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.

Efficient yet sufficient exploration remains a critical challenge in reinforcement learning (RL), especially for Markov Decision Processes (MDPs) with vast action spaces. Previous approaches have commonly involved projecting the original action space into a latent space or employing environmental action masks to reduce the action possibilities. Nevertheless, these methods often lack interpretability or rely on expert knowledge. In this study, we introduce a novel method for automatically reducing the action space in environments with discrete action spaces while preserving interpretability. The proposed approach learns state-specific masks with a dual purpose: (1) eliminating actions with minimal influence on the MDP and (2) aggregating actions with identical behavioral consequences within the MDP. Specifically, we introduce a novel concept called Bisimulation Metrics on Actions by States (BMAS) to quantify the behavioral consequences of actions within the MDP and design a dedicated mask model to ensure their binary nature. Crucially, we present a practical learning procedure for training the mask model, leveraging transition data collected by any RL policy. Our method is designed to be plug-and-play and adaptable to all RL policies, and to validate its effectiveness, an integration into two prominent RL algorithms, DQN and PPO, is performed. Experimental results obtained from Maze, Atari, and $\mu$RTS2 reveal a substantial acceleration in the RL learning process and noteworthy performance improvements facilitated by the introduced approach.

The imperative for swift and intelligent decision making in production scheduling has intensified in recent years. Deep reinforcement learning, akin to human cognitive processes, has heralded advancements in complex decision making and has found applicability in the production scheduling domain. Yet, its deployment in industrial settings is marred by large state spaces, protracted training times, and challenging convergence, necessitating a more efficacious approach. Addressing these concerns, this paper introduces an innovative, accelerated deep reinforcement learning framework—VSCS (Variational Autoencoder for State Compression in Soft Actor–Critic). The framework adeptly employs a variational autoencoder (VAE) to condense the expansive high-dimensional state space into a tractable low-dimensional feature space, subsequently leveraging these features to refine policy learning and augment the policy network’s performance and training efficacy. Furthermore, a novel methodology to ascertain the optimal dimensionality of these low-dimensional features is presented, integrating feature reconstruction similarity with visual analysis to facilitate informed dimensionality selection. This approach, rigorously validated within the realm of crude oil scheduling, demonstrates significant improvements over traditional methods. Notably, the convergence rate of the proposed VSCS method shows a remarkable increase of $77.5\%$, coupled with an $89.3\%$ enhancement in the reward and punishment values. Furthermore, this method substantiates the robustness and appropriateness of the chosen feature dimensions.