{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,20]],"date-time":"2026-02-20T01:54:58Z","timestamp":1771552498534,"version":"3.50.1"},"reference-count":55,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2023,2,9]],"date-time":"2023-02-09T00:00:00Z","timestamp":1675900800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2023,2,9]],"date-time":"2023-02-09T00:00:00Z","timestamp":1675900800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["52175251"],"award-info":[{"award-number":["52175251"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51875466"],"award-info":[{"award-number":["51875466"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Innovation Foundation for Doctor Dissertation of Northwestern Polytechnical University"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Complex Intell. Syst."],"published-print":{"date-parts":[[2023,8]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>This paper presents a bi-indicator-based surrogate-assisted evolutionary algorithm (BISAEA) for multi-objective optimization problems (MOPs) with computationally expensive objectives. In BISAEA, a Pareto-based bi-indictor strategy is proposed based on convergence and diversity indicators, where a nondominated sorting approach is adopted to carry out two-objective optimization (convergence and diversity indicators) problems. The radius-based function (RBF) models are used to approximate the objective values. In addition, the proposed algorithm adopts a one-by-one selection strategy to obtain promising samples from new samples for evaluating the true objectives by their angles and Pareto dominance relationship with real non-dominated solutions to improve the diversity. After the comparison with four state-of-the-art surrogate-assisted evolutionary algorithms and three evolutionary algorithms on 76 widely used benchmark problems, BISAEA shows high efficiency and a good balance between convergence and diversity. Finally, BISAEA is applied to the multidisciplinary optimization of blend-wing-body underwater gliders with 30 decision variables and three objectives, and the results demonstrate that BISAEA has superior performance on computationally expensive engineering problems.<\/jats:p>","DOI":"10.1007\/s40747-023-00969-w","type":"journal-article","created":{"date-parts":[[2023,2,9]],"date-time":"2023-02-09T15:11:04Z","timestamp":1675955464000},"page":"4673-4704","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Bi-indicator driven surrogate-assisted multi-objective evolutionary algorithms for computationally expensive problems"],"prefix":"10.1007","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5149-0519","authenticated-orcid":false,"given":"Wenxin","family":"Wang","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2471-3545","authenticated-orcid":false,"given":"Huachao","family":"Dong","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8745-320X","authenticated-orcid":false,"given":"Peng","family":"Wang","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2070-940X","authenticated-orcid":false,"given":"Jiangtao","family":"Shen","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,2,9]]},"reference":[{"issue":"3","key":"969_CR1","doi-asserted-by":"publisher","first-page":"62","DOI":"10.1109\/MCI.2009.933094","volume":"4","author":"Y Jin","year":"2009","unstructured":"Jin Y, Sendhoff B (2009) A systems approach to evolutionary multiobjective structural optimization and beyond. IEEE Comput Intell Mag 4(3):62\u201376. https:\/\/doi.org\/10.1109\/MCI.2009.933094","journal-title":"IEEE Comput Intell Mag"},{"key":"969_CR2","volume-title":"Nonlinear multiobjective optimization","author":"K Miettinen","year":"2012","unstructured":"Miettinen K (2012) Nonlinear multiobjective optimization, vol 12. Springer Science & Business Media, Berlin"},{"issue":"1","key":"969_CR3","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1162\/EVCO_a_00009","volume":"19","author":"J