{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,19]],"date-time":"2025-08-19T10:50:40Z","timestamp":1755600640594,"version":"3.40.3"},"reference-count":37,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2025,2,28]],"date-time":"2025-02-28T00:00:00Z","timestamp":1740700800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"},{"start":{"date-parts":[[2025,2,28]],"date-time":"2025-02-28T00:00:00Z","timestamp":1740700800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62373001"],"award-info":[{"award-number":["62373001"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Complex Intell. Syst."],"published-print":{"date-parts":[[2025,4]]},"DOI":"10.1007\/s40747-025-01809-9","type":"journal-article","created":{"date-parts":[[2025,2,28]],"date-time":"2025-02-28T02:19:48Z","timestamp":1740709188000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Pattern mining-based evolutionary multi-objective algorithm for beam angle optimization in intensity-modulated radiotherapy"],"prefix":"10.1007","volume":"11","author":[{"given":"Ruifen","family":"Cao","sequence":"first","affiliation":[]},{"given":"Wei","family":"Chen","sequence":"additional","affiliation":[]},{"given":"Tielu","family":"Zhang","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0009-0009-0476-7552","authenticated-orcid":false,"given":"Langchun","family":"Si","sequence":"additional","affiliation":[]},{"given":"Xi","family":"Pei","sequence":"additional","affiliation":[]},{"given":"Xingyi","family":"Zhang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,2,28]]},"reference":[{"issue":"4","key":"1809_CR1","doi-asserted-by":"crossref","first-page":"778","DOI":"10.1002\/ijc.33588","volume":"149","author":"J Ferlay","year":"2021","unstructured":"Ferlay J, Colombet M, Soerjomataram I et al (2021) Cancer statistics for the year 2020: an overview. Int J Cancer 149(4):778\u2013789","journal-title":"Int J Cancer"},{"issue":"1","key":"1809_CR2","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1111\/itor.12241","volume":"25","author":"GG Cabrera","year":"2018","unstructured":"Cabrera GG, Ehrgott M, Mason AJ et al (2018) A matheuristic approach to solve the multiobjective beam angle optimization problem in intensity-modulated radiation therapy. Int Trans Oper Res 25(1):243\u2013268","journal-title":"Int Trans Oper Res"},{"issue":"2","key":"1809_CR3","doi-asserted-by":"crossref","first-page":"198","DOI":"10.4236\/jct.2014.52025","volume":"5","author":"M Zaghian","year":"2014","unstructured":"Zaghian M, Lim G, Liu W et al (2014) An automatic approach for satisfying dose-volume constraints in linear fluence map optimization for impt. J Cancer Ther 5(2):198","journal-title":"J Cancer Ther"},{"issue":"3","key":"1809_CR4","doi-asserted-by":"crossref","first-page":"908","DOI":"10.1111\/itor.12587","volume":"26","author":"H Rocha","year":"2019","unstructured":"Rocha H, Dias JM, Ventura T et al (2019) Beam angle optimization in imrt: are we really optimizing what matters? Int Trans Oper Res 26(3):908\u2013928","journal-title":"Int Trans Oper Res"},{"key":"1809_CR5","doi-asserted-by":"crossref","unstructured":"Ehrgott M, Holder A, Reese J (2008) Beam selection in radiotherapy design linear algebr 428:1272\u2013312","DOI":"10.1016\/j.laa.2007.05.039"},{"key":"1809_CR6","doi-asserted-by":"crossref","unstructured":"Gutierrez M, Cabrera-Guerrero G, Lagos C (2023) A reduced variable neighbourhood search for the beam angle optimisation problem. IEEE Trans Emerg Top Comput Intell","DOI":"10.1109\/TETCI.2022.3230958"},{"issue":"7","key":"1809_CR7","doi-asserted-by":"crossref","first-page":"N127","DOI":"10.1088\/0031-9155\/52\/7\/N02","volume":"52","author":"D Craft","year":"2007","unstructured":"Craft D (2007) Local beam angle optimization with linear programming and gradient search. Phys Med Biol 52(7):N127","journal-title":"Phys Med Biol"},{"issue":"9","key":"1809_CR8","doi-asserted-by":"crossref","first-page":"2939","DOI":"10.1088\/0031-9155\/58\/9\/2939","volume":"58","author":"H