at both decision levels. At the high level, we redesign the decentralized actor network and integrate an attention mechanism to extract relevant global state information for each EB, decreasing the size of neural networks. At the low level, the Multi-Agent Proximal Policy Optimization (MAPPO) algorithm is incorporated into the DAC framework, enabling decentralized and coordinated charging power decisions, reducing computational complexity and enhancing convergence speed. Extensive experiments with real-world data demonstrate the superior performance and scalability of DAC-MAPPO-E in optimizing EB fleet charging schedules.

Electric Bus Charging Schedules Relying on Real Data-Driven Targets Based on Hierarchical Deep Reinforcement Learning

The charging scheduling problem of Electric Buses (EBs) is investigated based on Deep Reinforcement Learning (DRL). A Markov Decision Process (MDP) is conceived, where the time horizon includes multiple charging and operating periods in a day, while each period is further divided into multiple time steps. To overcome the challenge of long-range multi-phase planning with sparse reward, we conceive Hierarchical DRL (HDRL) for decoupling the original MDP into a high-level Semi-MDP (SMDP) and multiple low-level MDPs. The Hierarchical Double Deep Q-Network (HDDQN)-Hindsight Experience Replay (HER) algorithm is proposed for simultaneously solving the decision problems arising at different temporal resolutions. As a result, the high-level agent learns an effective policy for prescribing the charging targets for every charging period, while the low-level agent learns an optimal policy for setting the charging power of every time step within a single charging period, with the aim of minimizing the charging costs while meeting the charging target. It is proved that the flat policy constructed by superimposing the optimal high-level policy and the optimal low-level policy performs as well as the optimal policy of the original MDP. Since jointly learning both levels of policies is challenging due to the non-stationarity of the high-level agent and the sampling inefficiency of the low-level agent, we divide the joint learning process into two phases and exploit our new HER algorithm to manipulate the experience replay buffers for both levels of agents. Numerical experiments are performed with the aid of real-world data to evaluate the performance of the proposed algorithm.

Diffusion on the Probability Simplex

Diffusion models learn to reverse the progressive noising of a data distribution to create a generative model. However, the desired continuous nature of the noising process can be at odds with discrete data. To deal with this tension between continuous and discrete objects, we propose a method of performing diffusion on the probability simplex. Using the probability simplex naturally creates an interpretation where points correspond to categorical probability distributions. Our method uses the softmax function applied to an Ornstein-Unlenbeck Process, a well-known stochastic differential equation. We find that our methodology also naturally extends to include diffusion on the unit cube which has applications for bounded image generation.