{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,19]],"date-time":"2026-06-19T15:36:00Z","timestamp":1781883360927,"version":"3.54.5"},"reference-count":58,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2025,5,26]],"date-time":"2025-05-26T00:00:00Z","timestamp":1748217600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"2024 Key Research Platform Special Project of Universities in Guangdong Province","award":["2024ZDZX3027"],"award-info":[{"award-number":["2024ZDZX3027"]}]},{"name":"2024 Key Research Platform Special Project of Universities in Guangdong Province","award":["Yue Jiao Gao Han [2023] 4 hao, 105"],"award-info":[{"award-number":["Yue Jiao Gao Han [2023] 4 hao, 105"]}]},{"name":"Teaching Quality and Teaching Reform Project of Undergraduate Universities in Guangdong Province in 2022","award":["2024ZDZX3027"],"award-info":[{"award-number":["2024ZDZX3027"]}]},{"name":"Teaching Quality and Teaching Reform Project of Undergraduate Universities in Guangdong Province in 2022","award":["Yue Jiao Gao Han [2023] 4 hao, 105"],"award-info":[{"award-number":["Yue Jiao Gao Han [2023] 4 hao, 105"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Biomimetics"],"abstract":"<jats:p>To address the core challenges in multi-robot path planning (MRPP) within large-scale, complex environments\u2014namely path conflicts, suboptimal task allocation, and computational inefficiency\u2014this paper introduces a Hybrid Clustering-Enhanced Brain Storm Optimization (HC-BSO) algorithm designed to improve both path quality and computational efficiency significantly. For optimizing initial task assignment, the conventional K-Means clustering method is supplanted by a hybrid clustering methodology that integrates Mini-Batch K-Means with Density-Based Spatial Clustering of Applications with Noise (DBSCAN), facilitating an efficient and robust partitioning of task points. Concurrently, we incorporate a two-stage exploration\u2013perturbation evolutionary strategy. This strategy effectively balances global exploration with local exploitation, thereby enhancing solution diversity and search depth. Comparative analyses against the standard Brain Storm Optimization (BSO) and other prominent swarm intelligence algorithms reveal that HC-BSO exhibits significant advantages in terms of total path length, computational time, and path conflict avoidance. Notably, in large-scale, multi-task scenarios, HC-BSO consistently generates high-quality, conflict-free paths, demonstrating superior stability, convergence, and scalability.<\/jats:p>","DOI":"10.3390\/biomimetics10060347","type":"journal-article","created":{"date-parts":[[2025,5,27]],"date-time":"2025-05-27T09:29:36Z","timestamp":1748338176000},"page":"347","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Hybrid Clustering-Enhanced Brain Storm Optimization Algorithm for Efficient Multi-Robot Path Planning"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7390-5199","authenticated-orcid":false,"given":"Guangping","family":"Qiu","sequence":"first","affiliation":[{"name":"School of Artificial Intelligence, Zhujiang College of South China Agricultural University, Guangzhou 510900, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0002-1456-5494","authenticated-orcid":false,"given":"Jizhong","family":"Deng","sequence":"additional","affiliation":[{"name":"School of Artificial Intelligence, Zhujiang College of South China Agricultural University, Guangzhou 510900, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-0514-258X","authenticated-orcid":false,"given":"Jincan","family":"Li","sequence":"additional","affiliation":[{"name":"School of Artificial Intelligence, Zhujiang College of South China Agricultural University, Guangzhou 510900, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7373-7626","authenticated-orcid":false,"given":"Weixing","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Artificial Intelligence, Zhujiang College of South China Agricultural University, Guangzhou 510900, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,5,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"154","DOI":"10.1109\/MRA.2024.3352852","article-title":"Distributed optimization methods for multi-robot systems: Part 2\u2014A survey","volume":"31","author":"Shorinwa","year":"2024","journal-title":"IEEE Robot. Autom. Mag."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1109\/MRA.2011.2181683","article-title":"Robots for Environmental Monitoring: Significant Advancements and Applications","volume":"19","author":"Dunbabin","year":"2012","journal-title":"IEEE Robot. Autom. Mag."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Licardo, J.T., Domjan, M., and Orehova\u010dki, T. (2024). Intelligent Robotics\u2014A Systematic Review of Emerging Technologies and Trends. Electronics, 13.","DOI":"10.3390\/electronics13030542"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"41","DOI":"10.70112\/arme-2023.12.2.4230","article-title":"A Review on Robotics and Automation in the 21st Century: Shaping the Future of Manufacturing, Healthcare, and Service Sectors","volume":"12","author":"Husainy","year":"2023","journal-title":"Asian Rev. Mech. Eng."