Rocha","year":"2013","unstructured":"Rocha H, Dias JM, Ferreira BC et al (2013) Beam angle optimization for intensity-modulated radiation therapy using a guided pattern search method. Phys Med Biol 58(9):2939","journal-title":"Phys Med Biol"},{"issue":"2","key":"1809_CR9","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1088\/0031-9155\/38\/2\/006","volume":"38","author":"T Bortfeld","year":"1993","unstructured":"Bortfeld T, Schlegel W (1993) Optimization of beam orientations in radiation therapy: some theoretical considerations. Phys Med Biol 38(2):291","journal-title":"Phys Med Biol"},{"issue":"19","key":"1809_CR10","doi-asserted-by":"crossref","first-page":"3191","DOI":"10.1088\/0031-9155\/48\/19\/007","volume":"48","author":"D Djajaputra","year":"2003","unstructured":"Djajaputra D, Wu Q, Wu Y et al (2003) Algorithm and performance of a clinical imrt beam-angle optimization system. Phys Med Biol 48(19):3191","journal-title":"Phys Med Biol"},{"issue":"15","key":"1809_CR11","doi-asserted-by":"crossref","first-page":"3491","DOI":"10.1088\/0031-9155\/50\/15\/002","volume":"50","author":"Y Li","year":"2005","unstructured":"Li Y, Yao D, Yao J et al (2005) A particle swarm optimization algorithm for beam angle selection in intensity-modulated radiotherapy planning. Phys Med Biol 50(15):3491","journal-title":"Phys Med Biol"},{"issue":"3","key":"1809_CR12","first-page":"499","volume":"57","author":"Y Li","year":"2009","unstructured":"Li Y, Lei J (2009) A feasible solution to the beam-angle-optimization problem in radiotherapy planning with a dna-based genetic algorithm. IEEE Trans Biomed Eng 57(3):499\u2013508","journal-title":"IEEE Trans Biomed Eng"},{"key":"1809_CR13","doi-asserted-by":"crossref","unstructured":"Lei J, Li Y (2008) A dna genetic algorithm for beam angle selection in radiotherapy planning 1331\u20131336","DOI":"10.1109\/ICCIS.2008.4670912"},{"issue":"11","key":"1809_CR14","doi-asserted-by":"crossref","first-page":"2508","DOI":"10.1118\/1.1319377","volume":"27","author":"X Wu","year":"2000","unstructured":"Wu X, Zhu Y (2000) A mixed-encoding genetic algorithm with beam constraint for conformal radiotherapy treatment planning. Med Phys 27(11):2508\u20132516","journal-title":"Med Phys"},{"issue":"2","key":"1809_CR15","doi-asserted-by":"crossref","first-page":"951","DOI":"10.1118\/1.3676689","volume":"39","author":"S Breedveld","year":"2012","unstructured":"Breedveld S, Storchi PR, Voet PW et al (2012) icycle: integrated, multicriterial beam angle, and profile optimization for generation of coplanar and noncoplanar imrt plans. Med Phys 39(2):951\u2013963","journal-title":"Med Phys"},{"issue":"13","key":"1809_CR16","doi-asserted-by":"crossref","first-page":"3873","DOI":"10.1088\/0031-9155\/56\/13\/009","volume":"56","author":"X Zhang","year":"2011","unstructured":"Zhang X, Li X, Quan EM et al (2011) A methodology for automatic intensity-modulated radiation treatment planning for lung cancer. Phys Med Biol 56(13):3873","journal-title":"Phys Med Biol"},{"key":"1809_CR17","doi-asserted-by":"crossref","DOI":"10.3389\/fonc.2021.707464","volume":"11","author":"W Cheon","year":"2021","unstructured":"Cheon W, Ahn SH, Jeong S et al (2021) Beam angle optimization for double-scattering proton delivery technique using an eclipse application programming interface and convolutional neural network. Front Oncol 11:707464","journal-title":"Front Oncol"},{"issue":"3","key":"1809_CR18","doi-asserted-by":"crossref","first-page":"880","DOI":"10.1002\/mp.13986","volume":"47","author":"A Sadeghnejad Barkousaraie","year":"2020","unstructured":"Sadeghnejad Barkousaraie A, Ogunmolu O, Jiang S et al (2020) A fast deep learning approach for beam orientation optimization for prostate cancer treated with intensity-modulated radiation therapy. Med Phys 47(3):880\u2013897","journal-title":"Med