{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T22:09:35Z","timestamp":1740175775539,"version":"3.37.3"},"reference-count":77,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2024,6,22]],"date-time":"2024-06-22T00:00:00Z","timestamp":1719014400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2024,6,22]],"date-time":"2024-06-22T00:00:00Z","timestamp":1719014400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"Natural Science Foundation of Anhui Province of China","award":["2208085MF174"],"award-info":[{"award-number":["2208085MF174"]}]},{"name":"Industry-Academy-Research Innovation Fund of Ministry of Education of China","award":["2021ZYA06004"],"award-info":[{"award-number":["2021ZYA06004"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Complex Intell. Syst."],"published-print":{"date-parts":[[2024,10]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The primary objective of multi-objective evolutionary algorithms (MOEAs) is to find a set of evenly distributed nondominated solutions that approximate the Pareto front (PF) of a multi-objective optimization problem (MOP) or a many-objective optimization problem (MaOP). This implies that the approximated solution set obtained by MOEAs should be as close to PF as possible while remaining diverse, adhering to criteria of convergence and diversity. However, existing MOEAs exhibit an imbalance between achieving convergence and maintaining diversity in the objective space. As far as the diversity criterion is concerned, it is still a challenge to achieve an evenly distributed approximation set with different sizes for a problem with a complicated PF shape. Furthermore, Pareto dominance has its own weaknesses as the selection criterion in evolutionary multiobjective optimization. Algorithms based on Pareto criterion (PC) can suffer from problems such as slow convergence to the optimal front and inferior performance on problems with many objectives. To effectively address these challenges, we propose a multi-objective bean optimization algorithm (MOBOA). Given that the selection of parent species, representing global optimal solutions, directly influences the convergence and diversity of the algorithm, MOBOA incorporates a preference order equilibrium parent species selection strategy (POEPSS). By extending the Pareto criterion with the preference order optimization criterion, the algorithm effectively enhances parent species selection pressure across multiple objectives. To balance convergence and diversity, MOBOA proposes a multi-population global search strategy explicitly maintaining an external archive during the search process. Leveraging the inherent multi-population advantages of bean optimization algorithm (BOA), the algorithm facilitates information sharing among the main population, auxiliary populations, and historical archive solution sets. Additionally, a diversity enhancement strategy is employed in the environmental selection stage, introducing the environmental selection strategy of the SPEA2 algorithm to generate a set of evenly distributed nondominated solutions. Experimental results on a series of widely used MOPs and MaOPs demonstrate that the proposed algorithm exhibits higher effectiveness and competitiveness compared to state-of-the-art algorithms.