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Heselden, J.R., and Das, G.P. (2023). Heuristics and Rescheduling in Prioritised Multi-Robot Path Planning: A Literature Review. Machines, 11.","DOI":"10.20944\/preprints202309.1832.v1"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2750","DOI":"10.1109\/TASE.2021.3111888","article-title":"Integrated Task Allocation and Path Coordination for Large-Scale Robot Networks With Uncertainties","volume":"19","author":"Liu","year":"2022","journal-title":"IEEE Trans. Autom. Sci. Eng."},{"key":"ref_7","first-page":"10868v1","article-title":"Lifelong Multi-Agent Path Finding for Online Pickup and Delivery Tasks","volume":"Volume 1705","author":"Ma","year":"2017","journal-title":"Adaptive Agents and Multi-Agent Systems"},{"key":"ref_8","unstructured":"Okumura, K. (2024, January 20\u201327). Lacam: Search-based algorithm for quick multi-agent pathfinding. Proceedings of the AAAI Conference on Artificial Intelligence, Vancouver, BC, Canada."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"114660","DOI":"10.1016\/j.eswa.2021.114660","article-title":"Trajectory planning for multi-robot systems: Methods and applications","volume":"173","author":"Madridano","year":"2021","journal-title":"Expert Syst. Appl."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2079","DOI":"10.1017\/S0263574723000322","article-title":"A comprehensive review of the latest path planning developments for multi-robot formation systems","volume":"41","author":"Abujabal","year":"2023","journal-title":"Robotica"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"AbuJabal, N., Rabie, T., Baziyad, M., Kamel, I., and Almazrouei, K. (2024). Path Planning Techniques for Real-Time Multi-Robot Systems: A Systematic Review. Electronics, 13.","DOI":"10.3390\/electronics13122239"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Hou, S., Zhang, M., Cheng, S., and Yang, Z. (2020, January 3\u20135). Brain storm optimization algorithms: A brief review. Proceedings of the Neural Computing for Advanced Applications: First International Conference, NCAA 2020, Shenzhen, China. Proceedings 1.","DOI":"10.1007\/978-981-15-7670-6_24"},{"key":"ref_13","first-page":"jzae051","article-title":"Past five years on strategies and applications in hybrid brain storm optimization algorithms: A review","volume":"33","author":"Villar","year":"2024","journal-title":"Logic J. IGPL"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"80716","DOI":"10.1109\/ACCESS.2020.2988796","article-title":"Unsupervised K-Means Clustering Algorithm","volume":"8","author":"Sinaga","year":"2020","journal-title":"IEEE Access"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"178","DOI":"10.1016\/j.ins.2022.11.139","article-title":"K-means clustering algorithms: A comprehensive review, variants analysis, and advances in the era of big data","volume":"622","author":"Ikotun","year":"2022","journal-title":"Inf. Sci."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/3068335","article-title":"DBSCAN revisited, revisited: Why and how you should (still) use DBSCAN","volume":"42","author":"Schubert","year":"2017","journal-title":"ACM Trans. Database Syst. (TODS)"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Hicks, S.C., Liu, R., Ni, Y., Purdom, E., and Risso, D. (2020). mbkmeans: Fast clustering for single cell data using mini-batch k-means. PLoS Comput. Biol., 17.","DOI":"10.1101\/2020.05.27.119438"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"309","DOI":"10.4028\/www.scientific.net\/AST.105.309","article-title":"Time-Weighted Collaborative Filtering Algorithm Based on Improved Mini Batch K-Means Clustering","volume":"105","author":"Han","year":"2021","journal-title":"Adv. Sci. Technol."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1016\/j.procs.2023.07.017","article-title":"A Faster DBSCAN Algorithm Based on Self-Adaptive Determination of Parameters","volume":"221","author":"Ma","year":"2023","journal-title":"Procedia Comput. Sci."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"675","DOI":"10.1080\/02564602.2021.1894250","article-title":"Path planning for multiple targets interception by the swarm of UAVs based on swarm intelligence algorithms: A review","volume":"39","author":"Sharma","year":"2022","journal-title":"IETE Tech. Rev."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1007\/s00521-021-06569-4","article-title":"A review of artificial intelligence applied to path planning in UAV swarms","volume":"34","author":"Rivero","year":"2022","journal-title":"Neural Comput. Appl."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1192","DOI":"10.3390\/appliedmath4040064","article-title":"Swarm Intelligence-Based Multi-Robotics: A Comprehensive Review","volume":"4","author":"Nguyen","year":"2024","journal-title":"AppliedMath"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1320","DOI":"10.1038\/s41598-022-05386-6","article-title":"Path planning of scenic spots based on improved A* algorithm","volume":"12","author":"Wang","year":"2022","journal-title":"Sci. Rep."