Combinatorial optimization problems (COPs) are a class of NP-hard problems with great practical significance. Traditional approaches for COPs suffer from high computational time and reliance on expert knowledge, and machine learning (ML) methods, as powerful tools have been used to overcome these problems. In this review, the COPs in energy areas with a series of modern ML approaches, i.e., the interdisciplinary areas of COPs, ML and energy areas, are mainly investigated. Recent works on solving COPs using ML are sorted out firstly by methods which include supervised learning (SL), deep learning (DL), reinforcement learning (RL) and recently proposed game theoretic methods, and then problems where the timeline of the improvements for some fundamental COPs is the layout. Practical applications of ML methods in the energy areas, including the petroleum supply chain, steel-making, electric power system and wind power, are summarized for the first time, and challenges in this field are analyzed.

To optimize flapping foil performance, in the current study we apply deep reinforcement learning (DRL) to plan foil non-parametric motion, as the traditional control techniques and simplified motions cannot fully model nonlinear, unsteady and high-dimensional foil–vortex interactions. Therefore, a DRL training framework is proposed based on the proximal policy optimization algorithm and the transformer architecture, where the policy is initialized from the sinusoidal expert display. We first demonstrate the effectiveness of the proposed DRL-training framework, learning the coherent foil flapping motion to generate thrust. Furthermore, by adjusting reward functions and action thresholds, DRL-optimized foil trajectories can gain significant enhancement in both thrust and efficiency compared with the sinusoidal motion. Last, through visualization of wake morphology and instantaneous pressure distributions, it is found that DRL-optimized foil can adaptively adjust the phases between motion and shedding vortices to improve hydrodynamic performance. Our results give a hint of how to solve complex fluid manipulation problems using the DRL method.

Crude oil resource scheduling is one of the critical issues upstream in the crude oil industry chain. It aims to reduce transportation and inventory costs and avoid alerts of inventory limit violations by formulating reasonable crude oil transportation and inventory strategies. Two main difficulties coexist in this problem: the large problem scale and uncertain supply and demand. Traditional operations research (OR) methods, which rely on forecasting supply and demand, face significant challenges when applied to the complicated and uncertain short-term operational process of the crude oil supply chain. To address these challenges, this paper presents a novel hierarchical optimization framework and proposes a well-designed hierarchical reinforcement learning (HRL) algorithm. Specifically, reinforcement learning (RL), as an upper-level agent, is used to select the operational operators combined by various sub-goals and solving orders, while the lower-level agent finds a viable solution and provides penalty feedback to the upper-level agent based on the chosen operator. Additionally, we deploy a simulator based on real-world data and execute comprehensive experiments. Regarding the alert number, maximum alert penalty, and overall transportation cost, our HRL method outperforms existing OR and two RL algorithms in the majority of time steps.

Accurate spatiotemporal traffic forecasting is a critical prerequisite for proactive resource management in dense urban mobile networks. While Large Language Models (LLMs) have shown promise in time series analysis, they inherently struggle to model the complex spatial dependencies of grid-based traffic data. Effectively extending LLMs to this domain is challenging, as representing the vast amount of information from dense geographical grids can be inefficient and overwhelm the model's context. To address these challenges, we propose ST-Vision-LLM, a novel framework that reframes spatiotemporal forecasting as a vision-language fusion problem. Our approach leverages a Vision-LLM visual encoder to process historical global traffic matrices as image sequences, providing the model with a comprehensive global view to inform cell-level predictions. To overcome the inefficiency of LLMs in handling numerical data, we introduce an efficient encoding scheme that represents floating-point values as single tokens via a specialized vocabulary, coupled with a two-stage numerical alignment fine-tuning process. The model is first trained with Supervised Fine-Tuning (SFT) and then further optimized for predictive accuracy using Group Relative Policy Optimization (GRPO), a memory-efficient reinforcement learning method. Evaluations on real-world mobile traffic datasets demonstrate that ST-Vision-LLM outperforms existing methods by 15.6% in long-term prediction accuracy and exceeds the second-best baseline by over 30.04% in cross-domain few-shot scenarios. Our extensive experiments validate the model's strong generalization capabilities across various data-scarce environments.

Mobile Edge Computing (MEC) leverages computational heterogeneity between mobile devices and edge nodes to enable real-time applications requiring high information freshness. The Age-of-Information (AoI) metric serves as a crucial evaluator of information timeliness in such systems. Addressing AoI minimization in multi-user MEC environments presents significant challenges due to stochastic computing times. In this paper, we consider multiple users offloading tasks to heterogeneous edge servers in an MEC system, focusing on preemptive and non-preemptive task scheduling mechanisms. The problem is first reformulated as a Restless Multi-Arm Bandit (RMAB) problem, with a multi-layer Markov Decision Process (MDP) framework established to characterize AoI dynamics in the MEC system. Based on the multi-layer MDP, we propose a nested index framework and design a nested index policy with provably asymptotic optimality. This establishes a theoretical framework adaptable to various scheduling mechanisms, achieving efficient optimization through state stratification and index design in both preemptive and non-preemptive modes. Finally, the closed-form of the nested index is derived, facilitating performance trade-offs between computational complexity and accuracy while ensuring the universal applicability of the nested index policy across both scheduling modes. The experimental results show that in non-preemptive scheduling, compared with the benchmark method, the optimality gap is reduced by 25.43%, while in preemptive scheduling, the gap has reduced by 61.84%. As the system scale increases, it asymptotically converges in two scheduling modes and especially provides near-optimal performance in non-preemptive structure.