Bader","year":"2011","unstructured":"Bader J, Zitzler E (2011) HypE: an algorithm for fast hypervolume-based many-objective optimization. Evol Comput 19(1):45\u201376. https:\/\/doi.org\/10.1162\/EVCO_a_00009","journal-title":"Evol Comput"},{"issue":"4","key":"969_CR4","doi-asserted-by":"publisher","first-page":"577","DOI":"10.1109\/TEVC.2013.2281535","volume":"18","author":"K Deb","year":"2013","unstructured":"Deb K, Jain H (2013) An evolutionary many-objective optimization algorithm using reference-point-based nondominated sorting approach, part I: solving problems with box constraints. IEEE Trans Evol Comput 18(4):577\u2013601. https:\/\/doi.org\/10.1109\/TEVC.2013.2281535","journal-title":"IEEE Trans Evol Comput"},{"issue":"6","key":"969_CR5","doi-asserted-by":"publisher","first-page":"712","DOI":"10.1109\/TEVC.2007.892759","volume":"11","author":"Q Zhang","year":"2007","unstructured":"Zhang Q, Li H (2007) MOEA\/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans Evol Comput 11(6):712\u2013731. https:\/\/doi.org\/10.1109\/TEVC.2007.892759","journal-title":"IEEE Trans Evol Comput"},{"issue":"5","key":"969_CR6","doi-asserted-by":"publisher","first-page":"773","DOI":"10.1109\/TEVC.2016.2519378","volume":"20","author":"R Cheng","year":"2016","unstructured":"Cheng R, Jin Y, Olhofer M, Sendhoff B (2016) A reference vector guided evolutionary algorithm for many-objective optimization. IEEE Trans Evol Comput 20(5):773\u2013791. https:\/\/doi.org\/10.1109\/TEVC.2016.2519378","journal-title":"IEEE Trans Evol Comput"},{"issue":"1","key":"969_CR7","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1007\/s00500-003-0328-5","volume":"9","author":"Y Jin","year":"2005","unstructured":"Jin Y (2005) A comprehensive survey of fitness approximation in evolutionary computation. Soft Comput 9(1):3\u201312","journal-title":"Soft Comput"},{"key":"969_CR8","doi-asserted-by":"publisher","DOI":"10.1080\/0305215X.2022.2057480","author":"W Chen","year":"2022","unstructured":"Chen W, Wang P, Dong H (2022) Surrogate-based bilevel shape optimization for blended-wing\u2013body underwater gliders. Eng Optim. https:\/\/doi.org\/10.1080\/0305215X.2022.2057480","journal-title":"Eng Optim"},{"key":"969_CR9","doi-asserted-by":"publisher","DOI":"10.1016\/j.swevo.2022.101107","author":"J Li","year":"2022","unstructured":"Li J, Wang P, Dong H, Shen J (2022) A two-stage surrogate-assisted evolutionary algorithm (TS-SAEA) for expensive multi\/many-objective optimization. Swarm Evol Comput. https:\/\/doi.org\/10.1016\/j.swevo.2022.101107","journal-title":"Swarm Evol Comput"},{"key":"969_CR10","doi-asserted-by":"publisher","unstructured":"Li J, Wang P, Dong H, et al. (2022). A classification surrogate-assisted multi-objective evolutionary algorithm for expensive optimization. Knowledge-Based Systems, 242: 108416. https:\/\/doi.org\/10.1016\/j.knosys.2022.108416","DOI":"10.1016\/j.knosys.2022.108416"},{"issue":"3","key":"969_CR11","doi-asserted-by":"publisher","first-page":"285","DOI":"10.1080\/00401706.1996.10484509","volume":"38","author":"RF Gunst","year":"1996","unstructured":"Gunst RF, Myers RH, Montgomery DC (1996) Response surface methodology: process and product optimization using designed experiments|Clc. Technometrics 38(3):285. https:\/\/doi.org\/10.1080\/00401706.1996.10484509","journal-title":"Technometrics"},{"issue":"4","key":"969_CR12","doi-asserted-by":"publisher","first-page":"853","DOI":"10.2514\/1.8650","volume":"43","author":"JD Martin","year":"2004","unstructured":"Martin JD, Simpson TW (2004) Use of kriging models to approximate deterministic computer models. AIAA J 43(4):853\u2013863. https:\/\/doi.org\/10.2514\/1.8650","journal-title":"AIAA J"},{"issue":"1","key":"969_CR13","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1162\/neco.1992.4.1.1","volume":"4","author":"S Geman","year":"1992","unstructured":"Geman