{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T11:45:40Z","timestamp":1778586340828,"version":"3.51.4"},"reference-count":59,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2025,11,11]],"date-time":"2025-11-11T00:00:00Z","timestamp":1762819200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"},{"start":{"date-parts":[[2025,11,11]],"date-time":"2025-11-11T00:00:00Z","timestamp":1762819200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"}],"funder":[{"DOI":"10.13039\/501100020884","name":"Agencia Nacional de Investigaci\u00f3n y Desarrollo","doi-asserted-by":"publisher","award":["1241710"],"award-info":[{"award-number":["1241710"]}],"id":[{"id":"10.13039\/501100020884","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Artif Intell Rev"],"DOI":"10.1007\/s10462-025-11378-5","type":"journal-article","created":{"date-parts":[[2025,11,11]],"date-time":"2025-11-11T07:43:16Z","timestamp":1762846996000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Heuristics for the direct aperture optimisation in intensity modulated radiotion therapy: a systematic literature review"],"prefix":"10.1007","volume":"59","author":[{"given":"Mauricio","family":"Moyano","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vinicius Cabrera","family":"Jameli","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Keiny","family":"Meza-Vasquez","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Maximiliano","family":"Beltran-Villarroel","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sebastian","family":"Mu\u00f1oz-Bustos","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gonzalo","family":"Tello-Valenzuela","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nicolle","family":"Ojeda-Ortega","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guillermo","family":"Cabrera-Guerrero","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,11,11]]},"reference":[{"key":"11378_CR1","doi-asserted-by":"publisher","first-page":"36","DOI":"10.1002\/net.20047","volume":"45","author":"RK Ahuja","year":"2005","unstructured":"Ahuja RK, Hamacher HW (2005) A network flow algorithm to minimize beam-on time for unconstrained multileaf collimator problems in cancer radiation therapy. Networks 45:36\u201341","journal-title":"Networks"},{"key":"11378_CR2","doi-asserted-by":"publisher","first-page":"6","DOI":"10.1016\/j.dam.2005.04.008","volume":"152","author":"D Baatar","year":"2005","unstructured":"Baatar D, Hamacher H, Ehrgott M, Woeginger G (2005) Decomposition of integer matrices and multileaf collimator sequencing. Discret Appl Math 152:6\u201334. https:\/\/doi.org\/10.1016\/j.dam.2005.04.008","journal-title":"Discret Appl Math"},{"issue":"6","key":"11378_CR3","doi-asserted-by":"publisher","first-page":"1539","DOI":"10.1118\/1.1697670","volume":"31","author":"F Beaulieu","year":"2004","unstructured":"Beaulieu F, Beaulieu L, Tremblay D, Lachance B, Roy R (2004) Automatic generation of anatomy-based mlc fields in aperture-based imrt. Med Phys 31(6):1539\u20131545. https:\/\/doi.org\/10.1118\/1.1697670","journal-title":"Med Phys"},{"issue":"4","key":"11378_CR4","doi-asserted-by":"publisher","first-page":"944","DOI":"10.1118\/1.2163832","volume":"33","author":"JL Bedford","year":"2006","unstructured":"Bedford JL, Webb S (2006) Constrained segment shapes in direct-aperture optimization for step-and-shoot imrt. Med Phys 