{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,11]],"date-time":"2026-06-11T17:29:05Z","timestamp":1781198945582,"version":"3.54.1"},"reference-count":49,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2025,6,12]],"date-time":"2025-06-12T00:00:00Z","timestamp":1749686400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>With the rapid development of e-commerce and globalization, logistics distribution systems have become integral to modern economies, directly impacting transportation efficiency, resource utilization, and supply chain flexibility. However, solving the Vehicle and Multi-Drone Cooperative Delivery Problem with Delivery Restrictions is challenging due to complex constraints, including limited payloads, short endurance, regional restrictions, and multi-objective optimization. Traditional optimization methods, particularly genetic algorithms, struggle to address these complexities, often relying on static rules or single-objective optimization that fails to balance exploration and exploitation, resulting in local optima and slow convergence. The concept of symmetry plays a crucial role in optimizing the scheduling process, as many logistics problems inherently possess symmetrical properties. By exploiting these symmetries, we can reduce the problem\u2019s complexity and improve solution efficiency. This study proposes a novel and scalable scheduling approach to address the Vehicle and Multi-Drone Cooperative Delivery Problem with Delivery Restrictions, tackling its high complexity, constraint handling, and real-world applicability. Specifically, we propose a logistics scheduling method called Loegised, which integrates large language models with genetic algorithms while incorporating symmetry principles to enhance the optimization process. Loegised includes three innovative modules: a cognitive initialization module to accelerate convergence by generating high-quality initial solutions, a dynamic operator parameter adjustment module to optimize crossover and mutation rates in real-time for better global search, and a local optimum escape mechanism to prevent stagnation and improve solution diversity. The experimental results on benchmark datasets show that Loegised achieves an average delivery time of 14.80, significantly outperforming six state-of-the-art baseline methods, with improvements confirmed by Wilcoxon signed-rank tests (p&lt;0.001). In large-scale scenarios, Loegised reduces delivery time by over 20% compared to conventional methods, demonstrating strong scalability and practical applicability. These findings validate the effectiveness and real-world potential of symmetry-enhanced, language model-guided optimization for advanced logistics scheduling.<\/jats:p>","DOI":"10.3390\/sym17060934","type":"journal-article","created":{"date-parts":[[2025,6,12]],"date-time":"2025-06-12T07:44:23Z","timestamp":1749714263000},"page":"934","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Optimized Scheduling for Multi-Drop Vehicle\u2013Drone Collaboration with Delivery Constraints Using Large Language Models and Genetic Algorithms with Symmetry Principles"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7239-1819","authenticated-orcid":false,"given":"Mingyang","family":"Geng","sequence":"first","affiliation":[{"name":"College of Computer Science, National University of Defense Technology, Changsha 410073, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Anping","family":"Chen","sequence":"additional","affiliation":[{"name":"Department of Management Enginearing, Ma\u2019anshan Technical College, Ma\u2019anshan 243000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,6,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1016\/j.trc.2015.03.005","article-title":"The flying sidekick traveling salesman problem: Optimization of drone-assisted parcel delivery","volume":"54","author":"Murray","year":"2015","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"103763","DOI":"10.1016\/j.trc.2022.103763","article-title":"Heterogeneous multi-drone routing problem for parcel delivery","volume":"141","author":"Wen","year":"2022","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"118378","DOI":"10.1016\/j.eswa.2022.118378","article-title":"An intelligent green scheduling system for sustainable cold chain logistics","volume":"209","author":"Shi","year":"2022","journal-title":"Expert Syst. Appl."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"8275714","DOI":"10.1155\/2021\/8275714","article-title":"Research on logistics distribution vehicle scheduling based on heuristic genetic algorithm","volume":"2021","author":"Wang","year":"2021","journal-title":"Complexity"},{"key":"ref_5","first-page":"77","article-title":"Internet of things (IoT)","volume":"9","author":"Mouha","year":"2021","journal-title":"J. Data Anal. Inf. Process."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"192","DOI":"10.1016\/j.iotcps.2023.04.006","article-title":"Internet of things for smart factories in industry 4.0, a review","volume":"3","author":"Soori","year":"2023","journal-title":"Internet Things Cyber-Phys. Syst."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Korteling, J.H., van de Boer-Visschedijk, G.C., Blankendaal, R.A., Boonekamp, R.C., and Eikelboom, A.R. (2021). Human-versus artificial intelligence. Front. Artif. Intell., 4.","DOI":"10.3389\/frai.2021.622364"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"4","DOI":"10.1007\/s44163-022-00022-8","article-title":"Quo vadis artificial intelligence?","volume":"2","author":"Jiang","year":"2022","journal-title":"Discov. Artif. Intell."