Combinatorial optimization (CO) concerns decision-making over discrete solution spaces under constraints and lies at the core of many complex systems across science, engineering, and society. Yet current approaches to solving CO problems still rely heavily on expert-designed solvers and manual tuning. Large language models (LLMs), trained on massive corpora, offer a promising new avenue for enhancing CO solution methods with stronger capabilities for generalization and adaptation in complex or previously unseen scenarios. Some existing surveys provide high-level taxonomies without examining solver-level methods, while others focus narrowly on specific perspectives. To fill this gap, we present a methodology-oriented synthesis of recent LLM-assisted CO work, covering three mainstream solution paradigms: mathematical programming, heuristics, and end-to-end solvers. We first develop a hierarchical taxonomy that groups existing methods by solution paradigm and, within each paradigm, further classifies them by the workflow stage and the interaction pattern through which LLMs engage with the solver. We then formalize the workflow of each paradigm, clarify the functional role of LLMs, and analyze the core techniques in key modules. We further summarize the problem domains studied in the literature and discuss representative applications. Finally, we identify current limitations and outline future directions in architecture, methodology, and problem scope.

With the rapid digital transformation of manufacturing industries in recent years, effective production scheduling has become imperative for maintaining competitiveness and addressing operational challenges. Modern manufacturing involves a complex interplay of elements, such as equipment, raw materials, and operators, making effective scheduling crucial for timely and specification-compliant production. However, achieving accurate and efficient scheduling remains a formidable challenge. Deep Reinforcement Learning (DRL), which integrates Deep Learning (DL) and Reinforcement Learning (RL), has emerged as a powerful tool for tackling these complex scheduling problems. A considerable number of related researches have been published in the past five years, yet there exists no review literature for them. Therefore, this paper reviews 167 studies published between Jan. 2019 and July 2024 that utilized DRL methods to solve production scheduling problems. We classify these studies based on types of scheduling problems they address and summarize their approaches to state representation, action space, reward mechanisms, and training algorithms. Additionally, we explore the integration of the DRL methods with optimization algorithms. Finally, we analyze the current research trends and future directions for the application of DRL in production scheduling from both problem-centric and method-centric perspectives.

With the advancement of intelligence in Active Distribution Networks (ADNs), effective fault recovery methods have become increasingly crucial. In this study, a reconfiguration method combining the immune mechanism and Northern Goshawk Optimization algorithm (NGO) is proposed, aimed at swiftly restoring power post-fault, maximizing the recovery of lost power areas within ADN, and minimizing losses. Firstly, an identification model within the immune mechanism is crafted to precisely match failures in ADNs. Then, the successful matched failure types can be used to restore power supply by the direct invocation of the recovery strategy from the library of strategies. Secondly, the immune response of ADNs is modeled, known as the reconfiguration model. For faults beyond the recovery strategy library, NGO is leveraged to address distribution network failures, with restoration solutions integrated into the library. Additionally, a reversed learning approach and stochastic variation strategy enhance the robustness of algorithm, preventing it from converging to suboptimal solutions. Finally, through simulation experiments, it is demonstrated that the recovery scheme obtained using the algorithm can be used to recover failure as well as reduce network losses in an effective manner. When similar or identical faults recur, ADN failure recovery becomes swift and efficient.

On-demand food delivery (OFD) is gaining more and more popularity in modern society. As a kernel order assignment manner in OFD scenario, order recommendation directly influences the delivery efficiency of the platform and the delivery experience of riders. This paper addresses the dynamism of the order recommendation problem and proposes a reinforcement learning solution method. An actor-critic network based on long short term memory (LSTM) unit is designed to deal with the order-grabbing conflict between different riders. Besides, three rider sequencing rules are accordingly proposed to match different time steps of the LSTM unit with different riders. To test the performance of the proposed method, extensive experiments are conducted based on real data from Meituan delivery platform. The results demonstrate that the proposed reinforcement learning based order recommendation method can significantly increase the number of grabbed orders and reduce the number of order-grabbing conflicts, resulting in better delivery efficiency and experience for the platform and riders.

As the critical component of manufacturing systems, production scheduling aims to optimize objectives in terms of profit, efficiency, and energy consumption by reasonably determining the main factors including processing path, machine assignment, execute time and so on. Due to the large scale and strongly coupled constraints nature, as well as the real-time solving requirement in certain scenarios, it faces great challenges in solving the manufacturing scheduling problems. With the development of machine learning, Reinforcement Learning (RL) has made breakthroughs in a variety of decision-making problems. For manufacturing scheduling problems, in this paper we summarize the designs of state and action, tease out RL-based algorithm for scheduling, review the applications of RL for different types of scheduling problems, and then discuss the fusion modes of reinforcement learning and meta-heuristics. Finally, we analyze the existing problems in current research, and point out the future research direction and significant contents to promote the research and applications of RL-based scheduling optimization.

Nonlinear Equations (NEs), which may usually have multiple roots, are ubiquitous in diverse fields. One of the main purposes of solving NEs is to locate as many roots as possible simultaneously in a single run, however, it is a difficult and challenging task in numerical computation. In recent years, Intelligent Optimization Algorithms (IOAs) have shown to be particularly effective in solving NEs. This paper provides a comprehensive survey on IOAs that have been exploited to locate multiple roots of NEs. This paper first revisits the fundamental definition of NEs and reviews the most recent development of the transformation techniques. Then, solving NEs with IOAs is reviewed, followed by the benchmark functions and the performance comparison of several state-of-the-art algorithms. Finally, this paper points out the challenges and some possible open issues for solving NEs.

This paper addresses the Energy-Aware Distributed Hybrid Flow Shop Scheduling Problem with Multiprocessor Tasks (EADHFSPMT) by considering two objectives simultaneously, i.e., makespan and total energy consumption. It consists of three sub-problems, i.e., job assignment between factories, job sequence in each factory, and machine allocation for each job. We present a mixed inter linear programming model and propose a Novel Multi-Objective Evolutionary Algorithm based on Decomposition (NMOEA/D). We specially design a decoding scheme according to the characteristics of the EADHFSPMT. To initialize a population with certain diversity, four different rules are utilized. Moreover, a cooperative search is designed to produce new solutions based on different types of relationship between any solution and its neighbors. To enhance the quality of solutions, two local intensification operators are implemented according to the problem characteristics. In addition, a dynamic adjustment strategy for weight vectors is designed to balance the diversity and convergence, which can adaptively modify weight vectors according to the distribution of the non-dominated front. Extensive computational experiments are carried out by using a number of benchmark instances, which demonstrate the effectiveness of the above special designs. The statistical comparisons to the existing algorithms also verify the superior performances of the NMOEA/D.

Currently, manufacturing enterprises face increasingly fierce market competition due to the various demands of customers and the rapid development of economic globalization. Hence, they have to extend their production mode into distributed environments and establish multiple factories in various geographical locations. Nowadays, distributed manufacturing systems have been widely adopted in industrial production processes. In recent years, many studies have been done on the modeling and optimization of distributed scheduling problems. This work provides a literature review on distributed scheduling problems in intelligent manufacturing systems. By summarizing and evaluating existing studies on distributed scheduling problems, we analyze the achievements and current research status in this field and discuss ongoing studies. Insights regarding prior works are discussed to uncover future research directions, particularly swarm intelligence and evolutionary algorithms, which are used for managing distributed scheduling problems in manufacturing systems. This work focuses on journal papers discovered using Google Scholar. After reviewing the papers, in this work, we discuss the research trends of distributed scheduling problems and point out some directions for future studies.