<\/jats:p>","DOI":"10.1007\/s40747-024-01523-y","type":"journal-article","created":{"date-parts":[[2024,6,22]],"date-time":"2024-06-22T09:01:52Z","timestamp":1719046912000},"page":"6839-6865","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Moboa: a proposal for multiple objective bean optimization algorithm"],"prefix":"10.1007","volume":"10","author":[{"given":"Lele","family":"Xie","sequence":"first","affiliation":[]},{"given":"Xiaoli","family":"Lu","sequence":"additional","affiliation":[]},{"given":"Hang","family":"Liu","sequence":"additional","affiliation":[]},{"given":"Yongqiang","family":"Hu","sequence":"additional","affiliation":[]},{"given":"Xiaoming","family":"Zhang","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0837-5424","authenticated-orcid":false,"given":"Shangshang","family":"Yang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,6,22]]},"reference":[{"key":"1523_CR1","doi-asserted-by":"crossref","unstructured":"Zhong RY, Xu X, Klotz E, Newman ST (2017) Intelligent manufacturing in the context of industry 4.0: a review. Engineering 3(5):616\u2013630","DOI":"10.1016\/J.ENG.2017.05.015"},{"issue":"2","key":"1523_CR2","doi-asserted-by":"crossref","first-page":"106","DOI":"10.1109\/TETCI.2018.2872055","volume":"3","author":"Y Tian","year":"2018","unstructured":"Tian Y, Yang S, Zhang L, Duan F, Zhang X (2018) A surrogate-assisted multiobjective evolutionary algorithm for large-scale task-oriented pattern mining. IEEE Trans Emerg Top Comput Intell 3(2):106\u2013116","journal-title":"IEEE Trans Emerg Top Comput Intell"},{"issue":"4","key":"1523_CR3","doi-asserted-by":"crossref","first-page":"1778","DOI":"10.1109\/TCDS.2022.3179482","volume":"14","author":"S Yang","year":"2022","unstructured":"Yang S, Tian Y, Xiang X, Peng S, Zhang X (2022) Accelerating evolutionary neural architecture search via multifidelity evaluation. IEEE Trans Cogn Dev Syst 14(4):1778\u20131792","journal-title":"IEEE Trans Cogn Dev Syst"},{"key":"1523_CR4","doi-asserted-by":"crossref","unstructured":"Yang S, Wei H, Ma H, Tian Y, Zhang X, Cao Y, Jin Y (2023) Cognitive diagnosis-based personalized exercise group assembly via a multi-objective evolutionary algorithm. IEEE Trans Emerg Top Comput Intell 7(3):829\u2013844","DOI":"10.1109\/TETCI.2022.3220812"},{"key":"1523_CR5","unstructured":"Yang S, Ma H, Zhen C, Tian Y, Zhang L, Jin Y, Zhang X (2023) Designing novel cognitive diagnosis models via evolutionary multi-objective neural architecture search. arXiv preprint arXiv:2307.04429"},{"issue":"9","key":"1523_CR6","doi-asserted-by":"crossref","first-page":"4861","DOI":"10.1109\/TNNLS.2021.3061630","volume":"33","author":"S Yang","year":"2021","unstructured":"Yang S, Tian Y, He C, Zhang X, Tan KC, Jin Y (2021) A gradient-guided evolutionary approach to training deep neural networks. IEEE Trans Neural Netw Learn Syst 33(9):4861\u20134875","journal-title":"IEEE Trans Neural Netw Learn Syst"},{"issue":"12","key":"1523_CR7","doi-asserted-by":"crossref","first-page":"3665","DOI":"10.1109\/TFUZZ.2021.3089230","volume":"29","author":"X Cai","year":"2021","unstructured":"Cai X, Zhang J, Ning Z, Cui Z, Chen J (2021) A many-objective multistage optimization-based fuzzy decision-making model for coal production prediction. IEEE Trans Fuzzy Syst 29(12):3665\u20133675","journal-title":"IEEE Trans Fuzzy Syst"},{"issue":"5","key":"1523_CR8","doi-asserted-by":"crossref","first-page":"842","DOI":"10.1109\/TEVC.2021.3049131","volume":"25","author":"M Li","year":"2021","unstructured":"Li M, Wang Z, Li K, Liao X, Hone K, Liu X (2021) Task allocation on layered multiagent systems: when evolutionary many-objective optimization meets deep Q-learning. IEEE Trans Evol Comput 25(5):842\u2013855","journal-title":"IEEE Trans Evol Comput"},{"key":"1523_CR9","doi-asserted-by":"crossref","unstructured":"Zhan ZH, Shi L, Tan KC, Zhang J (2022) A survey on evolutionary computation for complex continuous optimization. Artif Intell Rev 55:59\u2013110","DOI":"10.1007\/s10462-021-10042-y"},{"issue":"6","key":"1523_CR10","doi-asserted-by":"crossref","first-page":"851","DOI":"10.1109\/TEVC.2017.2767023","volume":"22","author":"LM