33(4):944\u2013958. https:\/\/doi.org\/10.1118\/1.2163832","journal-title":"Med Phys"},{"issue":"2","key":"11378_CR5","doi-asserted-by":"publisher","first-page":"479","DOI":"10.1088\/0031-9155\/52\/2\/012","volume":"52","author":"JL Bedford","year":"2007","unstructured":"Bedford JL, Webb S (2007) Direct-aperture optimization applied to selection of beam orientations in intensity-modulated radiation therapy. Phys Med Biol 52(2):479\u2013498. https:\/\/doi.org\/10.1088\/0031-9155\/52\/2\/012","journal-title":"Phys Med Biol"},{"issue":"13","key":"11378_CR6","doi-asserted-by":"publisher","first-page":"4051","DOI":"10.1088\/0031-9155\/54\/13\/007","volume":"54","author":"L Bogner","year":"2009","unstructured":"Bogner L, Alt M, Dirscherl T, Morgenstern I, Latscha C, Rickhey M (2009) Fast direct monte carlo optimization using the inverse kernel approach. Phys Med Biol 54(13):4051\u20134067. https:\/\/doi.org\/10.1088\/0031-9155\/54\/13\/007","journal-title":"Phys Med Biol"},{"key":"11378_CR7","doi-asserted-by":"publisher","first-page":"143","DOI":"10.1016\/j.dib.2017.03.037","volume":"12","author":"S Breedveld","year":"2017","unstructured":"Breedveld S, Heijmen B (2017) Data for trots the radiotherapy optimisation test set. Data Brief 12:143\u2013149. https:\/\/doi.org\/10.1016\/j.dib.2017.03.037","journal-title":"Data Brief"},{"issue":"21","key":"11378_CR8","doi-asserted-by":"publisher","first-page":"6725","DOI":"10.1088\/0031-9155\/54\/21\/018","volume":"54","author":"D Cao","year":"2009","unstructured":"Cao D, Afghan MKN, Ye J, Chen F, Shepard DM (2009) A generalized inverse planning tool for volumetric-modulated arc therapy. Phys Med Biol 54(21):6725\u20136738. https:\/\/doi.org\/10.1088\/0031-9155\/54\/21\/018","journal-title":"Phys Med Biol"},{"issue":"23","key":"11378_CR9","doi-asserted-by":"publisher","first-page":"4152","DOI":"10.3760\/cma.j.issn.0366-6999.20130644","volume":"127","author":"R Cao","year":"2014","unstructured":"Cao R, Pei X, Zheng H, Hu L, Wu Y (2014) Direct aperture optimization based on genetic algorithm and conjugate gradient in intensity modulated radiation therapy. Chin Med J 127(23):4152\u20134153. https:\/\/doi.org\/10.3760\/cma.j.issn.0366-6999.20130644","journal-title":"Chin Med J"},{"issue":"9","key":"11378_CR10","doi-asserted-by":"publisher","first-page":"3828","DOI":"10.1118\/1.2964096","volume":"35","author":"F Carlsson","year":"2008","unstructured":"Carlsson F (2008) Combining segment generation with direct step-and-shoot optimization in intensity-modulated radiation therapy. Med Phys 35(9):3828\u20133838. https:\/\/doi.org\/10.1118\/1.2964096","journal-title":"Med Phys"},{"issue":"2","key":"11378_CR11","doi-asserted-by":"publisher","first-page":"301","DOI":"10.1088\/0031-9155\/58\/2\/301","volume":"58","author":"A Cassioli","year":"2013","unstructured":"Cassioli A, Unkelbach J (2013) Aperture shape optimization for imrt treatment planning. Phys Med Biol 58(2):301\u2013318. https:\/\/doi.org\/10.1088\/0031-9155\/58\/2\/301","journal-title":"Phys Med Biol"},{"issue":"1","key":"11378_CR12","doi-asserted-by":"publisher","first-page":"1","DOI":"10.3857\/roj.2018.00122","volume":"36","author":"B Cho","year":"2018","unstructured":"Cho B (2018) Intensity-modulated radiation therapy: a review with a physics perspective. Radiat Oncol J 36(1):1","journal-title":"Radiat Oncol