{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,15]],"date-time":"2026-06-15T14:29:59Z","timestamp":1781533799545,"version":"3.54.5"},"reference-count":43,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2026,4,7]],"date-time":"2026-04-07T00:00:00Z","timestamp":1775520000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100007085","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["72431011"],"award-info":[{"award-number":["72431011"]}],"id":[{"id":"10.13039\/501100007085","id-type":"DOI","asserted-by":"publisher"}]},{"award":["72431011"],"award-info":[{"award-number":["72431011"]}],"id":[{"id":"https:\/\/ror.org\/01h0zpd94","id-type":"ROR","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Systems"],"abstract":"<jats:p>Multi-agent systems (MASs), with unmanned aerial vehicles (UAVs) as a representative embodiment, have become increasingly vital in time-sensitive disaster response scenarios, where multiple agents must collaborate to execute \u201cobserve-and-intervene\u201d emergency tasks and jointly cope with dynamic environmental uncertainties. Existing research on task allocation mostly eliminates uncertainty through deterministic models; the few studies that directly consider uncertainty focus primarily on time uncertainty, overlooking the critical importance of demand uncertainty. To this end, this study accounts for the impact of harsh environmental conditions and incident complexity factors on intervention resource demands. We establish an uncertainty set for these demands and construct a two-stage robust optimization model to solve the coupled multi-agent task allocation problem. Compared with deterministic models, this framework enhances risk resistance while simultaneously reducing the conservatism of decisions. Furthermore, to overcome the computational challenges of large-scale instances, a Learning-Enhanced Column and Constraint Generation (LE-C&amp;CG) algorithm is proposed. Experimental results demonstrate that LE-C&amp;CG converges over an order of magnitude faster than standard Benders and C&amp;CG algorithms, consistently achieving a 0% optimality gap within fractions of a second, making it highly suitable for time-critical emergency applications.<\/jats:p>","DOI":"10.3390\/systems14040405","type":"journal-article","created":{"date-parts":[[2026,4,7]],"date-time":"2026-04-07T12:03:47Z","timestamp":1775563427000},"page":"405","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Two-Stage Robust Optimization for Coupled Multi-Agent Task Allocation in Disaster Response Under Demand Uncertainty"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0009-0001-5222-5805","authenticated-orcid":false,"given":"Chenxi","family":"Duan","sequence":"first","affiliation":[{"name":"College of Systems Engineering, National University of Defense Technology, Changsha 410073, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chongshuang","family":"Hu","sequence":"additional","affiliation":[{"name":"College of Systems Engineering, National University of Defense Technology, Changsha 410073, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Minghao","family":"Li","sequence":"additional","affiliation":[{"name":"College of Systems Engineering, National University of Defense Technology, Changsha 410073, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jiang","family":"Jiang","sequence":"additional","affiliation":[{"name":"College of Systems Engineering, National University of Defense Technology, Changsha 410073, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,4,7]]},"reference":[{"key":"ref_1","first-page":"222","article-title":"Survey on intelligent scheduling technologies for unmanned flying craft clusters","volume":"46","author":"Du","year":"2020","journal-title":"Acta Autom. Sin."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Alqefari, S., and Menai, M.E.B. (2025). Multi-UAV task assignment in dynamic environments: Current trends and future directions. Drones, 9.","DOI":"10.3390\/drones9010075"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"107913","DOI":"10.1016\/j.comnet.2021.107913","article-title":"A joint global and local path planning optimization for UAV task scheduling towards crowd air monitoring","volume":"193","author":"Tang","year":"2021","journal-title":"Comput. Netw."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Feng, O., Zhang, H., Tang, W., Wang, F., Feng, D., and Zhong, G. (2025). Digital Low-Altitude Airspace Unmanned Aerial Vehicle Path Planning and Operational Capacity Assessment in Urban Risk Environments. Drones, 9.","DOI":"10.3390\/drones9050320"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"109072","DOI":"10.1016\/j.knosys.2022.109072","article-title":"A task allocation algorithm for a swarm of unmanned aerial vehicles based on bionic wolf pack method","volume":"250","author":"Wang","year":"2022","journal-title":"Knowl.-Based Syst."