Antonio","year":"2017","unstructured":"Antonio LM, Coello CAC (2017) Coevolutionary multiobjective evolutionary algorithms: Survey of the state-of-the-art. IEEE Trans Evol Comput 22(6):851\u2013865","journal-title":"IEEE Trans Evol Comput"},{"key":"1523_CR11","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1007\/978-3-030-72062-9_1","volume-title":"International conference on evolutionary multi-criterion optimization","author":"Q Yang","year":"2021","unstructured":"Yang Q, Wang Z, Ishibuchi H (2021) It is hard to distinguish between dominance resistant solutions and extremely convex Pareto optimal solutions. International conference on evolutionary multi-criterion optimization. Springer International Publishing, Cham, pp 3\u201314"},{"issue":"3","key":"1523_CR12","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1504\/IJBIC.2020.111266","volume":"16","author":"MS Mohamed","year":"2020","unstructured":"Mohamed MS, Duan H (2020) Flight control system design using adaptive pigeon-inspired optimisation. Int J Bio-Insp Comput 16(3):133\u2013147","journal-title":"Int J Bio-Insp Comput"},{"key":"1523_CR13","doi-asserted-by":"crossref","first-page":"104","DOI":"10.1016\/j.knosys.2019.02.016","volume":"172","author":"A Majumder","year":"2019","unstructured":"Majumder A, Laha D, Suganthan PN (2019) Bacterial foraging optimization algorithm in robotic cells with sequence-dependent setup times. Knowl-Based Syst 172:104\u2013122","journal-title":"Knowl-Based Syst"},{"issue":"2","key":"1523_CR14","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, Meyarivan TAMT (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":"2","key":"1523_CR15","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1109\/TEVC.2013.2258025","volume":"18","author":"Z He","year":"2013","unstructured":"He Z, Yen GG, Zhang J (2013) Fuzzy-based Pareto optimality for many-objective evolutionary algorithms. IEEE Trans Evol Comput 18(2):269\u2013285","journal-title":"IEEE Trans Evol Comput"},{"issue":"5","key":"1523_CR16","doi-asserted-by":"crossref","first-page":"721","DOI":"10.1109\/TEVC.2012.2227145","volume":"17","author":"S Yang","year":"2013","unstructured":"Yang S, Li M, Liu X, Zheng J (2013) A grid-based evolutionary algorithm for many-objective optimization. IEEE Trans Evol Comput 17(5):721\u2013736","journal-title":"IEEE Trans Evol Comput"},{"key":"1523_CR17","doi-asserted-by":"crossref","unstructured":"Tian Y, Cheng R, Zhang X, Su Y, Jin Y (2018) A strengthened dominance relation considering convergence and diversity for evolutionary many-objective optimization. IEEE Trans Evol Comput 23(2):331\u2013345","DOI":"10.1109\/TEVC.2018.2866854"},{"key":"1523_CR18","unstructured":"Zitzler E, Laumanns M, Thiele L (2001) SPEA2: improving the strength Pareto evolutionary algorithm. TIK report, p 103"},{"issue":"3","key":"1523_CR19","doi-asserted-by":"crossref","first-page":"1653","DOI":"10.1016\/j.ejor.2006.08.008","volume":"181","author":"N Beume","year":"2007","unstructured":"Beume N, Naujoks B, Emmerich M (2007) SMS-EMOA: multiobjective selection based on dominated hypervolume. Eur J Oper Res 181(3):1653\u20131669","journal-title":"Eur J Oper Res"},{"key":"1523_CR20","doi-asserted-by":"crossref","unstructured":"Zhao L, Zhang Q (2023) Hypervolume-guided decomposition for parallel expensive multiobjective optimization. IEEE Trans Evol Comput 28(2):432\u2013444","DOI":"10.1109\/TEVC.2023.3265347"},{"issue":"6","key":"1523_CR21","doi-asserted-by":"crossref","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","journal-title":"IEEE Trans Evol Comput"},{"issue":"4","key":"1523_CR22","doi-asserted-by":"crossref","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","journal-title":"IEEE