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"3149","DOI":"10.3390\/s24103149","article-title":"Intelligent Vehicle Path Planning Based on Optimized A* Algorithm","volume":"24","author":"Chu","year":"2024","journal-title":"Sensors"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"9955","DOI":"10.3390\/app13179955","article-title":"Path Planning of Rail-Mounted Logistics Robots Based on the Improved Dijkstra Algorithm","volume":"13","author":"Zhou","year":"2023","journal-title":"Appl. Sci."},{"key":"ref_26","first-page":"5939","article-title":"Improved Dijkstra Algorithm for Mobile Robot Path Planning and Obstacle Avoidance","volume":"72","author":"Alshammrei","year":"2022","journal-title":"Comput. Mater. Contin."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Xu, T. (2024). Recent advances in Rapidly-exploring random tree: A review. Heliyon, 10.","DOI":"10.1016\/j.heliyon.2024.e32451"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1041","DOI":"10.3390\/s23021041","article-title":"Improved Bidirectional RRT* Algorithm for Robot Path Planning","volume":"23","author":"Xin","year":"2023","journal-title":"Sensors"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1005","DOI":"10.1007\/s12555-022-0495-8","article-title":"An Improved Dynamic Window Path Planning Algorithm Using Multi-algorithm Fusion","volume":"22","author":"Zhou","year":"2024","journal-title":"Int. J. Control. Autom. Syst."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"7387","DOI":"10.1007\/s00500-022-07300-8","article-title":"Mobile robot path planning using multi-objective genetic algorithm in industrial automation","volume":"26","author":"Suresh","year":"2022","journal-title":"Soft Comput."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"106","DOI":"10.1016\/j.eswa.2018.08.008","article-title":"Multi-objective multi-robot path planning in continuous environment using an enhanced genetic algorithm","volume":"115","author":"Nazarahari","year":"2019","journal-title":"Expert Syst. Appl."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Huo, L., Zhu, J., Wu, G., and Li, Z. (2020). A novel simulated annealing based strategy for balanced UAV task assignment and path planning. Sensors, 20.","DOI":"10.3390\/s20174769"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"225","DOI":"10.3934\/mbe.2022012","article-title":"LF-ACO: An effective formation path planning for multi-mobile robot","volume":"19","author":"Yang","year":"2021","journal-title":"Math. Biosci. Eng. MBE"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1313","DOI":"10.1007\/s12065-023-00821-7","article-title":"Improved ant colony algorithm in path planning of a single robot and multi-robots with multi-objective","volume":"17","author":"Pu","year":"2024","journal-title":"Evol. Intell."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"4052","DOI":"10.1109\/TSMC.2023.3239953","article-title":"Strength Learning Particle Swarm Optimization for Multiobjective Multirobot Task Scheduling","volume":"53","author":"Liu","year":"2023","journal-title":"IEEE Trans. Syst. Man Cybern. Syst."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"228","DOI":"10.1007\/s40430-024-04772-7","article-title":"Path planning and tracking of wheeled mobile robot: Using firefly algorithm and kinematic controller combined with sliding mode control","volume":"46","author":"Achouri","year":"2024","journal-title":"J. Braz. Soc. Mech. Sci. Eng."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Bhanaria, P., and Pandey, P.K. (2023). A Multi-objective Path\u2013Planning Based on Firefly Algorithm for Mobile Robots. International Conference on Advances in IoT and Security with AI, Springer.","DOI":"10.1007\/978-981-99-5085-0_14"},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Avcu, M.E., G\u00f6k\u00e7e, H., and \u015eahin, \u0130. (2024). A WOA-based path planning approach for UAVs to avoid collisions in cluttered areas. Handbook of Whale Optimization Algorithm, Elsevier.","DOI":"10.1016\/B978-0-32-395365-8.00038-5"},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"You, D., Kang, S., Yu, J., and Wen, C. (2024). Path Planning of Robot Based on Improved Multi-Strategy Fusion Whale Algorithm. Electronics, 13.","DOI":"10.3390\/electronics13173443"},{"key":"ref_40","first-page":"6181","article-title":"Path planning of spot welding robot based on multi-objective grey wolf algorithm","volume":"41","author":"Zhao","year":"2021","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1007\/s10846-021-01490-3","article-title":"A novel hybrid discrete grey wolf optimizer algorithm for multi-UAV path planning","volume":"103","author":"Huang","year":"2021","journal-title":"J. Intell. Robot. Syst."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"104748","DOI":"10.1016\/j.robot.2024.104748","article-title":"Cooperative path planning study of distributed multi-mobile robots based on optimised ACO algorithm","volume":"179","author":"Cai","year":"2024","journal-title":"Robot. Auton. Syst."