J"},{"issue":"18","key":"11378_CR13","doi-asserted-by":"publisher","first-page":"2987","DOI":"10.1088\/0031-9155\/48\/18\/303","volume":"48","author":"C Cotrutz","year":"2003","unstructured":"Cotrutz C, Xing L (2003) Segment-based dose optimization using a genetic algorithm. Phys Med Biol 48(18):2987\u20132998. https:\/\/doi.org\/10.1088\/0031-9155\/48\/18\/303","journal-title":"Phys Med Biol"},{"key":"11378_CR14","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1186\/2047-217X-3-37","volume":"3","author":"D Craft","year":"2015","unstructured":"Craft D, Bangert M, Long T, Papp D, Unkelbach J (2015) Shared data for intensity modulated radiation therapy (imrt) optimization research: the cort dataset. GigaScience 3:37. https:\/\/doi.org\/10.1186\/2047-217X-3-37","journal-title":"GigaScience"},{"key":"11378_CR15","doi-asserted-by":"publisher","first-page":"565","DOI":"10.1007\/s00345-019-02661-6","volume":"38","author":"T Daly","year":"2020","unstructured":"Daly T (2020) Evolution of definitive external beam radiation therapy in the treatment of prostate cancer. World J Urol 38:565\u2013591","journal-title":"World J Urol"},{"issue":"5","key":"11378_CR16","doi-asserted-by":"publisher","first-page":"979","DOI":"10.1118\/1.1568978","volume":"30","author":"JO Deasy","year":"2003","unstructured":"Deasy JO, Blanco AI, Clark VH (2003) Cerr: a computational environment for radiotherapy research. Med Phys 30(5):979\u2013985. https:\/\/doi.org\/10.1118\/1.1568978","journal-title":"Med Phys"},{"issue":"4","key":"11378_CR17","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1371\/journal.pone.0094371","volume":"9","author":"Y Dzierma","year":"2014","unstructured":"Dzierma Y, Nuesken FG, Fleckenstein J, Melchior P, Licht NP, R\u00fcbe C (2014) Comparative planning of flattening-filter-free and flat beam imrt for hypopharynx cancer as a function of beam and segment number. PLoS ONE 9(4):1\u201314. https:\/\/doi.org\/10.1371\/journal.pone.0094371","journal-title":"PLoS ONE"},{"key":"11378_CR18","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1007\/s10288-008-0083-7","volume":"6","author":"M Ehrgott","year":"2008","unstructured":"Ehrgott M, G\u00fcler \u00c7, Hamacher H, Shao L (2008) Mathematical optimization in intensity modulated radiation therapy. Ann Oper Res 6:199\u2013262. https:\/\/doi.org\/10.1007\/s10288-008-0083-7","journal-title":"Ann Oper Res"},{"issue":"2","key":"11378_CR19","doi-asserted-by":"publisher","first-page":"1","DOI":"10.22068\/ijiepr.33.2.2","volume":"33","author":"A Fallahi","year":"2022","unstructured":"Fallahi A, Mahnam M, Akhavan Niaki ST (2022) Direct aperture optimization for intensity modulated radiation therapy: two calibrated metaheuristics and liver cancer case study. Int J Ind Eng Prod Res 33(2):1\u201314. https:\/\/doi.org\/10.22068\/ijiepr.33.2.2","journal-title":"Int J Ind Eng Prod Res"},{"issue":"21","key":"11378_CR20","doi-asserted-by":"publisher","first-page":"7683","DOI":"10.1088\/0031-9155\/58\/21\/7683","volume":"58","author":"A Fredriksson","year":"2013","unstructured":"Fredriksson A, Bokrantz R (2013) Deliverable navigation for multicriteria imrt treatment planning by combining shared and individual apertures. Phys Med Biol 58(21):7683\u20137697. https:\/\/doi.org\/10.1088\/0031-9155\/58\/21\/7683","journal-title":"Phys Med Biol"},{"issue":"1","key":"11378_CR21","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1016\/S0166-218X(01)00261-X","volume":"118","author":"HW