Trans Evol Comput"},{"issue":"4","key":"1523_CR23","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":"5","key":"1523_CR24","doi-asserted-by":"crossref","first-page":"694","DOI":"10.1109\/TEVC.2014.2373386","volume":"19","author":"K Li","year":"2014","unstructured":"Li K, Deb K, Zhang Q, Kwong S (2014) An evolutionary many-objective optimization algorithm based on dominance and decomposition. IEEE Trans Evol Comput 19(5):694\u2013716","journal-title":"IEEE Trans Evol Comput"},{"issue":"2","key":"1523_CR25","doi-asserted-by":"crossref","first-page":"180","DOI":"10.1109\/TEVC.2015.2443001","volume":"20","author":"Y Yuan","year":"2015","unstructured":"Yuan Y, Xu H, Wang B, Zhang B, Yao X (2015) Balancing convergence and diversity in decomposition-based many-objective optimizers. IEEE Trans Evol Comput 20(2):180\u2013198","journal-title":"IEEE Trans Evol Comput"},{"issue":"2","key":"1523_CR26","doi-asserted-by":"crossref","first-page":"753","DOI":"10.1109\/TCYB.2018.2872803","volume":"50","author":"M Wu","year":"2018","unstructured":"Wu M, Li K, Kwong S, Zhang Q (2018) Evolutionary many-objective optimization based on adversarial decomposition. IEEE Trans Cybern 50(2):753\u2013764","journal-title":"IEEE Trans Cybern"},{"issue":"6","key":"1523_CR27","doi-asserted-by":"crossref","first-page":"909","DOI":"10.1109\/TEVC.2013.2293776","volume":"18","author":"K Li","year":"2013","unstructured":"Li K, Zhang Q, Kwong S, Li M, Wang R (2013) Stable matching-based selection in evolutionary multiobjective optimization. IEEE Trans Evol Comput 18(6):909\u2013923","journal-title":"IEEE Trans Evol Comput"},{"issue":"6","key":"1523_CR28","doi-asserted-by":"crossref","first-page":"821","DOI":"10.1109\/TEVC.2016.2521175","volume":"20","author":"R Wang","year":"2016","unstructured":"Wang R, Zhang Q, Zhang T (2016) Decomposition-based algorithms using Pareto adaptive scalarizing methods. IEEE Trans Evol Comput 20(6):821\u2013837","journal-title":"IEEE Trans Evol Comput"},{"issue":"5","key":"1523_CR29","doi-asserted-by":"crossref","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","journal-title":"IEEE Trans Evol Comput"},{"issue":"4","key":"1523_CR30","doi-asserted-by":"crossref","first-page":"609","DOI":"10.1109\/TEVC.2017.2749619","volume":"22","author":"Y Tian","year":"2017","unstructured":"Tian Y, Cheng R, Zhang X, Cheng F, Jin Y (2017) An indicator-based multiobjective evolutionary algorithm with reference point adaptation for better versatility. IEEE Trans Evol Comput 22(4):609\u2013622","journal-title":"IEEE Trans Evol Comput"},{"issue":"1","key":"1523_CR31","doi-asserted-by":"crossref","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","journal-title":"Evol Comput"},{"issue":"5","key":"1523_CR32","doi-asserted-by":"crossref","first-page":"839","DOI":"10.1109\/TEVC.2020.2964705","volume":"24","author":"K Shang","year":"2020","unstructured":"Shang K, Ishibuchi H (2020) A new hypervolume-based evolutionary algorithm for many-objective optimization. IEEE Trans Evol Comput 24(5):839\u2013852","journal-title":"IEEE Trans Evol Comput"},{"issue":"2","key":"1523_CR33","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1109\/TEVC.2018.2791283","volume":"23","author":"Y Sun","year":"2018","unstructured":"Sun Y, Yen GG, Yi Z (2018) IGD indicator-based evolutionary algorithm for many-objective optimization problems. IEEE Trans Evol Comput 23(2):173\u2013187","journal-title":"IEEE Trans Evol Comput"},{"issue":"2","key":"1523_CR34","doi-asserted-by":"crossref","first-page":"445","DOI":"10.1109\/TSMCB.2012.2209115","volume":"43","author":"ZH Zhan","year":"2013","unstructured":"Zhan