S, Bienenstock E, Doursat R (1992) Neural networks and the bias\/variance dilemma. Neural Comput 4(1):1\u201358. https:\/\/doi.org\/10.1162\/neco.1992.4.1.1","journal-title":"Neural Comput"},{"issue":"2","key":"969_CR14","doi-asserted-by":"publisher","first-page":"639","DOI":"10.1137\/0907043","volume":"7","author":"N Dyn","year":"1986","unstructured":"Dyn N, Levin D, Rippa S (1986) Numerical procedures for surface fitting of scattered data by radial functions. SIAM J Sci Stat Comput 7(2):639\u2013659. https:\/\/doi.org\/10.1137\/0907043","journal-title":"SIAM J Sci Stat Comput"},{"issue":"99","key":"969_CR15","doi-asserted-by":"publisher","first-page":"815","DOI":"10.1109\/TEVC.2019.2890818","volume":"23","author":"X Wang","year":"2019","unstructured":"Wang X, Wang GG, Song B, Wang P, Wang Y (2019) A novel evolutionary sampling assisted optimization method for high dimensional expensive problems. IEEE Trans Evol Comput 23(99):815\u2013827. https:\/\/doi.org\/10.1109\/TEVC.2019.2890818","journal-title":"IEEE Trans Evol Comput"},{"key":"969_CR16","doi-asserted-by":"publisher","first-page":"100713","DOI":"10.1016\/j.swevo.2020.100713","volume":"57","author":"H Dong","year":"2020","unstructured":"Dong H, Dong Z (2020) Surrogate-assisted Grey wolf optimization for high-dimensional, computationally expensive black-box problems. Swarm Evolut Comput 57:100713. https:\/\/doi.org\/10.1016\/j.swevo.2020.100713","journal-title":"Swarm Evolut Comput"},{"issue":"2","key":"969_CR17","doi-asserted-by":"publisher","first-page":"106934","DOI":"10.1016\/j.asoc.2020.106934","volume":"99","author":"H Dong","year":"2020","unstructured":"Dong H, Wang P, Yu X, Song B (2020) Surrogate-assisted teaching-learning-based optimization for high-dimensional and computationally expensive problems. Appl Soft Comput 99(2):106934. https:\/\/doi.org\/10.1016\/j.asoc.2020.106934","journal-title":"Appl Soft Comput"},{"issue":"1","key":"969_CR18","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1109\/TEVC.2016.2622301","volume":"22","author":"T Chugh","year":"2018","unstructured":"Chugh T, Jin Y, Miettinen K, Hakanen J, Sindhya K (2018) A surrogate-assisted reference vector guided evolutionary algorithm for computationally expensive many-objective optimization. IEEE Trans Evol Comput 22(1):129\u2013142. https:\/\/doi.org\/10.1109\/TEVC.2016.2622301","journal-title":"IEEE Trans Evol Comput"},{"issue":"6","key":"969_CR19","doi-asserted-by":"publisher","first-page":"956","DOI":"10.1109\/TEVC.2017.2697503","volume":"21","author":"D Zhan","year":"2017","unstructured":"Zhan D, Cheng Y, Liu J (2017) Expected improvement matrix-based infill criteria for expensive multiobjective optimization. IEEE Trans Evol Comput 21(6):956\u2013975. https:\/\/doi.org\/10.1109\/TEVC.2017.2697503","journal-title":"IEEE Trans Evol Comput"},{"key":"969_CR20","doi-asserted-by":"publisher","DOI":"10.1109\/TSMC.2022.3163129","author":"Q Liu","year":"2022","unstructured":"Liu Q, Cheng R, Jin Y, Heiderich M, Rodemann T (2022) Reference vector-assisted adaptive model management for surrogate-assisted many-objective optimization. IEEE Trans Syst Man Cybernet Syst. https:\/\/doi.org\/10.1109\/TSMC.2022.3163129","journal-title":"IEEE Trans Syst Man Cybernet Syst"},{"issue":"6","key":"969_CR21","doi-asserted-by":"publisher","first-page":"1013","DOI":"10.1109\/TEVC.2021.3073648","volume":"25","author":"Z Song","year":"2021","unstructured":"Song Z, Wang H, He C, Jin Y (2021) A Kriging-assisted two-archive evolutionary algorithm for expensive many-objective optimization. IEEE Trans Evol Comput 25(6):1013\u20131027. https:\/\/doi.org\/10.1109\/TEVC.2021.3073648","journal-title":"IEEE Trans Evol Comput"},{"issue":"3","key":"969_CR22","doi-asserted-by":"publisher","first-page":"456","DOI":"10.1109\/TEVC.2009.2033671","volume":"14","author":"Q Zhang","year":"2010","unstructured":"Zhang Q, Liu W, Tsang