Hamacher","year":"2002","unstructured":"Hamacher HW, K\u00fcfer K-H (2002) Inverse radiation therapy planning - a multiple objective optimization approach. Discret Appl Math 118(1):145\u2013161. https:\/\/doi.org\/10.1016\/S0166-218X(01)00261-X","journal-title":"Discret Appl Math"},{"key":"11378_CR22","doi-asserted-by":"publisher","first-page":"1819","DOI":"10.1038\/sj.bjc.6602577","volume":"92","author":"T Hong","year":"2005","unstructured":"Hong T, Ritter M, Tome W, Harari P (2005) Intensity-modulated radiation therapy: emerging cancer treatment technology. Br J Cancer 92:1819\u201324. https:\/\/doi.org\/10.1038\/sj.bjc.6602577","journal-title":"Br J Cancer"},{"issue":"1","key":"11378_CR23","doi-asserted-by":"publisher","first-page":"48","DOI":"10.13538\/j.1001-8042\/nst.26.010502","volume":"26","author":"W Jie","year":"2015","unstructured":"Jie W, Xi P, Rui-Fen C, Li-Qin H, Yi-Can W (2015) A multiphase direct aperture optimization for inverse planning in radiotherapy. Nucl Sci Tech 26(1):48\u201353. https:\/\/doi.org\/10.13538\/j.1001-8042\/nst.26.010502","journal-title":"Nucl Sci Tech"},{"key":"11378_CR24","unstructured":"Keele S, et al (2007) Guidelines for performing systematic literature reviews in software engineering. Technical report, Technical report, Ver. 2.3 EBSE Technical Report. EBSE"},{"issue":"20","key":"11378_CR25","doi-asserted-by":"publisher","first-page":"3353","DOI":"10.1088\/0031-9155\/48\/20\/007","volume":"48","author":"Y Li","year":"2003","unstructured":"Li Y, Yao J, Yao D (2003) Genetic algorithm based deliverable segments optimization for static intensity-modulated radiotherapy. Phys Med Biol 48(20):3353\u201374","journal-title":"Phys Med Biol"},{"issue":"10","key":"11378_CR26","doi-asserted-by":"publisher","first-page":"5624","DOI":"10.1002\/mp.15155","volume":"48","author":"C Liu","year":"2021","unstructured":"Liu C, Ni X, Jin X, Si W (2021) Neuraldao: incorporating neural network generated dose into direct aperture optimization for end-to-end imrt planning. Med Phys 48(10):5624\u20135638. https:\/\/doi.org\/10.1002\/mp.15155","journal-title":"Med Phys"},{"issue":"6","key":"11378_CR27","doi-asserted-by":"publisher","first-page":"3445","DOI":"10.1118\/1.4720218","volume":"39","author":"T Long","year":"2012","unstructured":"Long T, Matuszak M, Feng M, Fraass BA, Ten Haken RK, Romeijn HE (2012) Sensitivity analysis for lexicographic ordering in radiation therapy treatment planning. Med Phys 39(6):3445\u20133455. https:\/\/doi.org\/10.1118\/1.4720218","journal-title":"Med Phys"},{"issue":"3","key":"11378_CR28","doi-asserted-by":"publisher","first-page":"807","DOI":"10.1088\/0031-9155\/53\/3\/018","volume":"53","author":"E Ludlum","year":"2009","unstructured":"Ludlum E, Xia P (2009) Comparison of imrt planning with two-step and one-step optimization a way to simplify imrt. Phys Med Biol 53(3):807\u2013821. https:\/\/doi.org\/10.1088\/0031-9155\/53\/3\/018","journal-title":"Phys Med Biol"},{"issue":"3","key":"11378_CR29","doi-asserted-by":"publisher","first-page":"1127","DOI":"10.1002\/mp.13368","volume":"46","author":"M MacFarlane","year":"2019","unstructured":"MacFarlane M, Hoover DA, Wong E, Goldman P, Battista JJ, Chen JZ (2019) A fast inverse direct aperture optimization algorithm for intensity-modulated radiation therapy. Med Phys 46(3):1127\u20131139. https:\/\/doi.org\/10.1002\/mp.13368","journal-title":"Med