ZH, Li J, Cao J, Zhang J, Chung HSH, Shi YH (2013) Multiple populations for multiple objectives: a coevolutionary technique for solving multiobjective optimization problems. IEEE Trans Cybern 43(2):445\u2013463","journal-title":"IEEE Trans Cybern"},{"issue":"4","key":"1523_CR35","first-page":"587","volume":"23","author":"XF Liu","year":"2018","unstructured":"Liu XF, Zhan ZH, Gao Y, Zhang J, Kwong S, Zhang J (2018) Coevolutionary particle swarm optimization with bottleneck objective learning strategy for many-objective optimization. IEEE Trans Evol Comput 23(4):587\u2013602","journal-title":"IEEE Trans Evol Comput"},{"key":"1523_CR36","doi-asserted-by":"crossref","unstructured":"Yang QT, Zhan ZH, Kwong S, Zhang J (2022) Multiple populations for multiple objectives framework with bias sorting for many-objective optimization. IEEE Transp Evol Comput 27(5):1340\u20131354","DOI":"10.1109\/TEVC.2022.3212058"},{"issue":"2","key":"1523_CR37","doi-asserted-by":"crossref","first-page":"1117","DOI":"10.1007\/s40747-021-00543-2","volume":"9","author":"Z Wang","year":"2023","unstructured":"Wang Z, Li Q, Yang Q, Ishibuchi H (2023) The dilemma between eliminating dominance-resistant solutions and preserving boundary solutions of extremely convex Pareto fronts. Complex Intell Syst 9(2):1117\u20131126","journal-title":"Complex Intell Syst"},{"key":"1523_CR38","doi-asserted-by":"crossref","unstructured":"Zhang Q, Liu W, Li H (2009) The performance of a new version of MOEA\/D on CEC09 unconstrained MOP test instances. In: 2009 IEEE congress on evolutionary computation. IEEE, pp 203\u2013208","DOI":"10.1109\/CEC.2009.4982949"},{"key":"1523_CR39","doi-asserted-by":"crossref","unstructured":"He L, Camacho A, Ishibuchi H (2020) Another difficulty of inverted triangular pareto fronts for decomposition-based multi-objective algorithms. In: Proceedings of the 2020 genetic and evolutionary computation conference, pp 498\u2013506","DOI":"10.1145\/3377930.3390196"},{"issue":"1","key":"1523_CR40","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/TEVC.2020.3013290","volume":"25","author":"K Shang","year":"2020","unstructured":"Shang K, Ishibuchi H, He L, Pang LM (2020) A survey on the hypervolume indicator in evolutionary multiobjective optimization. IEEE Trans Evol Comput 25(1):1\u201320","journal-title":"IEEE Trans Evol Comput"},{"issue":"4","key":"1523_CR41","doi-asserted-by":"crossref","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","journal-title":"IEEE Trans Evol Comput"},{"key":"1523_CR42","unstructured":"Xiao Z, Ru W (2008) A novel evolutionary algorithm\u2013seed optimization algorithm. Pattern Recogn Artif Intell 21(5):677\u2013681"},{"key":"1523_CR43","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1007\/BF01210689","volume":"18","author":"I Das","year":"1999","unstructured":"Das I (1999) A preference ordering among various Pareto optimal alternatives. Struct Optim 18:30\u201335","journal-title":"Struct Optim"},{"key":"1523_CR44","doi-asserted-by":"crossref","unstructured":"Dai W, Au OC, Li S, Sun L, Zou R (2012) Adaptive search range algorithm based on Cauchy distribution. In: 2012 Visual communications and image processing. IEEE, pp 1\u20135","DOI":"10.1109\/VCIP.2012.6410741"},{"key":"1523_CR45","doi-asserted-by":"crossref","unstructured":"Zhang X, Sun B, Mei T, Wang R (2010) Post-disaster restoration based on fuzzy preference relation and bean optimization algorithm. In: 2010 IEEE Youth conference on information, computing and telecommunications. IEEE, pp 271\u2013274","DOI":"10.1109\/YCICT.2010.5713097"},{"issue":"4","key":"1523_CR46","doi-asserted-by":"crossref","first-page":"609","DOI":"10.1080\/18756891.2013.802110","volume":"6","author":"X