Phys"},{"issue":"9","key":"1809_CR19","doi-asserted-by":"crossref","first-page":"5217","DOI":"10.1118\/1.3615622","volume":"38","author":"J Fiege","year":"2011","unstructured":"Fiege J, McCurdy B, Potrebko P et al (2011) Pareto: a novel evolutionary optimization approach to multiobjective imrt planning. Med Phys 38(9):5217\u20135229","journal-title":"Med Phys"},{"issue":"1","key":"1809_CR20","doi-asserted-by":"crossref","first-page":"159","DOI":"10.3390\/math10010159","volume":"10","author":"G Cabrera-Guerrero","year":"2022","unstructured":"Cabrera-Guerrero G, Lagos C (2022) Comparing multi-objective local search algorithms for the beam angle selection problem. Mathematics 10(1):159","journal-title":"Mathematics"},{"key":"1809_CR21","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1007\/s10732-018-9365-1","volume":"24","author":"G Cabrera-Guerrero","year":"2018","unstructured":"Cabrera-Guerrero G, Mason AJ, Raith A et al (2018) Pareto local search algorithms for the multi-objective beam angle optimisation problem. J Heurist 24:205\u2013238","journal-title":"J Heurist"},{"issue":"5","key":"1809_CR22","doi-asserted-by":"crossref","first-page":"747","DOI":"10.1088\/0031-9155\/49\/5\/007","volume":"49","author":"E Schreibmann","year":"2004","unstructured":"Schreibmann E, Lahanas M, Xing L et al (2004) Multiobjective evolutionary optimization of the number of beams, their orientations and weights for intensity-modulated radiation therapy. Phys Med Biol 49(5):747","journal-title":"Phys Med Biol"},{"key":"1809_CR23","doi-asserted-by":"crossref","unstructured":"Li Y, Yao J, Yao D (2004) Automatic beam angle selection in imrt planning using genetic algorithm. Phys Med Biol 49(10):1915","DOI":"10.1088\/0031-9155\/49\/10\/007"},{"issue":"19","key":"1809_CR24","doi-asserted-by":"crossref","first-page":"6205","DOI":"10.1088\/0031-9155\/56\/19\/004","volume":"56","author":"X Jia","year":"2011","unstructured":"Jia X, Men C, Lou Y et al (2011) Beam orientation optimization for intensity modulated radiation therapy using adaptive l2, 1-minimization. Phys Med Biol 56(19):6205","journal-title":"Phys Med Biol"},{"key":"1809_CR25","unstructured":"Zitzler E, Laumanns M, Thiele L (2001) Spea2: improving the strength pareto evolutionary algorithm. TIK report 103"},{"issue":"7","key":"1809_CR26","doi-asserted-by":"crossref","first-page":"6784","DOI":"10.1109\/TCYB.2020.3041325","volume":"52","author":"Y Tian","year":"2020","unstructured":"Tian Y, Lu C, Zhang X et al (2020) A pattern mining-based evolutionary algorithm for large-scale sparse multiobjective optimization problems. IEEE Trans Cybern 52(7):6784\u20136797","journal-title":"IEEE Trans Cybern"},{"issue":"1","key":"1809_CR27","doi-asserted-by":"crossref","first-page":"102","DOI":"10.1109\/TEVC.2020.3004012","volume":"25","author":"Y Tian","year":"2020","unstructured":"Tian Y, Zhang T, Xiao J et al (2020) A coevolutionary framework for constrained multiobjective optimization problems. IEEE Trans Evol Comput 25(1):102\u2013116","journal-title":"IEEE Trans Evol Comput"},{"key":"1809_CR28","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1016\/j.asoc.2013.10.008","volume":"14","author":"L Jiao","year":"2014","unstructured":"Jiao L, Luo J, Shang R et al (2014) A modified objective function method with feasible-guiding strategy to solve constrained multi-objective optimization problems. Appl Soft Comput 14:363\u2013380","journal-title":"Appl Soft Comput"},{"issue":"5","key":"1809_CR29","doi-asserted-by":"crossref","first-page":"1361","DOI":"10.1016\/S0360-3016(01)01736-9","volume":"51","author":"A Pugachev","year":"2001","unstructured":"Pugachev A, Xing L (2001) Pseudo beam\u2019s-eye-view as applied to beam orientation selection in intensity-modulated radiation therapy. Int J Radiat Oncol Biol Phys 51(5):1361\u20131370","journal-title":"Int J Radiat Oncol Biol Phys"},{"issue":"5","key":"1809_CR30","doi-asserted-by":"crossref","first-page":"4051","DOI":"10.1007\/s40747-022-00697-7","volume":"8","author":"R