Phys"},{"issue":"24","key":"11378_CR30","doi-asserted-by":"publisher","first-page":"7333","DOI":"10.1088\/0031-9155\/52\/24\/009","volume":"52","author":"C Men","year":"2007","unstructured":"Men C, Romeijn HE, Taskin ZC, Dempsey JF (2007) An exact approach to direct aperture optimization in imrt treatment planning. Phys Med Biol 52(24):7333\u20137352. https:\/\/doi.org\/10.1088\/0031-9155\/52\/24\/009","journal-title":"Phys Med Biol"},{"issue":"15","key":"11378_CR31","doi-asserted-by":"publisher","first-page":"4309","DOI":"10.1088\/0031-9155\/55\/15\/008","volume":"55","author":"C Men","year":"2010","unstructured":"Men C, Jia X, Jiang SB (2010) Gpu-based ultra-fast direct aperture optimization for online adaptive radiation therapy. Phys Med Biol 55(15):4309\u20134319. https:\/\/doi.org\/10.1088\/0031-9155\/55\/15\/008","journal-title":"Phys Med Biol"},{"key":"11378_CR32","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1109\/TETCI.2023.3265360","volume":"8","author":"M Moyano","year":"2023","unstructured":"Moyano M, Cabrera-Guerrero G, Tello-Valenzuela G, Lagos C (2023) An hybrid local search for the direct aperture optimisation problem. IEEE Trans Emerg Topics Comput Intell 8:95\u2013109. https:\/\/doi.org\/10.1109\/TETCI.2023.3265360","journal-title":"IEEE Trans Emerg Topics Comput Intell"},{"key":"11378_CR33","doi-asserted-by":"crossref","unstructured":"Moyano M, Cabrera-Guerrero G (2020) Local search for the direct aperture optimisation in imrt. In: 2020 39th International Conference of the Chilean Computer Science Society (SCCC), pp. 1\u20136 . IEEE","DOI":"10.1109\/SCCC51225.2020.9281199"},{"issue":"7","key":"11378_CR34","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6560\/ac58db","volume":"67","author":"S Mueller","year":"2022","unstructured":"Mueller S, Guyer G, Risse T, Tessarini S, Aebersold DM, Stampanoni MFM, Fix MK, Manser P (2022) A hybrid column generation and simulated annealing algorithm for direct aperture optimization. Phys Med Biol 67(7):075003. https:\/\/doi.org\/10.1088\/1361-6560\/ac58db","journal-title":"Phys Med Biol"},{"issue":"11","key":"11378_CR35","doi-asserted-by":"publisher","first-page":"5596","DOI":"10.1002\/mp.12529","volume":"44","author":"D Nguyen","year":"2017","unstructured":"Nguyen D, O\u2019Connor D, Ruan D, Sheng K (2017) Deterministic direct aperture optimization using multiphase piecewise constant segmentation. Med Phys 44(11):5596\u20135609. https:\/\/doi.org\/10.1002\/mp.12529","journal-title":"Med Phys"},{"key":"11378_CR36","doi-asserted-by":"publisher","DOI":"10.1136\/bmj.n71","author":"MJ Page","year":"2021","unstructured":"Page MJ, McKenzie JE, Bossuyt PM, Boutron I, Hoffmann TC, Mulrow CD, Shamseer L, Tetzlaff JM, Akl EA, Brennan SE, Chou R, Glanville J, Grimshaw JM, Hr\u00f3bjartsson A, Lalu MM, Li T, Loder EW, Mayo-Wilson E, McDonald S, McGuinness LA, Stewart LA, Thomas J, Tricco AC, Welch VA, Whiting P, Moher D (2021) The prisma 2020 statement: an updated guideline for reporting systematic reviews. BMJ. https:\/\/doi.org\/10.1136\/bmj.n71","journal-title":"BMJ"},{"issue":"1","key":"11378_CR37","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1002\/mp.13840","volume":"47","author":"JM Pakela","year":"2020","unstructured":"Pakela JM, Tseng H-H, Matuszak MM, Ten Haken RK, McShan DL, El Naqa I (2020) Quantum-inspired algorithm for radiotherapy