Zhang","year":"2013","unstructured":"Zhang X, Wang H, Sun B, Li W, Wang R (2013) The Markov model of bean optimization algorithm and its convergence analysis. Int J Comput Intell Syst 6(4):609\u2013615","journal-title":"Int J Comput Intell Syst"},{"key":"1523_CR47","doi-asserted-by":"crossref","unstructured":"Feng T, Xie Q, Hu H, Song L, Cui C, Zhang X (2015) Bean optimization algorithm based on negative Binomial Distribution. In Advances in swarm and computational intelligence: 6th international conference, ICSI 2015, held in conjunction with the second BRICS congress, CCI 2015, Beijing, China, June 25\u201328, 2015, Proceedings, Part I 6. Springer International Publishing, pp 82\u201388","DOI":"10.1007\/978-3-319-20466-6_9"},{"key":"1523_CR48","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1007\/s00500-016-2322-8","volume":"22","author":"X Zhang","year":"2018","unstructured":"Zhang X, Feng T (2018) Chaotic bean optimization algorithm. Soft Comput 22:67\u201377","journal-title":"Soft Comput"},{"issue":"1","key":"1523_CR49","doi-asserted-by":"crossref","first-page":"159","DOI":"10.2991\/ijcis.d.201109.001","volume":"14","author":"X Zhang","year":"2021","unstructured":"Zhang X, Hu Y, Li T (2021) A novel target searching algorithm for swarm UAVs inspired from spatial distribution patterns of plant population. Int J Comput Intell Syst 14(1):159\u2013167","journal-title":"Int J Comput Intell Syst"},{"key":"1523_CR50","doi-asserted-by":"crossref","unstructured":"Wang C, Zhang X, Liu H, Wu H (2021, October) RBOA algorithm based on region segmentation and point update. In: 2021 China automation congress (CAC). IEEE, pp 6983\u20136988","DOI":"10.1109\/CAC53003.2021.9728593"},{"key":"1523_CR51","unstructured":"Liu H, Zhang X, Wang C (2021) Bean optimization algorithm based on Cauchy distribution and parent rotation mechanism. Pattern Recogn Artif Intell 34(7):581\u2013591"},{"issue":"1","key":"1523_CR52","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1109\/TEVC.2006.876362","volume":"11","author":"F Di Pierro","year":"2007","unstructured":"Di Pierro F, Khu ST, Savic DA (2007) An investigation on preference order ranking scheme for multiobjective evolutionary optimization. IEEE Trans Evol Comput 11(1):17\u201345","journal-title":"IEEE Trans Evol Comput"},{"issue":"2","key":"1523_CR53","first-page":"115","volume":"9","author":"K Deb","year":"1995","unstructured":"Deb K, Agrawal RB (1995) Simulated binary crossover for continuous search space. Complex Syst 9(2):115\u2013148","journal-title":"Complex Syst"},{"issue":"2","key":"1523_CR54","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1162\/106365600568202","volume":"8","author":"E Zitzler","year":"2000","unstructured":"Zitzler E, Deb K, Thiele L (2000) Comparison of multiobjective evolutionary algorithms: empirical results. Evol Comput 8(2):173\u2013195","journal-title":"Evol Comput"},{"key":"1523_CR55","unstructured":"Zhang Q, Zhou A, Zhao S, Suganthan PN, Liu W, Tiwari S (2008) Multiobjective optimization test instances for the CEC 2009 special session and competition"},{"key":"1523_CR56","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1007\/s40747-017-0039-7","volume":"3","author":"R Cheng","year":"2017","unstructured":"Cheng R, Li M, Tian Y, Zhang X, Yang S, Jin Y, Yao X (2017) A benchmark test suite for evolutionary many-objective optimization. Complex Intell Syst 3:67\u201381","journal-title":"Complex Intell Syst"},{"issue":"7","key":"1523_CR57","doi-asserted-by":"crossref","first-page":"2758","DOI":"10.1109\/TCYB.2018.2834466","volume":"49","author":"Y Hua","year":"2018","unstructured":"Hua Y, Jin Y, Hao K (2018) A clustering-based adaptive evolutionary