E, Virgians B (2010) Expensive multiobjective optimization by MOEA\/D with gaussian process model. IEEE Trans Evol Comput 14(3):456\u2013474. https:\/\/doi.org\/10.1109\/TEVC.2009.2033671","journal-title":"IEEE Trans Evol Comput"},{"issue":"99","key":"969_CR23","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1109\/TSMC.2020.3044418","volume":"PP","author":"D Guo","year":"2021","unstructured":"Guo D, Wang X, Gao K, Jin Y, Ding J, Chai T (2021) Evolutionary optimization of high-dimensional multiobjective and many-objective expensive problems assisted by a dropout neural network. IEEE Trans Syst Man Cybern Syst PP(99):1\u201314. https:\/\/doi.org\/10.1109\/TSMC.2020.3044418","journal-title":"IEEE Trans Syst Man Cybern Syst"},{"issue":"1","key":"969_CR24","doi-asserted-by":"publisher","first-page":"271","DOI":"10.1007\/s40747-021-00362-5","volume":"8","author":"J Lin","year":"2022","unstructured":"Lin J, He C, Cheng R (2022) Adaptive dropout for high-dimensional expensive multiobjective optimization. Complex Intell Syst 8(1):271\u2013285. https:\/\/doi.org\/10.1007\/s40747-021-00362-5","journal-title":"Complex Intell Syst"},{"issue":"3","key":"969_CR25","doi-asserted-by":"publisher","first-page":"1012","DOI":"10.1109\/TCYB.2018.2794503","volume":"49","author":"D Guo","year":"2018","unstructured":"Guo D, Jin Y, Ding J, Chai T (2018) Heterogeneous ensemble-based infill criterion for evolutionary multiobjective optimization of expensive problems. IEEE Trans Cybern 49(3):1012\u20131025. https:\/\/doi.org\/10.1109\/TCYB.2018.2794503","journal-title":"IEEE Trans Cybern"},{"issue":"1","key":"969_CR26","doi-asserted-by":"publisher","first-page":"74","DOI":"10.1109\/TEVC.2018.2802784","volume":"23","author":"L Pan","year":"2018","unstructured":"Pan L, He C, Tian Y, Wang H, Zhang X, Jin Y (2018) A classification-based surrogate-assisted evolutionary algorithm for expensive many-objective optimization. IEEE Trans Evol Comput 23(1):74\u201388. https:\/\/doi.org\/10.1109\/TEVC.2018.2802784","journal-title":"IEEE Trans Evol Comput"},{"key":"969_CR27","doi-asserted-by":"publisher","unstructured":"Zhang J, Zhou A, Zhang G (2015) A classification and Pareto domination based multiobjective evolutionary algorithm. In: 2015 IEEE congress on evolutionary computation (CEC). IEEE, pp 2883\u20132890. https:\/\/doi.org\/10.1109\/CEC.2015.7257247","DOI":"10.1109\/CEC.2015.7257247"},{"key":"969_CR28","doi-asserted-by":"publisher","unstructured":"Yevseyeva I, Guerreiro AP, Emmerich M, Fonseca CM (2014) A portfolio optimization approach to selection in multiobjective evolutionary algorithms. In: International conference on parallel problem solving from nature. Springer, Cham, pp 672\u2013681. https:\/\/doi.org\/10.1007\/978-3-319-10762-2_66","DOI":"10.1007\/978-3-319-10762-2_66"},{"issue":"4","key":"969_CR29","doi-asserted-by":"publisher","first-page":"609","DOI":"10.1109\/TEVC.2017.2749619","volume":"22","author":"Y Tian","year":"2017","unstructured":"Tian Y, Cheng R, Zhang X et al (2017) An indicator-based multiobjective evolutionary algorithm with reference point adaptation for better versatility. IEEE Trans Evol Comput 22(4):609\u2013622. https:\/\/doi.org\/10.1109\/TEVC.2017.2749619","journal-title":"IEEE Trans Evol Comput"},{"key":"969_CR30","doi-asserted-by":"publisher","unstructured":"G\u00f3mez RH, Coello CAC (2013) MOMBI: a new metaheuristic for many-objective optimization based on the R2 indicator. In: 2013 IEEE congress on evolutionary computation. IEEE, pp 2488\u20132495. https:\/\/doi.org\/10.1109\/CEC.2013.6557868","DOI":"10.1109\/CEC.2013.6557868"},{"key":"969_CR31","doi-asserted-by":"publisher","unstructured":"Hern\u00e1ndez G\u00f3mez R, Coello Coello C A. (2015). Improved metaheuristic based on the R2 indicator for many-objective optimization\/\/Proceedings of the 2015 annual conference on genetic and evolutionary computation, 