planning optimization. Med Phys 47(1):5\u201318. https:\/\/doi.org\/10.1002\/mp.13840","journal-title":"Med Phys"},{"key":"11378_CR38","doi-asserted-by":"publisher","first-page":"108","DOI":"10.1007\/978-3-030-05983-5_8","volume-title":"Hybrid Metaheuristics","author":"L P\u00e9rez C\u00e1ceres","year":"2019","unstructured":"P\u00e9rez C\u00e1ceres L, Araya I, Soto D, Cabrera-Guerrero G (2019) Stochastic local search algorithms for the direct aperture optimisation problem in imrt. In: Blesa Aguilera MJ, Blum C, Gambini Santos H, Pinacho-Davidson P, Campo J (eds) Hybrid Metaheuristics. Springer, Cham, pp 108\u2013123"},{"key":"11378_CR39","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2021.115206","volume":"182","author":"L P\u00e9rez C\u00e1ceres","year":"2021","unstructured":"P\u00e9rez C\u00e1ceres L, Araya I, Cabrera-Guerrero G (2021) Stochastic local search for the direct aperture optimisation problem. Expert Syst Appl 182:115206. https:\/\/doi.org\/10.1016\/j.eswa.2021.115206","journal-title":"Expert Syst Appl"},{"issue":"2","key":"11378_CR40","doi-asserted-by":"publisher","first-page":"319","DOI":"10.1007\/s10107-004-0527-6","volume":"101","author":"F Preciado-Walters","year":"2004","unstructured":"Preciado-Walters F, Rardin R, Langer M, Thai V (2004) A coupled column generation, mixed integer approach to optimal planning of intensity modulated radiation therapy for cancer. Math Program 101(2):319\u2013338. https:\/\/doi.org\/10.1007\/s10107-004-0527-6","journal-title":"Math Program"},{"issue":"1","key":"11378_CR41","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1007\/s10479-006-0080-1","volume":"148","author":"F Preciado-Walters","year":"2006","unstructured":"Preciado-Walters F, Langer MP, Rardin RL, Thai V (2006) Column generation for imrt cancer therapy optimization with implementable segments. Ann Oper Res 148(1):65\u201379. https:\/\/doi.org\/10.1007\/s10479-006-0080-1","journal-title":"Ann Oper Res"},{"key":"11378_CR42","unstructured":"Research E (2023) Global intensity modulated radiotherapy (imrt) market size. GlobeNewswire"},{"key":"11378_CR43","doi-asserted-by":"publisher","DOI":"10.1287\/ijoc.2022.1167","author":"D Ripsman","year":"2022","unstructured":"Ripsman D, Purdie T, Chan T, Mahmoudzadeh H (2022) Robust direct aperture optimization for radiation therapy treatment planning. INFORMS J Comput. https:\/\/doi.org\/10.1287\/ijoc.2022.1167","journal-title":"INFORMS J Comput"},{"key":"11378_CR44","doi-asserted-by":"publisher","first-page":"1969","DOI":"10.1016\/j.mcm.2011.11.056","volume":"55","author":"H Rocha","year":"2012","unstructured":"Rocha H, Matos Dias J, Ferreira B, Lopes MDC (2012) Discretization of optimal beamlet intensities in imrt: a binary integer programming approach. Math Comput Model 55:1969\u20131980. https:\/\/doi.org\/10.1016\/j.mcm.2011.11.056","journal-title":"Math Comput Model"},{"issue":"3","key":"11378_CR45","doi-asserted-by":"publisher","first-page":"838","DOI":"10.1137\/040606612","volume":"15","author":"HE Romeijn","year":"2005","unstructured":"Romeijn HE, Ahuja RK, Dempsey JF, Kumar A (2005) A column generation approach to radiation therapy treatment planning using aperture modulation. SIAM J Optim 15(3):838\u2013862. https:\/\/doi.org\/10.1137\/040606612","journal-title":"SIAM J Optim"},{"issue":"3","key":"11378_CR46","doi-asserted-by":"publisher","first-page":"838","DOI":"10.1137\/040606612","volume":"15","author":"HE