algorithm for multiobjective optimization with irregular Pareto fronts. IEEE Trans Cybern 49(7):2758\u20132770","journal-title":"IEEE Trans Cybern"},{"issue":"5","key":"1523_CR58","doi-asserted-by":"crossref","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","journal-title":"IEEE Trans Evol Comput"},{"issue":"11","key":"1523_CR59","doi-asserted-by":"crossref","first-page":"2841","DOI":"10.1109\/TFUZZ.2019.2945241","volume":"28","author":"Y Tian","year":"2019","unstructured":"Tian Y, Yang S, Zhang X (2019) An evolutionary multiobjective optimization based fuzzy method for overlapping community detection. IEEE Trans Fuzzy Syst 28(11):2841\u20132855","journal-title":"IEEE Trans Fuzzy Syst"},{"key":"1523_CR60","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1016\/j.engappai.2018.09.009","volume":"77","author":"L Zhang","year":"2019","unstructured":"Zhang L, Yang S, Wu X, Cheng F, Xie Y, Lin Z (2019) An indexed set representation based multi-objective evolutionary approach for mining diversified top-k high utility patterns. Eng Appl Artif Intell 77:9\u201320","journal-title":"Eng Appl Artif Intell"},{"issue":"2","key":"1523_CR61","doi-asserted-by":"crossref","first-page":"268","DOI":"10.1109\/TAI.2022.3168038","volume":"4","author":"Y Tian","year":"2022","unstructured":"Tian Y, Pan J, Yang S, Zhang X, He S, Jin Y (2022) Imperceptible and sparse adversarial attacks via a dual-population-based constrained evolutionary algorithm. IEEE Trans Artif Intell 4(2):268\u2013281","journal-title":"IEEE Trans Artif Intell"},{"key":"1523_CR62","doi-asserted-by":"crossref","unstructured":"Liu Y, Liu J, Ding J, Yang S, Jin Y (2023) A surrogate-assisted differential evolution with knowledge transfer for expensive incremental optimization problems. IEEE Trans Evol Comput","DOI":"10.1109\/TEVC.2023.3291697"},{"key":"1523_CR63","doi-asserted-by":"crossref","unstructured":"Si L, Zhang X, Tian Y, Yang S, Zhang L, Jin Y (2023) Linear subspace surrogate modeling for large-scale expensive single\/multi-objective optimization. IEEE Trans Evol Comput 1\u201316","DOI":"10.1109\/TEVC.2023.3319640"},{"key":"1523_CR64","unstructured":"Yang S, Yu X, Tian Y, Yan X, Ma H, Zhang X (2024) Evolutionary neural architecture search for transformer in knowledge tracing. Adv Neural Inf Process Syst 36"},{"key":"1523_CR65","doi-asserted-by":"crossref","unstructured":"Yang S, Zhen C, Tian Y, Ma H, Liu Y, Zhang P, Zhang X (2023) Evolutionary multi-objective neural architecture search for generalized cognitive diagnosis models. In: 2023 5th International conference on data-driven optimization of complex systems (DOCS). IEEE, pp 1\u201310","DOI":"10.1109\/DOCS60977.2023.10294588"},{"key":"1523_CR66","doi-asserted-by":"crossref","unstructured":"Yang S, Sun X, Xu K, Liu Y, Tian Y, Zhang X (2024) Hybrid architecture-based evolutionary robust neural architecture search. IEEE Trans Emerg Top Comput Intell","DOI":"10.1109\/TETCI.2024.3400867"},{"issue":"1","key":"1523_CR67","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1109\/TEVC.2016.2631279","volume":"22","author":"Q Lin","year":"2016","unstructured":"Lin Q, Liu S, Zhu Q, Tang C, Song R, Chen J, Zhang J (2016) Particle swarm optimization with a balanceable fitness estimation for many-objective optimization problems. IEEE Trans Evol Comput 22(1):32\u201346","journal-title":"IEEE Trans Evol Comput"},{"key":"1523_CR68","doi-asserted-by":"publisher","unstructured":"Tian Y, Zheng X, Zhang X, Jin Y (2019) Efficient large-scale multi-objective optimization based on a competitive swarm optimizer. IEEE Trans Cybern. https:\/\/doi.org\/10.1109\/TCYB.2019.2906383","DOI":"10.1109\/TCYB.2019.2906383"},{"issue":"10","key":"1523_CR69","doi-asserted-by":"crossref","first-page":"6222","DOI":"10.1109\/TSMC.2022.3143657","volume":"52","author":"F