{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,25]],"date-time":"2026-07-25T16:46:17Z","timestamp":1784997977020,"version":"3.55.0"},"reference-count":78,"publisher":"Association for Computing Machinery (ACM)","issue":"2","license":[{"start":{"date-parts":[[2025,5,15]],"date-time":"2025-05-15T00:00:00Z","timestamp":1747267200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Evol. Learn. Optim."],"published-print":{"date-parts":[[2025,6,30]]},"abstract":"<jats:p>\n            <jats:bold>Bayesian optimisation (BO)<\/jats:bold>\n            is an efficient approach for solving expensive optimisation problems, where acquisition functions play a major role in achieving the tradeoff between exploitation and exploration. The exploitation\u2013exploration tradeoff is challenging; excessive focus on exploitation can stagnate the search, while too much exploration can slow convergence. Multi-objectivisation has been explored as an effective approach to mitigate the exploitation\u2013exploration tradeoff problem. Along this line, in this article, we propose a\n            <jats:bold>Multi-Objectivisation-Based Adaptive Exploitation\u2013Exploration Tradeoff Framework (MOEE)<\/jats:bold>\n            to balance exploitation and exploration in BO. MOEE considers the nondominated front formed by the exploitation and exploration objectives and adaptively switches the focus on exploration and exploitation on the basis of the search status. We verify our method on the 19 synthetic and practical problem instances with 1\u201320 dimensions, and the results show that our proposed multi-objectivisation framework can achieve a good balance between exploitation and exploration.\n          <\/jats:p>","DOI":"10.1145\/3716504","type":"journal-article","created":{"date-parts":[[2025,2,7]],"date-time":"2025-02-07T17:26:31Z","timestamp":1738949191000},"page":"1-33","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":5,"title":["Multi-Objectivising Acquisition Functions in Bayesian Optimisation"],"prefix":"10.1145","volume":"5","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5693-6463","authenticated-orcid":false,"given":"Chao","family":"Jiang","sequence":"first","affiliation":[{"name":"University of Birmingham, Birmingham, United Kingdom of Great Britain and Northern Ireland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8607-9607","authenticated-orcid":false,"given":"Miqing","family":"Li","sequence":"additional","affiliation":[{"name":"University of Birmingham, Birmingham, United Kingdom of Great Britain and Northern Ireland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2025,5,15]]},"reference":[{"key":"e_1_3_2_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/3184066.3184080"},{"key":"e_1_3_2_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.apacoust.2020.107256"},{"key":"e_1_3_2_4_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.bspc.2021.103141"},{"key":"e_1_3_2_5_1","first-page":"21524","article-title":"BoTorch: A framework for efficient Monte-Carlo Bayesian optimization","volume":"33","author":"Balandat Maximilian","year":"2020","unstructured":"Maximilian Balandat, Brian Karrer, Daniel Jiang, Samuel Daulton, Ben Letham, Andrew G. Wilson, and Eytan Bakshy. 2020. BoTorch: A framework for efficient Monte-Carlo Bayesian optimization. In Advances in Neural Information Processing Systems. H. Larochelle, M. Ranzato, R. Hadsell, M. F. Balcan, and H. Lin (Eds.), Vol. 33. Curran Associates, Inc., 21524\u201321538.","journal-title":"Advances in Neural Information Processing Systems"},{"key":"e_1_3_2_6_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2012.05.056"},{"key":"e_1_3_2_7_1","doi-asserted-by":"publisher","DOI":"10.1145\/3583133.3590753"},{"key":"e_1_3_2_8_1","first-page":"2546","article-title":"Algorithms for hyper-parameter optimization","volume":"24","author":"Bergstra James","year":"2011","unstructured":"James Bergstra, R\u00e9mi Bardenet, Yoshua Bengio, and Bal\u00e1zs K\u00e9gl. 