Romeijn","year":"2005","unstructured":"Romeijn HE, Ahuja RK, Dempsey JF, Kumar A (2005) A column generation approach to radiation therapy treatment planning using aperture modulation. SIAM J Optim 15(3):838\u2013862. https:\/\/doi.org\/10.1137\/040606612","journal-title":"SIAM J Optim"},{"issue":"4","key":"11378_CR47","doi-asserted-by":"publisher","first-page":"518","DOI":"10.1287\/ijoc.1110.0474","volume":"24","author":"E Salari","year":"2012","unstructured":"Salari E, Romeijn HE (2012) Quantifying the trade-off between imrt treatment plan quality and delivery efficiency using direct aperture optimization. INFORMS J Comput 24(4):518\u2013533. https:\/\/doi.org\/10.1287\/ijoc.1110.0474","journal-title":"INFORMS J Comput"},{"issue":"3","key":"11378_CR48","doi-asserted-by":"publisher","first-page":"621","DOI":"10.1088\/0031-9155\/58\/3\/621","volume":"58","author":"E Salari","year":"2013","unstructured":"Salari E, Unkelbach J (2013) A column-generation-based method for multi-criteria direct aperture optimization. Phys Med Biol 58(3):621\u2013639. https:\/\/doi.org\/10.1088\/0031-9155\/58\/3\/621","journal-title":"Phys Med Biol"},{"issue":"3","key":"11378_CR49","doi-asserted-by":"publisher","first-page":"1266","DOI":"10.1118\/1.3547722","volume":"38","author":"E Salari","year":"2011","unstructured":"Salari E, Men C, Romeijn HE (2011) Accounting for the tongue-and-groove effect using a robust direct aperture optimization approach. Med Phys 38(3):1266\u20131279. https:\/\/doi.org\/10.1118\/1.3547722","journal-title":"Med Phys"},{"issue":"6","key":"11378_CR50","doi-asserted-by":"publisher","first-page":"1007","DOI":"10.1118\/1.1477415","volume":"29","author":"DM Shepard","year":"2002","unstructured":"Shepard DM, Earl MA, Li X, Naqvi S, Yu CX (2002) Direct aperture optimization: a turnkey solution for step-and-shoot imrt. Med Phys 29(6):1007\u201318","journal-title":"Med Phys"},{"issue":"19","key":"11378_CR51","doi-asserted-by":"publisher","first-page":"4868","DOI":"10.3390\/cancers15194868","volume":"15","author":"G Tello-Valenzuela","year":"2023","unstructured":"Tello-Valenzuela G, Moyano M, Cabrera-Guerrero G (2023) Particle swarm optimisation applied to the direct aperture optimisation problem in radiation therapy. Cancers 15(19):4868. https:\/\/doi.org\/10.3390\/cancers15194868","journal-title":"Cancers"},{"issue":"2","key":"11378_CR52","doi-asserted-by":"publisher","first-page":"1388","DOI":"10.1109\/TETCI.2023.3330513","volume":"8","author":"Y Tian","year":"2023","unstructured":"Tian Y, Guang Y, Si L, Cao R, Pei X, Zhang X (2023) Efficient direct aperture optimization via evolutionary computation with customized variation operators. IEEE Trans Emerg Topics Comput Intell 8(2):1388\u20131401. https:\/\/doi.org\/10.1109\/TETCI.2023.3330513","journal-title":"IEEE Trans Emerg Topics Comput Intell"},{"issue":"4","key":"11378_CR53","doi-asserted-by":"publisher","first-page":"1758","DOI":"10.1002\/mp.12819","volume":"45","author":"J Yang","year":"2018","unstructured":"Yang J, Gui Z, Zhang L, Zhang P (2018) Aperture generation based on threshold segmentation for intensity modulated radiotherapy treatment planning. Med Phys 45(4):1758\u20131770. https:\/\/doi.org\/10.1002\/mp.12819","journal-title":"Med Phys"},{"issue":"2","key":"11378_CR54","doi-asserted-by":"publisher","first-page":"58","DOI":"10.1002\/mp.12819","volume":"4","author":"J