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Song, Y., Ma, Z., Chen, N., Zhou, S., and Srigrarom, S. (2025). Comparative analysis of centralized and distributed multi-UAV task allocation algorithms: A unified evaluation framework. Drones, 9.","DOI":"10.3390\/drones9080530"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Liu, H., Shao, Z., Zhou, Q., Tu, J., and Zhu, S. (2025). Task Allocation Algorithm for Heterogeneous UAV Swarm with Temporal Task Chains. Drones, 9.","DOI":"10.3390\/drones9080574"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Cui, W., Li, R., Feng, Y., and Yang, Y. (2022). Distributed task allocation for a multi-UAV system with time window constraints. Drones, 6.","DOI":"10.3390\/drones6090226"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"5926","DOI":"10.1109\/TITS.2020.3042670","article-title":"An iterative two-phase optimization method based on divide and conquer framework for integrated scheduling of multiple UAVs","volume":"22","author":"Liu","year":"2020","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Hu, C., Wang, R., Lei, T., Zhang, X., Li, M., and Jiang, J. (2025). Dynamic multi-objective optimization based on integrated incremental long short-term memory and inverse model prediction strategy. IEEE Trans. Evol. Comput.","DOI":"10.1109\/TEVC.2025.3594781"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"298","DOI":"10.1109\/TMLCN.2024.3368367","article-title":"On learning generalized wireless MAC communication protocols via a feasible multi-agent reinforcement learning framework","volume":"2","author":"Miuccio","year":"2024","journal-title":"IEEE Trans. Mach. Learn. Commun. Netw."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"39392","DOI":"10.1109\/ACCESS.2021.3063263","article-title":"Cooperative multiple task assignment problem with target precedence constraints using a waitable path coordination and modified genetic algorithm","volume":"9","author":"Zhao","year":"2021","journal-title":"IEEE Access"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"41090","DOI":"10.1109\/ACCESS.2019.2907544","article-title":"Swarm UAVs task and resource dynamic assignment algorithm based on task sequence mechanism","volume":"7","author":"Fu","year":"2019","journal-title":"IEEE Access"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"432","DOI":"10.1007\/s11771-020-4307-0","article-title":"Cooperative task allocation for heterogeneous multi-UAV using multi-objective optimization algorithm","volume":"27","author":"Wang","year":"2020","journal-title":"J. Cent. South Univ."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"100369","DOI":"10.1109\/ACCESS.2021.3097094","article-title":"Multi-UAV task allocation based on improved genetic algorithm","volume":"9","author":"Wu","year":"2021","journal-title":"IEEE Access"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"101545","DOI":"10.1016\/j.jocs.2021.101545","article-title":"An efficient multi-objective ant colony optimization for task allocation of heterogeneous unmanned aerial vehicles","volume":"58","author":"Chen","year":"2022","journal-title":"J. Comput. Sci."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Yu, X., Gao, X., Wang, L., Wang, X., Ding, Y., Lu, C., and Zhang, S. (2022). Cooperative multi-UAV task assignment in cross-regional joint operations considering ammunition inventory. Drones, 6.","DOI":"10.3390\/drones6030077"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Zhang, S., Hu, C., Zhao, D., Yang, K., Xu, Z., and Li, M. (2025). A Two-Stage Multi-UAV Task Allocation Approach Based on Graph Theory and a Learning-Inspired Immune Algorithm. Drones, 9.","DOI":"10.3390\/drones9090599"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Liu, B., Wang, S., Li, Q., Zhao, X., Pan, Y., and Wang, C. (2023). Task assignment of UAV swarms based on deep reinforcement learning. Drones, 7.","DOI":"10.3390\/drones7050297"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Dong, X., Shi, C., Wen, W., and Zhou, J. (2023). Multi-Mission Oriented Joint Optimization of Task Assignment and Flight Path Planning for Heterogeneous UAV Cluster. Remote Sens., 15.","DOI":"10.3390\/rs15225315"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"7155","DOI":"10.1007\/s00500-021-05675-8","article-title":"Multi-UAV reconnaissance task allocation for heterogeneous targets using grouping ant colony optimization algorithm","volume":"25","author":"Gao","year":"2021","journal-title":"Soft Comput."},{"key":"ref_22","first-page":"566","article-title":"Distributed task assignment method based on local information consensus and target estimation","volume":"35","author":"Wu","year":"2018","journal-title":"Control Theory Appl."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/3727989","article-title":"A user study evaluation of predictive formal modelling at runtime in human-swarm interaction","volume":"14","author":"Abioye","year":"2025","journal-title":"ACM Trans. Hum.-Robot Interact."},{"key":"ref_24","first-page":"100469","article-title":"Task assignment algorithms for unmanned aerial vehicle networks: A comprehensive survey","volume":"35","author":"Poudel","year":"2022","journal-title":"Veh. Commun."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"10676","DOI":"10.1109\/JIOT.2021.3125784","article-title":"Cooperative path optimization for multiple UAVs surveillance in uncertain environment","volume":"9","author":"Liu","year":"2021","journal-title":"IEEE Internet Things J."