2011. Algorithms for hyper-parameter optimization. In Advances in Neural Information Processing Systems. J. Shawe-Taylor, R. Zemel, P. Bartlett, F. Pereira, and K. Q. Weinberger (Eds.), Vol. 24. Curran Associates, Inc., 2546\u20132554.","journal-title":"Advances in Neural Information Processing Systems"},{"key":"e_1_3_2_9_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2007.03.003"},{"key":"e_1_3_2_10_1","doi-asserted-by":"publisher","DOI":"10.1145\/3545611"},{"key":"e_1_3_2_11_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-09584-4_17"},{"key":"e_1_3_2_12_1","unstructured":"Eric Brochu Vlad M. Cora and Nando De Freitas. 2010. A tutorial on Bayesian optimization of expensive cost functions with application to active user modeling and hierarchical reinforcement learning. arXiv:1012.2599. Retrieved from https:\/\/arxiv.org\/abs\/1012.2599"},{"issue":"88","key":"e_1_3_2_13_1","first-page":"2879","article-title":"Convergence rates of efficient global optimization algorithms","volume":"12","author":"Bull Adam D.","year":"2011","unstructured":"Adam D. Bull. 2011. Convergence rates of efficient global optimization algorithms. Journal of Machine Learning Research 12, 88 (2011), 2879\u20132904.","journal-title":"Journal of Machine Learning Research"},{"key":"e_1_3_2_14_1","doi-asserted-by":"publisher","DOI":"10.1145\/3653025"},{"key":"e_1_3_2_15_1","doi-asserted-by":"publisher","DOI":"10.1145\/3468264.3468555"},{"key":"e_1_3_2_16_1","unstructured":"Zhehui Chen Simon Mak and C. F. Wu. 2019. A hierarchical expected improvement method for Bayesian optimization. arXiv:1911.07285. Retrieved from https:\/\/arxiv.org\/abs\/1911.07285"},{"key":"e_1_3_2_17_1","doi-asserted-by":"publisher","DOI":"10.1145\/3520304.3533654"},{"key":"e_1_3_2_18_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-99259-4_24"},{"key":"e_1_3_2_19_1","first-page":"578","volume-title":"Proceedings of the 37th Conference on Uncertainty in Artificial Intelligence","volume":"161","author":"De Ath George","year":"2021","unstructured":"George De Ath, Richard M. Everson, and Jonathan E. Fieldsend. 2021a. Asynchronous \\(\\varepsilon\\) -Greedy Bayesian optimisation. In Proceedings of the 37th Conference on Uncertainty in Artificial Intelligence, Vol. 161. PMLR, 578\u2013588."},{"key":"e_1_3_2_20_1","doi-asserted-by":"publisher","DOI":"10.1145\/3377930.3390154"},{"key":"e_1_3_2_21_1","doi-asserted-by":"publisher","DOI":"10.1145\/3425501"},{"key":"e_1_3_2_22_1","unstructured":"Carola Doerr Hao Wang Furong Ye Sander van Rijn and Thomas B\u00e4ck. 2018. IOHprofiler: A benchmarking and profiling tool for iterative optimization heuristics. arXiv:1810.05281. Retrieved from https:\/\/arxiv.org\/abs\/1810.05281"},{"key":"e_1_3_2_23_1","first-page":"5496","article-title":"Scalable global optimization via local Bayesian optimization","volume":"32","author":"Eriksson David","year":"2019","unstructured":"David Eriksson, Michael Pearce, Jacob Gardner, Ryan D. Turner, and Matthias Poloczek. 2019. Scalable global optimization via local Bayesian optimization. In Advances in Neural Information Processing Systems. H. Wallach, H. Larochelle, A. Beygelzimer, F. d\u2019Alch\u00e9-Buc, E. Fox, and R. Garnett (Eds.), Vol. 32. Curran Associates, Inc., 5496\u20135507.","journal-title":"Advances in Neural Information Processing Systems"},{"key":"e_1_3_2_24_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10898-014-0210-2"},{"key":"e_1_3_2_25_1","doi-asserted-by":"publisher","DOI":"10.1137\/070693424"},{"key":"e_1_3_2_26_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10287-020-00376-3"},{"key":"e_1_3_2_27_1","first-page":"648","article-title":"Batch Bayesian optimization via local penalization","volume":"51","author":"Gonz\u00e1lez Javier","year":"2016","unstructured":"Javier Gonz\u00e1lez, Zhenwen Dai, Philipp Hennig, and Neil Lawrence. 