Yang","year":"2019","unstructured":"Yang J, Gui Z-G, Zhang L-Y, Zhang P-C (2019) Aperture generation for intensity-modulated radiotherapy scheme based on gradient information. J Netw Intell 4(2):58\u201370. https:\/\/doi.org\/10.1002\/mp.12819","journal-title":"J Netw Intell"},{"issue":"5","key":"11378_CR55","doi-asserted-by":"publisher","first-page":"0197926","DOI":"10.1371\/journal.pone.0197926","volume":"13","author":"X Zeng","year":"2018","unstructured":"Zeng X, Gao H, Wei X (2018) Rapid direct aperture optimization via dose influence matrix based piecewise aperture dose model. PLoS ONE 13(5):0197926. https:\/\/doi.org\/10.1371\/journal.pone.0197926","journal-title":"PLoS ONE"},{"key":"11378_CR56","doi-asserted-by":"publisher","first-page":"157623","DOI":"10.1109\/ACCESS.2019.2949871","volume":"7","author":"L Zhang","year":"2019","unstructured":"Zhang L, Zhang P, Yang J, Li J, Gui Z (2019a) Aperture shape generation based on gradient descent with momentum. IEEE Access 7:157623\u2013157632. https:\/\/doi.org\/10.1109\/ACCESS.2019.2949871","journal-title":"IEEE Access"},{"key":"11378_CR57","doi-asserted-by":"publisher","first-page":"31123","DOI":"10.1109\/ACCESS.2019.2896175","volume":"7","author":"L Zhang","year":"2019","unstructured":"Zhang L, Gui Z, Yang J, Zhang P (2019b) A column generation approach based on region growth. IEEE Access 7:31123\u201331139. https:\/\/doi.org\/10.1109\/ACCESS.2019.2896175","journal-title":"IEEE Access"},{"issue":"9","key":"11378_CR58","doi-asserted-by":"publisher","first-page":"140","DOI":"10.1007\/s41365-023-01300-5","volume":"34","author":"L-Y Zhang","year":"2023","unstructured":"Zhang L-Y, Gui Z-G, Zhang P-C, Yang J (2023) Aperture shape optimization in intensity-modulated radiation therapy planning. Nucl Sci Tech 34(9):140. https:\/\/doi.org\/10.1007\/s41365-023-01300-5","journal-title":"Nucl Sci Tech"},{"issue":"2","key":"11378_CR59","doi-asserted-by":"publisher","first-page":"50","DOI":"10.1120\/jacmp.v15i2.4545","volume":"15","author":"X Zhu","year":"2014","unstructured":"Zhu X, Cullip T, Tracton G, Tang X, Lian J, Dooley J, Chang SX (2014) Direct aperture optimization using an inverse form of back-projection. J Appl Clin Med Phys 15(2):50\u201359. https:\/\/doi.org\/10.1120\/jacmp.v15i2.4545","journal-title":"J Appl Clin Med Phys"}],"container-title":["Artificial Intelligence Review"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10462-025-11378-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10462-025-11378-5","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10462-025-11378-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,27]],"date-time":"2026-01-27T03:08:31Z","timestamp":1769483311000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10462-025-11378-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,11,11]]},"references-count":59,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2026,1]]}},"alternative-id":["11378"],"URL":"https:\/\/doi.org\/10.1007\/s10462-025-11378-5","relation":{},"ISSN":["1573-7462"],"issn-type":[{"value":"1573-7462","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,11,11]]},"assertion":[{"value":"26 September 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"31 August 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 November 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"3"}}