Ming","year":"2022","unstructured":"Ming F, Gong W, Wang L (2022) A two-stage evolutionary algorithm with balanced convergence and diversity for many-objective optimization. IEEE Trans Syst Man Cybern Syst 52(10):6222\u20136234","journal-title":"IEEE Trans Syst Man Cybern Syst"},{"key":"1523_CR70","doi-asserted-by":"crossref","unstructured":"Liu Z, Han F, Ling Q, Han H, Jiang J (2023) A many-objective optimization evolutionary algorithm based on hyper-dominance degree. Swarm Evol Comput 83:101411","DOI":"10.1016\/j.swevo.2023.101411"},{"key":"1523_CR71","doi-asserted-by":"crossref","unstructured":"Panichella A (2022, July) An improved Pareto front modeling algorithm for large-scale many-objective optimization. In: Proceedings of the genetic and evolutionary computation conference, pp 565\u2013573","DOI":"10.1145\/3512290.3528732"},{"issue":"1","key":"1523_CR72","doi-asserted-by":"crossref","first-page":"623","DOI":"10.1109\/TSMC.2022.3186546","volume":"53","author":"Y Tian","year":"2022","unstructured":"Tian Y, Si L, Zhang X, Tan KC, Jin Y (2022) Local model-based Pareto front estimation for multiobjective optimization. IEEE Trans Syst Man Cybern Syst 53(1):623\u2013634","journal-title":"IEEE Trans Syst Man Cybern Syst"},{"issue":"4","key":"1523_CR73","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, Jin Y (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"},{"key":"1523_CR74","first-page":"30","volume":"26","author":"K Deb","year":"1996","unstructured":"Deb K, Goyal M (1996) A combined genetic adaptive search (GeneAS) for engineering design. Comput Sci Inf 26:30\u201345","journal-title":"Comput Sci Inf"},{"key":"1523_CR75","first-page":"171","volume":"1","author":"F Wilcoxon","year":"1970","unstructured":"Wilcoxon F, Katti SK, Wilcox RA (1970) Critical values and probability levels for the Wilcoxon rank sum test and the Wilcoxon signed rank test. Selected tables in mathematical statistics 1:171\u2013259","journal-title":"Selected tables in mathematical statistics"},{"issue":"2","key":"1523_CR76","doi-asserted-by":"crossref","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","journal-title":"IEEE Trans Evol Comput"},{"issue":"1","key":"1523_CR77","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, Huband S (2006) A faster algorithm for calculating hypervolume. IEEE Trans Evol Comput 10(1):29\u201338","journal-title":"IEEE Trans Evol Comput"}],"container-title":["Complex &amp; Intelligent Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40747-024-01523-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40747-024-01523-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40747-024-01523-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,14]],"date-time":"2024-09-14T15:18:04Z","timestamp":1726327084000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40747-024-01523-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,6,22]]},"references-count":77,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2024,10]]}},"alternative-id":["1523"],"URL":"https:\/\/doi.org\/10.1007\/s40747-024-01523-y","relation":{},"ISSN":["2199-4536","2198-6053"],"issn-type":[{"type":"print","value":"2199-4536"},{"type":"electronic","value":"2198-6053"}],"subject":[],"published":{"date-parts":[[2024,6,22]]},"assertion":[{"value":"11 December 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 May 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 June 2024","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 have no conflict of interest in the publication of this paper.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}