2016a. Batch Bayesian optimization via local penalization. In Artificial Intelligence and Statistics, Vol. 51. PMLR, 648\u2013657.","journal-title":"Artificial Intelligence and Statistics"},{"key":"e_1_3_2_28_1","first-page":"790","article-title":"GLASSES: Relieving the myopia of Bayesian optimisation","volume":"51","author":"Gonz\u00e1lez Javier","year":"2016","unstructured":"Javier Gonz\u00e1lez, Michael Osborne, and Neil Lawrence. 2016b. GLASSES: Relieving the myopia of Bayesian optimisation. In Artificial Intelligence and Statistics. Gretton Arthur and Robert C. Christian (Eds.), Vol. 51. PMLR, 790\u2013799.","journal-title":"In Artificial Intelligence and Statistics"},{"key":"e_1_3_2_29_1","unstructured":"Ryan-Rhys Griffiths and Jos\u00e9 Miguel Hern\u00e1ndez-Lobato. 2017. Constrained Bayesian optimization for automatic chemical design. arXiv:1709.05501. Retrieved from https:\/\/arxiv.org\/abs\/1709.05501"},{"key":"e_1_3_2_30_1","first-page":"205","volume-title":"World Congress of Structural and Multidisciplinary Optimisation","author":"Grobler Carla","year":"2017","unstructured":"Carla Grobler, Schalk Kok, and Daniel N. Wilke. 2017. Simple intuitive multi-objective parallelization of efficient global optimization: Simple-ego. In World Congress of Structural and Multidisciplinary Optimisation. Schumacher Axel, Vietor Thomas, Fiebig Sierk, Bletzinger Kai-Uwe, and Maute Kurt (Eds.), Springer, 205\u2013220."},{"key":"e_1_3_2_31_1","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2022.3214241"},{"key":"e_1_3_2_32_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00158-021-03038-3"},{"key":"e_1_3_2_33_1","volume-title":"Real-Parameter Black-Box Optimization Benchmarking 2009: Noiseless Functions Definitions","author":"Hansen Nikolaus","year":"2009","unstructured":"Nikolaus Hansen, Steffen Finck, Raymond Ros, and Anne Auger. 2009. Real-Parameter Black-Box Optimization Benchmarking 2009: Noiseless Functions Definitions. Ph.D. Dissertation. INRIA."},{"key":"e_1_3_2_34_1","first-page":"65","article-title":"A simple sequentially rejective multiple test procedure","volume":"6","author":"Holm Sture","year":"1979","unstructured":"Sture Holm. 1979. A simple sequentially rejective multiple test procedure. Scandinavian Journal of Statistics 6 (1979), 65\u201370.","journal-title":"Scandinavian Journal of Statistics"},{"key":"e_1_3_2_35_1","first-page":"11494","article-title":"Joint entropy search for maximally-informed Bayesian optimization","volume":"35","author":"Hvarfner Carl","year":"2022","unstructured":"Carl Hvarfner, Frank Hutter, and Luigi Nardi. 2022. Joint entropy search for maximally-informed Bayesian optimization. Advances in Neural Information Processing Systems 35 (2022), 11494\u201311506.","journal-title":"Advances in Neural Information Processing Systems"},{"key":"e_1_3_2_36_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-48318-9"},{"key":"e_1_3_2_37_1","doi-asserted-by":"publisher","DOI":"10.1109\/TNNLS.2021.3051012"},{"key":"e_1_3_2_38_1","doi-asserted-by":"publisher","DOI":"10.1609\/aaai.v39i25.34909"},{"key":"e_1_3_2_39_1","doi-asserted-by":"publisher","DOI":"10.1109\/TEVC.2018.2869001"},{"key":"e_1_3_2_40_1","doi-asserted-by":"publisher","DOI":"10.1023\/A:1008306431147"},{"key":"e_1_3_2_41_1","first-page":"528","volume-title":"Proceedings of the 20th International Conference on Artificial Intelligence and Statistics","volume":"54","author":"Klein Aaron","year":"2017","unstructured":"Aaron Klein, Stefan Falkner, Simon Bartels, Philipp Hennig, and Frank Hutter. 2017. Fast Bayesian optimization of machine learning hyperparameters on large datasets. In Proceedings of the 20th International Conference on Artificial Intelligence and Statistics, Vol. 54. PMLR, 528\u2013536."},{"key":"e_1_3_2_42_1","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-44719-9_19"},{"key":"e_1_3_2_43_1","doi-asserted-by":"publisher","DOI":"10.1115\/1.3653121"},{"key":"e_1_3_2_44_1","doi-asserted-by":"publisher","DOI":"10.1016\/0196-8858(85)90002-8"},{"key":"e_1_3_2_45_1","doi-asserted-by":"publisher","DOI":"10.1145\/3512290.3528836"},{"key":"e_1_3_2_46_1","doi-asserted-by":"publisher","DOI":"10.5555\/1626686"},{"key":"e_1_3_2_47_1","first-page":"944","volume-title":"Proceedings of the 20th International Joint Conference on Artificial Intelligence, Vol","volume":"7","author":"Lizotte Daniel J.","year":"2007","unstructured":"Daniel J. Lizotte, Tao Wang, Michael H. Bowling, and Dale Schuurmans. 