},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Tian, T., Liang, Z., Wei, Y., Luo, Q., and Zhou, Y. (2024). Hybrid Whale Optimization with a Firefly Algorithm for Function Optimization and Mobile Robot Path Planning. Biomimetics, 9.","DOI":"10.3390\/biomimetics9010039"},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Dong, L., Yuan, X., Yan, B., Song, Y., Xu, Q., and Yang, X. (2022). An improved grey wolf optimization with multi-strategy ensemble for robot path planning. Sensors, 22.","DOI":"10.3390\/s22186843"},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Yuan, Y., Yang, P., Jiang, H., and Shi, T. (2024). A Multi-Robot Task Allocation Method Based on the Synergy of the K-Means++ Algorithm and the Particle Swarm Algorithm. Biomimetics, 9.","DOI":"10.3390\/biomimetics9110694"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"851","DOI":"10.1007\/s42235-024-00637-w","article-title":"An Asynchronous Genetic Algorithm for Multi-agent Path Planning Inspired by Biomimicry","volume":"22","author":"Liu","year":"2025","journal-title":"J. Bionic. Eng."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"210","DOI":"10.23919\/CSMS.2024.0006","article-title":"Adaptive Memetic Algorithm with Dual-Level Local Search for Cooperative Route Planning of Multi-Robot Surveillance Systems","volume":"4","author":"Cheng","year":"2024","journal-title":"Complex Syst. Model. Simul."},{"key":"ref_48","first-page":"303","article-title":"Brain storm optimization algorithm","volume":"Volume 6728","author":"Wang","year":"2011","journal-title":"Advances in Swarm Intelligence: Second International Conference, ICSI 2011, Chongqing, China, 12\u201315 June 2011; Proceedings, Part I 2"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"445","DOI":"10.1007\/s10462-016-9471-0","article-title":"Brain storm optimization algorithm: A review","volume":"46","author":"Cheng","year":"2016","journal-title":"Artif. Intell. Rev."},{"key":"ref_50","first-page":"3301","article-title":"Path Planning for Unified Scheduling of Multi-Robot Based on BSO Algorithm","volume":"33","author":"Qiu","year":"2023","journal-title":"J. Circuits Syst. Comput."},{"key":"ref_51","doi-asserted-by":"crossref","unstructured":"Zhao, Y., Cheng, J., Cai, J., and Qi, B. (2024). Global-best brain storm optimization algorithm based on chaotic difference step and opposition-based learning. Sci. Rep., 14.","DOI":"10.1038\/s41598-024-56919-0"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"1289","DOI":"10.1007\/s10489-019-01600-7","article-title":"Multi-strategy brain storm optimization algorithm with dynamic parameters adjustment","volume":"50","author":"Liu","year":"2020","journal-title":"Appl. Intell."},{"key":"ref_53","doi-asserted-by":"crossref","unstructured":"Monath, N., Dubey, K.A., Guruganesh, G., Zaheer, M., Ahmed, A., McCallum, A., Mergen, G., Najork, M., Terzihan, M., and Tjanaka, B. (2020, January 21). Scalable Hierarchical Agglomerative Clustering. Proceedings of the 27th ACM SIGKDD Conference on Knowledge Discovery & Data Mining, New York, NY, USA.","DOI":"10.1145\/3447548.3467404"},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"6891","DOI":"10.1109\/LRA.2023.3313945","article-title":"An Integrated Hierarchical Approach for Real-Time Mapping With Gaussian Mixture Model","volume":"8","author":"Gao","year":"2023","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_55","first-page":"2399","article-title":"Appropriate Combination of Crossover Operator andMutation Operator in Genetic Algorithms for the Travelling Salesman Problem","volume":"79","author":"Ahmed","year":"2024","journal-title":"Comput. Mater. Contin."},{"key":"ref_56","doi-asserted-by":"crossref","unstructured":"Kofie, S.N., and Sackey, S.H. (2020, January 17\u201320). A study of population diversity using an enhanced brain storm optimization. Proceedings of the 2020 6th International Conference on Computing and Artificial Intelligence, Hohhot, China.","DOI":"10.1145\/3404555.3404606"},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"11930","DOI":"10.1109\/TII.2024.3413335","article-title":"Scheduling and Logistics Optimization for Batch Manufacturing Processes With Temperature Constraints and Alternative Thermal Devices","volume":"20","author":"Zhao","year":"2024","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"4449","DOI":"10.1080\/03610918.2022.2154793","article-title":"Factor screening with modified one-factor-at-a-time experiments","volume":"53","author":"Yu","year":"2024","journal-title":"Commun. Stat. Simul. Comput."}],"container-title":["Biomimetics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2313-7673\/10\/6\/347\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T17:40:28Z","timestamp":1760031628000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2313-7673\/10\/6\/347"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,5,26]]},"references-count":58,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2025,6]]}},"alternative-id":["biomimetics10060347"],"URL":"https:\/\/doi.org\/10.3390\/biomimetics10060347","relation":{},"ISSN":["2313-7673"],"issn-type":[{"value":"2313-7673","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,5,26]]}}}