},{"key":"ref_9","first-page":"100224","article-title":"Study on artificial intelligence: The state of the art and future prospects","volume":"23","author":"Zhang","year":"2021","journal-title":"J. Ind. Inf. Integr."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"106559","DOI":"10.1016\/j.cor.2024.106559","article-title":"Exact solution method for vehicle-and-drone cooperative delivery routing of blood products","volume":"164","author":"Yin","year":"2024","journal-title":"Comput. Oper. Res."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"823","DOI":"10.1142\/S2301385024300014","article-title":"A review on the truck and drone cooperative delivery problem","volume":"12","author":"Zhang","year":"2024","journal-title":"Unmanned Syst."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"10483","DOI":"10.1109\/JIOT.2019.2939397","article-title":"Routing and scheduling for hybrid truck-drone collaborative parcel delivery with independent and truck-carried drones","volume":"6","author":"Wang","year":"2019","journal-title":"IEEE Internet Things J."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1812","DOI":"10.3390\/vehicles6040088","article-title":"Multi-Depot Electric Vehicle\u2013Drone Collaborative-Delivery Routing Optimization with Time-Varying Vehicle Travel Time","volume":"6","author":"Peng","year":"2024","journal-title":"Vehicles"},{"key":"ref_14","first-page":"2258","article-title":"Hybrid Shuffled Frog Leaping Algorithm for Solving Vehicle-Drone Cooperative Delivery Problem","volume":"58","author":"Duan","year":"2024","journal-title":"J. Zhejiang Univ. Eng. Sci"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Geng, M., Wang, S., Dong, D., Wang, H., Li, G., Jin, Z., Mao, X., and Liao, X. (2024, January 14\u201320). Large language models are few-shot summarizers: Multi-intent comment generation via in-context learning. Proceedings of the 46th IEEE\/ACM International Conference on Software Engineering, Lisbon, Portugal.","DOI":"10.1145\/3597503.3608134"},{"key":"ref_16","unstructured":"Geng, R., Geng, M., Wang, S., Wang, H., Lin, Z., and Dong, D. (2025). Mitigating Sensitive Information Leakage in LLMs4Code through Machine Unlearning. arXiv."},{"key":"ref_17","unstructured":"Ugare, S., Suresh, T., Kang, H., Misailovic, S., and Singh, G. (2024). Improving llm code generation with grammar augmentation. arXiv."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Feng, Z., Zhang, Y., Li, H., Liu, W., Lang, J., Feng, Y., Wu, J., and Liu, Z. (2024). Improving llm-based machine translation with systematic self-correction. arXiv.","DOI":"10.18653\/v1\/2025.findings-naacl.218"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Yang, Z., Liu, F., Yu, Z., Keung, J.W., Li, J., Liu, S., Hong, Y., Ma, X., Jin, Z., and Li, G. (2024). Exploring and unleashing the power of large language models in automated code translation. arXiv.","DOI":"10.1145\/3660778"},{"key":"ref_20","unstructured":"Dong, Y., Ding, J., Jiang, X., Li, G., Li, Z., and Jin, Z. (2023). Codescore: Evaluating code generation by learning code execution. arXiv."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Ahmed, T., Pai, K.S., Devanbu, P., and Barr, E. (2024, January 14\u201320). Automatic semantic augmentation of language model prompts (for code summarization). Proceedings of the IEEE\/ACM 46th International Conference on Software Engineering, Lisbon, Portugal.","DOI":"10.1145\/3597503.3639183"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Li, B., Sun, Z., Huang, T., Zhang, H., Wan, Y., Li, G., Jin, Z., and Lyu, C. (2024). IRCoCo: Immediate Rewards-Guided Deep Reinforcement Learning for Code Completion. arXiv.","DOI":"10.1145\/3643735"},{"key":"ref_23","unstructured":"Zhang, K., Zhang, H., Li, G., Li, J., Li, Z., and Jin, Z. (2023). Toolcoder: Teach code generation models to use api search tools. arXiv."},{"key":"ref_24","unstructured":"Wang, Z., Li, J., Li, G., and Jin, Z. (2023). ChatCoder: Chat-based Refine Requirement Improves LLMs\u2019 Code Generation. arXiv."},{"key":"ref_25","unstructured":"Dong, Y., Jiang, X., Jin, Z., and Li, G. (2023). Self-collaboration code generation via ChatGPT. arXiv."},{"key":"ref_26","unstructured":"Microsoft Research Asia (2024, January 10\u201312). Parrot: Optimizing logistics with semantic variables using large language models. Proceedings of the 18th USENIX Symposium on Operating Systems Design and Implementation, Santa Clara, CA, USA."},{"key":"ref_27","unstructured":"Ilin, V., Simi\u0107, D., and Sauli\u0107, N. (2019, January 23\u201325). Logistics industry 4.0: Challenges and opportunities. Proceedings of the 4th Logistics International Conference, Belgrade, Serbia."},{"key":"ref_28","unstructured":"Mongaillard, T., Lasaulce, S., Hicheur, O., Zhang, C., Bariah, L., Varma, V.S., Zou, H., Zhao, Q., and Debbah, M. (2024, January 21\u201324). Large language models for power scheduling: A user-centric approach. Proceedings of the 2024 22nd International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks (WiOpt), Seoul, Republic of Korea."},{"key":"ref_29","first-page":"176","article-title":"\u201cDrone-Vehicle\u201d Distribution Routing Optimization Model","volume":"21","author":"Liu","year":"2021","journal-title":"J. Transp. Syst. Eng. Inf. Technol."},{"key":"ref_30","first-page":"201","article-title":"The cooperative delivery of multiple vehicles and multiple drones based on adaptive large neighborhood search","volume":"38","author":"Wu","year":"2023","journal-title":"Control Decis."