679\u2013686. https:\/\/doi.org\/10.1145\/2739480.2754776","DOI":"10.1145\/2739480.2754776"},{"key":"969_CR32","doi-asserted-by":"publisher","unstructured":"Zitzler E, K\u00fcnzli S (2004) Indicator-based selection in multiobjective search. In: International conference on parallel problem solving from nature, Springer, Berlin, Heidelberg, pp 832\u2013842. https:\/\/doi.org\/10.1007\/978-3-540-30217-9_84","DOI":"10.1007\/978-3-540-30217-9_84"},{"issue":"2","key":"969_CR33","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1109\/TEVC.2003.810758","volume":"7","author":"E Zitzler","year":"2003","unstructured":"Zitzler E, Thiele L, Laumanns M, Fonseca CM, Da Fonseca VG (2003) Performance assessment of multiobjective optimizers: an analysis and review. IEEE Trans Evol Comput 7(2):117\u2013132. https:\/\/doi.org\/10.1109\/TEVC.2003.810758","journal-title":"IEEE Trans Evol Comput"},{"issue":"4","key":"969_CR34","doi-asserted-by":"publisher","first-page":"524","DOI":"10.1109\/TEVC.2014.2350987","volume":"19","author":"H Wang","year":"2014","unstructured":"Wang H, Jiao L, Yao X (2014) Two_Arch2: an improved two-archive algorithm for many-objective optimization. IEEE Trans Evol Comput 19(4):524\u2013541. https:\/\/doi.org\/10.1109\/TEVC.2014.2350987","journal-title":"IEEE Trans Evol Comput"},{"issue":"6","key":"969_CR35","doi-asserted-by":"publisher","first-page":"924","DOI":"10.1109\/TEVC.2016.2549267","volume":"20","author":"B Li","year":"2016","unstructured":"Li B, Tang K, Li J, Yao X (2016) Stochastic ranking algorithm for many-objective optimization based on multiple indicators. IEEE Trans Evol Comput 20(6):924\u2013938. https:\/\/doi.org\/10.1109\/TEVC.2016.2549267","journal-title":"IEEE Trans Evol Comput"},{"issue":"5","key":"969_CR36","doi-asserted-by":"publisher","first-page":"645","DOI":"10.1109\/TEVC.2015.2504730","volume":"20","author":"M Li","year":"2015","unstructured":"Li M, Yang S, Liu X (2015) Pareto or non-Pareto: bi-criterion evolution in multiobjective optimization. IEEE Trans Evol Comput 20(5):645\u2013665. https:\/\/doi.org\/10.1109\/TEVC.2015.2504730","journal-title":"IEEE Trans Evol Comput"},{"issue":"1","key":"969_CR37","doi-asserted-by":"publisher","first-page":"1","DOI":"10.2514\/6.2000-4801","volume":"23","author":"R Jin","year":"2001","unstructured":"Jin R, Simpson TW (2001) Comparative studies of metamodeling techniques under multiple modeling criteria. Struct Multidiscip Optim 23(1):1\u201313. https:\/\/doi.org\/10.2514\/6.2000-4801","journal-title":"Struct Multidiscip Optim"},{"issue":"2","key":"969_CR38","doi-asserted-by":"publisher","first-page":"365","DOI":"10.1109\/TEVC.2019.2919762","volume":"24","author":"X Cai","year":"2019","unstructured":"Cai X, Gao L, Li X (2019) Efficient generalized surrogate-assisted evolutionary algorithm for high-dimensional expensive problems. IEEE Trans Evol Comput 24(2):365\u2013379. https:\/\/doi.org\/10.1109\/TEVC.2019.2919762","journal-title":"IEEE Trans Evol Comput"},{"issue":"1","key":"969_CR39","doi-asserted-by":"publisher","first-page":"55","DOI":"10.1080\/00401706.2000.10485979","volume":"42","author":"MD McKay","year":"2000","unstructured":"McKay MD, Beckman RJ, Conover WJ (2000) A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 42(1):55\u201361. https:\/\/doi.org\/10.1080\/00401706.2000.10485979","journal-title":"Technometrics"},{"issue":"1","key":"969_CR40","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1016\/S0951-8320(03)00058-9","volume":"81","author":"JC Helton","year":"2003","unstructured":"Helton JC, Davis FJ (2003) Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems. Reliab Eng Syst Saf 81(1):23\u201369. https:\/\/doi.org\/10.1016\/S0951-8320(03)00058-9","journal-title":"Reliab Eng Syst Saf"},{"issue":"6","key":"969_CR41","doi-asserted-by":"publisher","first-page":"1028","DOI":"10.1109\/TEVC.2021.3076514","volume":"25","author":"L He","year":"2021","unstructured":"He