{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,14]],"date-time":"2026-07-14T17:15:17Z","timestamp":1784049317821,"version":"3.55.0"},"reference-count":38,"publisher":"American Institute of Aeronautics and Astronautics (AIAA)","issue":"5","content-domain":{"domain":["arc.aiaa.org"],"crossmark-restriction":true},"short-container-title":["Journal of Aerospace Information Systems"],"published-print":{"date-parts":[[2025,5]]},"abstract":"<jats:p> This paper considers an [Formula: see text]-pursuer\u2013[Formula: see text]-evader scenario involving [Formula: see text] virtual targets. The virtual targets serve as an intermediary target for the pursuers, allowing the pursuers to delay their final assignment to the evaders. However, upon reaching the virtual target, the pursuers must decide which evader to capture. It is assumed that there are more pursuers than evaders and that the pursuers are faster than the evaders. The objective is two-part: first, assign each pursuer to a virtual target and evader such that the pursuer team\u2019s energy is minimized, and, second, choose the virtual targets\u2019 locations for this minimization problem. The approach taken is to consider the Apollonius geometry between each pursuer\u2019s virtual target location and each evader. Using the constructed Apollonius circles, the pursuer\u2019s travel distance and maneuver at a virtual target are obtained. These metrics serve as a gauge for the total energy required to capture a particular evader and are used to solve the joint virtual target selection and pursuer\u2013evader assignment problem. This paper provides a mathematical definition of this problem, the solution approach taken, and an example. Following the example, a Monte Carlo analysis is performed, demonstrating the efficacy of the algorithm and its suitability for real-time applications. <\/jats:p>","DOI":"10.2514\/1.i011510","type":"journal-article","created":{"date-parts":[[2025,2,10]],"date-time":"2025-02-10T17:09:26Z","timestamp":1739207366000},"page":"391-400","update-policy":"https:\/\/doi.org\/10.2514\/aiaa_crossmarkpolicy","source":"Crossref","is-referenced-by-count":0,"title":["Virtual Target Selection for a Multiple-Pursuer\u2013Multiple-Evader Scenario"],"prefix":"10.2514","volume":"22","author":[{"given":"Isaac E.","family":"Weintraub","sequence":"first","affiliation":[{"name":"Air Force Research Laboratory"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alexander","family":"Von Moll","sequence":"additional","affiliation":[{"name":"Air Force Research Laboratory"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"David W.","family":"Casbeer","sequence":"additional","affiliation":[{"name":"Air Force Research Laboratory"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Satyanarayana G.","family":"Manyam","sequence":"additional","affiliation":[{"name":"Infoscitex Corporation"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1387","reference":[{"key":"r1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cor.2018.10.015"},{"key":"r2","doi-asserted-by":"publisher","DOI":"10.1016\/j.omega.2021.102562"},{"key":"r3","volume-title":"Differential Games: A Mathematical Theory with Applications to Optimization, Control and Warfare","author":"Isaacs R.","year":"1965"},{"key":"r4","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-64793-3_26"},{"key":"r5","unstructured":"DayM. \u201cMulti-Agent Task Negotiation Among UAVs to Defend Against Swarm Attacks,\u201d Ph.D. Thesis, Naval Postgraduate School, Monteray, CA, 2012, https:\/\/apps.dtic.mil\/sti\/pdfs\/ADA560588.pdf."},{"key":"r6","doi-asserted-by":"publisher","DOI":"10.1007\/s10957-004-1713-7"},{"key":"r7","doi-asserted-by":"publisher","DOI":"10.1142\/S0219198910002489"},{"key":"r8","doi-asserted-by":"publisher","DOI":"10.1109\/7.976974"},{"key":"r9","doi-asserted-by":"publisher","DOI":"10.1109\/CDC.2002.1184476"},{"key":"r10","doi-asserted-by":"publisher","DOI":"10.3182\/20050703-6-CZ-1902.00935"},{"key":"r11","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2020.3003840"},{"key":"r12","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2022.110207"},{"key":"r15","doi-asserted-by":"publisher","DOI":"10.2514\/6.2022-2215"},{"key":"r16","doi-asserted-by":"publisher","DOI":"10.2514\/6.2021-1861"},{"key":"r17","doi-asserted-by":"publisher","DOI":"10.1109\/LCSYS.2021.3092950"},{"key":"r20","doi-asserted-by":"publisher","DOI":"10.1002\/rnc.1193"},{"key":"r21","doi-asserted-by":"publisher","DOI":"10.2514\/1.25329"},{"key":"r22","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2016.2577619"},{"key":"r23","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2017.11.035"},{"key":"r24","doi-asserted-by":"publisher","DOI":"10.1007\/s10846-015-0315-y"},{"key":"r25","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2016.05.007"},{"key":"r27","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2012.06.003"},{"key":"r28","doi-asserted-by":"publisher","DOI":"10.1007\/s13235-019-00319-x"},{"key":"r29","doi-asserted-by":"publisher","DOI":"10.1007\/s10625-005-0198-y"},{"key":"r30","doi-asserted-by":"publisher","DOI":"10.3934\/math.2023332"},{"key":"r32","first-page":"3184","volume-title":"8th World Congress on Intelligent Control and Automation","author":"Jin S.","year":"2010"},{"key":"r33","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2016.04.012"},{"key":"r34","doi-asserted-by":"publisher","DOI":"10.2514\/1.G004393"},{"key":"r35","doi-asserted-by":"publisher","DOI":"10.2514\/1.G006494"},{"key":"r37","doi-asserted-by":"publisher","DOI":"10.2514\/6.2023-1472"},{"key":"r38","volume-title":"Combinatorial Optimization: Algorithms and Complexity","author":"Papadimitriou C. 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