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"564","DOI":"10.1016\/j.asoc.2017.12.031","article-title":"A comparative study of improved GA and PSO in solving multiple traveling salesmen problem","volume":"64","author":"Zhou","year":"2018","journal-title":"Appl. Soft Comput."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"965","DOI":"10.1287\/trsc.2017.0791","article-title":"Optimization approaches for the traveling salesman problem with drone","volume":"52","author":"Agatz","year":"2018","journal-title":"Transp. Sci."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"657","DOI":"10.1016\/j.trc.2020.02.030","article-title":"Truck-drone team logistics: A heuristic approach to multi-drop route planning","volume":"114","author":"Canca","year":"2020","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"5772","DOI":"10.1109\/TITS.2020.2992549","article-title":"Synchronized truck and drone routing in package delivery logistics","volume":"22","author":"Das","year":"2020","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"13011","DOI":"10.1109\/TITS.2021.3119080","article-title":"Hybrid multi-objective optimization approach with Pareto local search for collaborative truck-drone routing problems considering flexible time windows","volume":"23","author":"Luo","year":"2021","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_36","first-page":"144","article-title":"Research on vehicle routing problem with truck and drone considering regional restriction","volume":"30","author":"Yan","year":"2022","journal-title":"Chin. J. Manag. Sci."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"103172","DOI":"10.1016\/j.trc.2021.103172","article-title":"The multi-visit traveling salesman problem with multi-drones","volume":"128","author":"Luo","year":"2021","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"103733","DOI":"10.1016\/j.trc.2022.103733","article-title":"A hierarchical solution evaluation method and a hybrid algorithm for the vehicle routing problem with drones and multiple visits","volume":"141","author":"Gu","year":"2022","journal-title":"Transp. Res. Part C Emerg. Technol."},{"key":"ref_39","first-page":"90","article-title":"Research on cooperative delivery route optimization of vehicle-carried drones based on multi-depot","volume":"39","author":"Du","year":"2021","journal-title":"Syst. Eng."},{"key":"ref_40","first-page":"73","article-title":"Optimization of truck-drone collaborative distribution route considering impact of epidemic","volume":"33","author":"Peng","year":"2020","journal-title":"China J. Highw. Transp."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"116264","DOI":"10.1016\/j.eswa.2021.116264","article-title":"Vehicle routing problem with drones considering time windows","volume":"191","author":"Kuo","year":"2022","journal-title":"Expert Syst. Appl."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1080\/03052150500384759","article-title":"Shuffled frog-leaping algorithm: A memetic meta-heuristic for discrete optimization","volume":"38","author":"Eusuff","year":"2006","journal-title":"Eng. Optim."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"7155","DOI":"10.1109\/TII.2020.3042872","article-title":"Dynamic network function provisioning to enable network in box for industrial applications","volume":"17","author":"Sun","year":"2020","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Huang, F., Bei, Y., Yang, Z., Jiang, J., Chen, H., Shen, Q., Wang, S., Karray, F., and Yu, P.S. (2025, January 10\u201314). Large Language Model Simulator for Cold-Start Recommendation. Proceedings of the Eighteenth ACM International Conference on Web Search and Data Mining, Hannover, Germany.","DOI":"10.1145\/3701551.3703546"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"7550","DOI":"10.1109\/TVT.2018.2828651","article-title":"Bus-trajectory-based street-centric routing for message delivery in urban vehicular ad hoc networks","volume":"67","author":"Sun","year":"2018","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"4125","DOI":"10.1109\/TSC.2024.3478730","article-title":"Proportional fairness-aware task scheduling in space-air-ground integrated networks","volume":"17","author":"Sun","year":"2024","journal-title":"IEEE Trans. Serv. Comput."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1007\/s11227-024-06499-7","article-title":"Enhancing Chinese comprehension and reasoning for large language models: An efficient LoRA fine-tuning and tree of thoughts framework","volume":"81","author":"Chen","year":"2025","journal-title":"J. Supercomput."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"699","DOI":"10.1287\/opre.14.4.699","article-title":"Branch-and-bound methods: A survey","volume":"14","author":"Lawler","year":"1966","journal-title":"Oper. Res."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"703","DOI":"10.1137\/0108053","article-title":"The cutting-plane method for solving convex programs","volume":"8","author":"Kelley","year":"1960","journal-title":"J. Soc. Ind. Appl. Math."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/6\/934\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T17:50:41Z","timestamp":1760032241000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/6\/934"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,6,12]]},"references-count":49,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2025,6]]}},"alternative-id":["sym17060934"],"URL":"https:\/\/doi.org\/10.3390\/sym17060934","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,6,12]]}}}