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Zhong, H., Yang, R., Zheng, A., Zheng, M., and Mei, Y. (2025). Two-Stage Uncertain UAV Combat Mission Assignment Problem Based on Uncertainty Theory. Aerospace, 12.","DOI":"10.3390\/aerospace12060553"},{"key":"ref_27","first-page":"148","article-title":"Task allocation of heterogeneous multi-UAVs in uncertain environment based on multi-strategy integrated GWO","volume":"44","author":"Zhang","year":"2023","journal-title":"Acta Aeronaut. Astronaut. Sin."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"102373","DOI":"10.1109\/ACCESS.2022.3208870","article-title":"A novel tent-levy fireworks algorithm for the UAV task allocation problem under uncertain environment","volume":"10","author":"Yu","year":"2022","journal-title":"IEEE Access"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"4372","DOI":"10.1109\/TVT.2022.3228198","article-title":"Multi-agent reinforcement learning-based coordinated dynamic task allocation for heterogenous UAVs","volume":"72","author":"Liu","year":"2022","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Qin, B., Zhang, D., Tang, S., and Wang, M. (2022). Distributed grouping cooperative dynamic task assignment method of UAV swarm. Appl. Sci., 12.","DOI":"10.3390\/app12062865"},{"key":"ref_31","first-page":"107","article-title":"Hybrid genetic algorithm for solving fuzzy demand and time windows vehicle routing problem","volume":"29","author":"Fan","year":"2020","journal-title":"J. Syst. Manag."},{"key":"ref_32","first-page":"1644","article-title":"Fuzzy game decision-making of unmanned aerial vehicles air-to-ground attack based on the particle swarm optimization integrating multiply strategies","volume":"36","author":"Zhao","year":"2019","journal-title":"Control Theory Appl."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"2177","DOI":"10.1287\/opre.2023.0569","article-title":"Hardness of pricing routes for two-stage stochastic vehicle routing problems with scenarios","volume":"73","author":"Ota","year":"2025","journal-title":"Oper. Res."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"3287","DOI":"10.1109\/LRA.2021.3062337","article-title":"Task planning on stochastic aisle graphs for precision agriculture","volume":"6","author":"Kan","year":"2021","journal-title":"IEEE Robot. Autom. Lett."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"112","DOI":"10.1016\/j.ast.2018.01.025","article-title":"Cooperative multiple task assignment problem with stochastic velocities and time windows for heterogeneous unmanned aerial vehicles using a genetic algorithm","volume":"76","author":"Jia","year":"2018","journal-title":"Aerosp. Sci. Technol."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"2853","DOI":"10.1109\/TAES.2018.2831138","article-title":"Multi-UAV task assignment with parameter and time-sensitive uncertainties using modified two-part wolf pack search algorithm","volume":"54","author":"Chen","year":"2018","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"455","DOI":"10.1109\/TCE.2026.3652706","article-title":"Event-Triggered Zero-Sum Game for Input Saturated Nonlinear Systems with State Constraints","volume":"72","author":"Qin","year":"2026","journal-title":"IEEE Trans. Consum. Electron."},{"key":"ref_38","first-page":"838","article-title":"Unmanned aerial vehicle carriers scheduling problem based on two-stage robust optimization","volume":"35","author":"He","year":"2020","journal-title":"J. Syst. Eng."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10489-018-1169-3","article-title":"Addressing robustness in time-critical, distributed, task allocation algorithms","volume":"49","author":"Whitbrook","year":"2019","journal-title":"Appl. Intell."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Zheng, X., Qin, S., Zhang, Y., and Huo, J. (2025). Integrated Two-Stage Optimization of Strategic Unmanned Aerial Vehicle Allocation and Operational Scheduling Under Demand Uncertainty. Appl. Sci., 15.","DOI":"10.3390\/app152011249"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"1560","DOI":"10.1109\/JIOT.2021.3090442","article-title":"Two-stage robust edge service placement and sizing under demand uncertainty","volume":"9","author":"Nguyen","year":"2021","journal-title":"IEEE Internet Things J."},{"key":"ref_42","first-page":"3552","article-title":"Two-Stage Robust Optimization Method for UAV Task Assignment Under Uncertain Demand","volume":"52","author":"Wang","year":"2024","journal-title":"Acta Electron. Sin."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1016\/j.orl.2013.05.003","article-title":"Solving two-stage robust optimization problems using a column-and-constraint generation method","volume":"41","author":"Zeng","year":"2013","journal-title":"Oper. Res. Lett."}],"container-title":["Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-8954\/14\/4\/405\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,7]],"date-time":"2026-04-07T12:27:48Z","timestamp":1775564868000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-8954\/14\/4\/405"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,4,7]]},"references-count":43,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2026,4]]}},"alternative-id":["systems14040405"],"URL":"https:\/\/doi.org\/10.3390\/systems14040405","relation":{},"ISSN":["2079-8954"],"issn-type":[{"value":"2079-8954","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,4,7]]}}}