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.
This paper focuses on the hybrid flow shop scheduling problem with sequence-dependent setup time (HFSP-SDST) with minimizing the makespan. To address this problem, this paper designs a hybrid migrating birds optimization (HMBO) algorithm that integrates migrating birds optimization (MBO) algorithm, variable neighborhood descent search (VND) algorithm, problem-based local search (LS) algorithm, and constraint programming (CP) model. Specifically, HMBO consists of three primary stages. The first stage employs a hybrid algorithm (MBOVND) that integrates MBO and VND with permutation encoding and decoding. Because the solution space of permutation encoding and decoding cannot cover the full solutions of HFSP-SDST, LS and CP are used to enlarge the solution space of MBOVND in the second and third stages respectively. Specifically, LS algorithm is used in the second stage to explore the solutions that are not in the solution space of MBOVND, and CP model is used in the third phase to further enlarge the solution space of MBOVND and LS algorithm. The efficacy of the proposed VND, LS, CP, and HMBO are verified. Experimental results demonstrate that VND, LS, and CP are effective to improve the solving ability of MBO, and HMBO improves 89 out of the 120 best-known solutions for the benchmark instances.
BRT-lane-sharing, which allows regular buses to operate on Bus Rapid Transit (BRT) lanes without disrupting scheduled BRT operations, has gained prominence. It is helpful to increase the utilization of BRT lanes and enhance the efficiency of the bus transit system. However, the current approaches for designing bus transit networks and setting frequencies do not incorporate BRT-lane-sharing, thereby neglecting its potential benefits, including improved speeds, easier transfers, and cost savings. This paper proposes a pioneering study for the Bus Transit Network Design and Frequency Setting (BTNDFS) problem incorporating BRT-lane-sharing. A novel road network description is presented, specifically tailored to accommodate BRT-lane-sharing through the introduction of BRT nodes and BRT-lane arcs. Furthermore, a bi-level model is built for the BTNDFS problem incorporating BRT-lane-sharing. To solve this model, a Priority-Based Genetic Algorithm (PBGA) is proposed, in which a priority-based chromosome is defined, whilst priority-based crossover and mutation operators are devised. Experimental results on the standard Mandl's benchmark instances indicate that the PBGA outperforms other metaheuristic approaches, with outcomes closely approximating optimal solutions. Further experiments are carried out on a real-world network featuring BRT-lane-sharing in the city of Linyi. The results show that the proposed model and the PBGA can reduce costs for passengers and operators, while simultaneously increasing the utilization of BRT lanes.
In aerodynamic design, high-quality multiblock mesh generation serves as the cornerstone for accurate lift-drag analysis of wings. However, conventional computational fluid dynamics (CFD) workflows offered by industrial software reveals critical limitations in labor-intensive manual operations. While automatic meshing in 2D wing cross-section is well-established, its extension to 3D wing meshing faces unresolved challenges, including excessive block generation, complex feature alignment, and incomplete simulation-ready pipelines. This paper presents an automatic multiblock mesh generation framework specifically targeting these commercial software shortcomings for 3D wing analysis. Our methodology addresses three persistent challenges: (1) a parameterization-based tip surface meshing method with optimized cell quality, (2) an extrusion-based wing body meshing approach ensuring precise feature alignment at joints and leading edges, and (3) an end-to-end pipeline from geometric pre-processing to CFD-ready multiblock mesh generation. Experiments demonstrate the framework's ability to produce high-quality meshes with minimal manual intervention, streamlining the workflow for aerodynamic simulations.
Driven by the “dual-carbon” goals, new energy power generation is gradually dominant, yet distributed energy's intermittency and volatility challenges power system operation. Focusing on potential flexible resources in power systems and large-scale grid connection of new energy vehicles (EVs), this paper innovatively introduces EVs penetration rate and the weight coefficient for encouraging new energy power generation, and constructs a virtual power plants (VPP) optimal scheduling model considering such penetration rate and flexible electrical and thermal loads. To achieve coordinated optimization of flexible loads on both supply and user sides, with the goal of reducing the total operating cost of the VPP, an electrical load model with load shifting, transfer, and reduction functions is built. Case studies analyze the impact of different EVs penetration rates on its optimal dispatching, verified by multiple scenario comparisons. The research results show that as the penetration rate of EVs increases to 50%, the total operating cost of the VPP continues to decrease, with new energy output increasing by 9.2% and gas turbine output decreasing by 15.4%. This reduces reliance on traditional fossil fuels and accelerates the green and low-carbon transformation of energy systems, but also strengthens the substitution effect of new energy power generation for traditional energy based power generation.