L, Ishibuchi H, Trivedi A, Wang H, Nan Y, Srinivasan D (2021) A survey of normalization methods in multiobjective evolutionary algorithms. IEEE Trans Evol Comput 25(6):1028\u20131048. https:\/\/doi.org\/10.1109\/TEVC.2021.3076514","journal-title":"IEEE Trans Evol Comput"},{"issue":"5","key":"969_CR42","doi-asserted-by":"publisher","first-page":"904","DOI":"10.1109\/TEVC.2018.2883094","volume":"23","author":"HK Singh","year":"2018","unstructured":"Singh HK, Bhattacharjee KS, Ray T (2018) Distance-based subset selection for benchmarking in evolutionary multi\/many-objective optimization. IEEE Trans Evol Comput 23(5):904\u2013912. https:\/\/doi.org\/10.1109\/TEVC.2018.2883094","journal-title":"IEEE Trans Evol Comput"},{"issue":"2","key":"969_CR43","doi-asserted-by":"publisher","first-page":"536","DOI":"10.1109\/TCYB.2018.2869674","volume":"50","author":"H Wang","year":"2018","unstructured":"Wang H, Jin Y (2018) A random forest-assisted evolutionary algorithm for data-driven constrained multiobjective combinatorial optimization of trauma systems. IEEE Trans Cybern 50(2):536\u2013549. https:\/\/doi.org\/10.1109\/TCYB.2018.2869674","journal-title":"IEEE Trans Cybern"},{"key":"969_CR44","doi-asserted-by":"publisher","DOI":"10.1109\/MCI.2017.2742868","author":"Y Tian","year":"2017","unstructured":"Tian Y, Cheng R, Zhang X, Jin Y (2017) PlatEMO: a MATLAB platform for evolutionary multi-objective optimization. IEEE Comput Intell Mag. https:\/\/doi.org\/10.1109\/MCI.2017.2742868","journal-title":"IEEE Comput Intell Mag"},{"key":"969_CR45","doi-asserted-by":"publisher","unstructured":"Deb K (2005) Scalable test problems for evolutionary multiobejctive optimization. Evolutionary multiobjective optimization: theoretical advances and applications. https:\/\/doi.org\/10.1007\/1-84628-137-7_6","DOI":"10.1007\/1-84628-137-7_6"},{"issue":"3","key":"969_CR46","doi-asserted-by":"publisher","first-page":"205","DOI":"10.1162\/evco.1999.7.3.205","volume":"7","author":"K Deb","year":"1999","unstructured":"Deb K (1999) Multi-objective genetic algorithms: problem difficulties and construction of test problems. Evol Comput 7(3):205\u2013230. https:\/\/doi.org\/10.1162\/evco.1999.7.3.205","journal-title":"Evol Comput"},{"issue":"1","key":"969_CR47","doi-asserted-by":"publisher","first-page":"34","DOI":"10.1002\/(SICI)1099-1360(199801)7:1%3C34::AID-MCDA161%3E3.0.CO;2-6","volume":"7","author":"P Czyz\u017cak","year":"1998","unstructured":"Czyz\u017cak P, Jaszkiewicz A (1998) Pareto simulated annealing-a metaheuristic technique for multiple-objective combinatorial optimization. J Multi-criteria Decis Anal 7(1):34\u201347. https:\/\/doi.org\/10.1002\/(SICI)1099-1360(199801)7:1%3C34::AID-MCDA161%3E3.0.CO;2-6","journal-title":"J Multi-criteria Decis Anal"},{"key":"969_CR48","doi-asserted-by":"publisher","first-page":"23","DOI":"10.3389\/frobt.2016.00023","volume":"3","author":"A Stuntz","year":"2016","unstructured":"Stuntz A, Kelly JS, Smith RN (2016) Enabling persistent autonomy for underwater gliders with ocean model predictions and terrain-based navigation. Front Robot AI 3:23. https:\/\/doi.org\/10.3389\/frobt.2016.00023","journal-title":"Front Robot AI"},{"key":"969_CR49","doi-asserted-by":"publisher","unstructured":"Bachmayer R, Leonard NE, Graver J, Fiorelli E, Bhatta P, Paley D (2004) Underwater gliders: Recent developments and future applications. In: Underwater Technology. UT '04. 