Cao","year":"2022","unstructured":"Cao R, Si L, Li X et al (2022) A conjugate gradient-assisted multi-objective evolutionary algorithm for fluence map optimization in radiotherapy treatment. Complex Intell Syst 8(5):4051\u20134077","journal-title":"Complex Intell Syst"},{"issue":"2","key":"1809_CR31","doi-asserted-by":"crossref","first-page":"182","DOI":"10.1109\/4235.996017","volume":"6","author":"K Deb","year":"2002","unstructured":"Deb K, Pratap A, Agarwal S et al (2002) A fast and elitist multiobjective genetic algorithm: Nsga-ii. IEEE Trans Evol Comput 6(2):182\u2013197","journal-title":"IEEE Trans Evol Comput"},{"issue":"4","key":"1809_CR32","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1109\/MCI.2017.2742868","volume":"12","author":"Y Tian","year":"2017","unstructured":"Tian Y, Cheng R, Zhang X et al (2017) Platemo: a matlab platform for evolutionary multi-objective optimization [educational forum]. IEEE Comput Intell Mag 12(4):73\u201387","journal-title":"IEEE Comput Intell Mag"},{"issue":"4","key":"1809_CR33","doi-asserted-by":"crossref","first-page":"602","DOI":"10.1109\/TEVC.2013.2281534","volume":"18","author":"H Jain","year":"2013","unstructured":"Jain H, Deb K (2013) An evolutionary many-objective optimization algorithm using reference-point based nondominated sorting approach, part ii: Handling constraints and extending to an adaptive approach. IEEE Trans Evol Comput 18(4):602\u2013622","journal-title":"IEEE Trans Evol Comput"},{"issue":"2","key":"1809_CR34","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1109\/TEVC.2018.2855411","volume":"23","author":"K Li","year":"2018","unstructured":"Li K, Chen R, Fu G et al (2018) Two-archive evolutionary algorithm for constrained multiobjective optimization. IEEE Trans Evol Comput 23(2):303\u2013315","journal-title":"IEEE Trans Evol Comput"},{"key":"1809_CR35","doi-asserted-by":"crossref","unstructured":"Schreibmann E, Xing L (2004) Feasibility study of beam orientation class-solutions for prostate imrt: Beam orientation class-solutions for prostate imrt. Med Phys 31(10):2863\u20132870","DOI":"10.1118\/1.1797571"},{"issue":"4","key":"1809_CR36","doi-asserted-by":"crossref","first-page":"1992","DOI":"10.1118\/1.4908000","volume":"42","author":"G Amit","year":"2015","unstructured":"Amit G, Purdie TG, Levinshtein A et al (2015) Automatic learning-based beam angle selection for thoracic imrt. Med Phys 42(4):1992\u20132005","journal-title":"Med Phys"},{"issue":"1","key":"1809_CR37","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1109\/TEVC.2005.851275","volume":"10","author":"L While","year":"2006","unstructured":"While L, Hingston P, Barone L et al (2006) A faster algorithm for calculating hypervolume. IEEE Trans Evol Comput 10(1):29\u201338","journal-title":"IEEE Trans Evol Comput"}],"container-title":["Complex & Intelligent Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40747-025-01809-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40747-025-01809-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40747-025-01809-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,3,30]],"date-time":"2025-03-30T21:20:51Z","timestamp":1743369651000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40747-025-01809-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,2,28]]},"references-count":37,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2025,4]]}},"alternative-id":["1809"],"URL":"https:\/\/doi.org\/10.1007\/s40747-025-01809-9","relation":{},"ISSN":["2199-4536","2198-6053"],"issn-type":[{"type":"print","value":"2199-4536"},{"type":"electronic","value":"2198-6053"}],"subject":[],"published":{"date-parts":[[2025,2,28]]},"assertion":[{"value":"26 September 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 January 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 February 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 that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"188"}}