2004 international symposium on 2004. https:\/\/doi.org\/10.1109\/UT.2004.1405540","DOI":"10.1109\/UT.2004.1405540"},{"issue":"5","key":"969_CR50","doi-asserted-by":"publisher","first-page":"3107","DOI":"10.1121\/1.4782033","volume":"121","author":"GL D\u2019Spain","year":"2007","unstructured":"D\u2019Spain GL, Zimmerman R, Jenkins SA, Luby JC, Brodsky P (2007) Underwater acoustic measurements with a flying wing glider. J Acoust Soc Am 121(5):3107\u20133107. https:\/\/doi.org\/10.1121\/1.4782033","journal-title":"J Acoust Soc Am"},{"issue":"3","key":"969_CR51","doi-asserted-by":"publisher","first-page":"227","DOI":"10.1080\/17445302.2019.1611989","volume":"15","author":"J Li","year":"2020","unstructured":"Li J, Wang P, Dong H, Wu X, Chen X, Chen C (2020) Shape optimization of blended-wing-body underwater gliders based on free-form deformation. Ships Offshore Struct 15(3):227\u2013235. https:\/\/doi.org\/10.1080\/17445302.2019.1611989","journal-title":"Ships Offshore Struct"},{"key":"969_CR52","doi-asserted-by":"publisher","DOI":"10.1080\/17445302.2022.2126126","author":"W Wang","year":"2022","unstructured":"Wang W, Dong H, Wang P, Li J, Shen J (2022) A model-based multidisciplinary conceptual design for blended-wing-body underwater gliders. Ships Offshore Struct. https:\/\/doi.org\/10.1080\/17445302.2022.2126126","journal-title":"Ships Offshore Struct"},{"issue":"6","key":"969_CR53","doi-asserted-by":"publisher","first-page":"995","DOI":"10.1515\/ijnaoe-2015-0069","volume":"7","author":"C Sun","year":"2015","unstructured":"Sun C, Song B, Peng W (2015) Parametric geometric model and shape optimization of an underwater glider with blended-wing-body. Int J Naval Archit Ocean Eng 7(6):995\u20131006. https:\/\/doi.org\/10.1515\/ijnaoe-2015-0069","journal-title":"Int J Naval Archit Ocean Eng"},{"issue":"006","key":"969_CR54","doi-asserted-by":"publisher","first-page":"709","DOI":"10.1007\/s13344-017-0081-7","volume":"31","author":"ZY Wang","year":"2017","unstructured":"Wang ZY, Jian-Cheng YU, Zhang AQ, Wang YX, Zhao WT (2017) Parametric geometric model and hydrodynamic shape optimization of a flying-wing structure underwater glider. China Ocean Eng 31(006):709\u2013715. https:\/\/doi.org\/10.1007\/s13344-017-0081-7","journal-title":"China Ocean Eng"},{"issue":"7","key":"969_CR55","doi-asserted-by":"publisher","first-page":"407","DOI":"10.2514\/3.58379","volume":"15","author":"RM Hicks","year":"1978","unstructured":"Hicks RM, Henne PA (1978) Wing design by numerical optimization. J Aircr 15(7):407\u2013412. https:\/\/doi.org\/10.2514\/3.58379","journal-title":"J Aircr"}],"container-title":["Complex &amp; Intelligent Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40747-023-00969-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40747-023-00969-w\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40747-023-00969-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,7,27]],"date-time":"2023-07-27T13:35:45Z","timestamp":1690464945000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40747-023-00969-w"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,2,9]]},"references-count":55,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2023,8]]}},"alternative-id":["969"],"URL":"https:\/\/doi.org\/10.1007\/s40747-023-00969-w","relation":{},"ISSN":["2199-4536","2198-6053"],"issn-type":[{"value":"2199-4536","type":"print"},{"value":"2198-6053","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,2,9]]},"assertion":[{"value":"12 September 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 January 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 February 2023","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 conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"This article is ethical, and this research has been agreed upon.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethics approval"}},{"value":"The picture materials quoted in this article have no copyright requirements, and the source has been indicated.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent for publication"}},{"value":"Informed consent was obtained from all individual participants included in the study.","order":5,"name":"Ethics","group":{"name":"EthicsHeading","label":"Informed consent"}},{"value":"We use no animals in this research.","order":6,"name":"Ethics","group":{"name":"EthicsHeading","label":"Human and animal rights"}}]}}