2007. Automatic gait optimization with Gaussian process regression. In Proceedings of the 20th International Joint Conference on Artificial Intelligence, Vol. 7. Morgan Kaufmann Publishers Inc., 944\u2013949."},{"key":"e_1_3_2_48_1","first-page":"3306","volume-title":"Proceedings of the 35th International Conference on Machine Learning","volume":"80","author":"Lyu Wenlong","year":"2018","unstructured":"Wenlong Lyu, Fan Yang, Changhao Yan, Dian Zhou, and Xuan Zeng. 2018. Batch Bayesian optimization via multi-objective acquisition ensemble for automated analog circuit design. In Proceedings of the 35th International Conference on Machine Learning, Vol. 80. PMLR, 3306\u20133314."},{"key":"e_1_3_2_49_1","doi-asserted-by":"publisher","DOI":"10.1109\/TCYB.2021.3120788"},{"key":"e_1_3_2_50_1","first-page":"133","article-title":"Introduction to Gaussian processes","volume":"168","author":"MacKay David J. C.","year":"1998","unstructured":"David J. C. MacKay. 1998. Introduction to Gaussian processes. NATO ASI Series F Computer and Systems Sciences 168 (1998), 133\u2013166.","journal-title":"NATO ASI Series F Computer and Systems Sciences"},{"issue":"2","key":"e_1_3_2_51_1","first-page":"117","article-title":"The application of Bayesian methods for seeking the extremum","volume":"2","author":"Mockus Jonas","year":"1978","unstructured":"Jonas Mockus, Vytautas Tiesis, and Antanas Zilinskas. 1978. The application of Bayesian methods for seeking the extremum. Towards Global Optimization 2, 2 (1978), 117\u2013129.","journal-title":"Towards Global Optimization"},{"key":"e_1_3_2_52_1","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/78.3.691"},{"key":"e_1_3_2_53_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2020.11.056"},{"key":"e_1_3_2_54_1","unstructured":"Ashish Anil Pawar and Ujwal Warbhe. 2021. Optimizing Bayesian acquisition functions in Gaussian processes. arXiv:2111.04930. Retrieved from https:\/\/arxiv.org\/abs\/2111.04930"},{"key":"e_1_3_2_55_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-031-14714-2_22"},{"key":"e_1_3_2_56_1","unstructured":"J. Rapin and O. Teytaud. 2018. Nevergrad\u2014A gradient-free optimization platform. Retrieved from https:\/\/GitHub.com\/FacebookResearch\/Nevergrad"},{"key":"e_1_3_2_57_1","doi-asserted-by":"publisher","DOI":"10.1145\/3670683"},{"key":"e_1_3_2_58_1","first-page":"148","volume-title":"Proceedings of IEEE","volume":"104","author":"Shahriari Bobak","year":"2015","unstructured":"Bobak Shahriari, Kevin Swersky, Ziyu Wang, Ryan P. Adams, and Nando De Freitas. 2015. Taking the human out of the loop: A review of Bayesian optimization. Proceedings of IEEE 104, 1 (2015), 148\u2013175."},{"key":"e_1_3_2_59_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00158-020-02787-x"},{"key":"e_1_3_2_60_1","doi-asserted-by":"publisher","DOI":"10.1097\/00005053-195707000-00032"},{"key":"e_1_3_2_61_1","article-title":"Practical Bayesian optimization of machine learning algorithms","volume":"25","author":"Snoek Jasper","year":"2012","unstructured":"Jasper Snoek, Hugo Larochelle, and Ryan P. Adams. 2012. Practical Bayesian optimization of machine learning algorithms. Advances in Neural Information Processing Systems 25 (2012).","journal-title":"Advances in Neural Information Processing Systems"},{"key":"e_1_3_2_62_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10898-004-6733-1"},{"key":"e_1_3_2_63_1","unstructured":"Niranjan Srinivas Andreas Krause Sham M. Kakade and Matthias Seeger. 2009. Gaussian process optimization in the bandit setting: No regret and experimental design. arXiv:0912.3995. Retrieved from https:\/\/arxiv.org\/abs\/0912.3995"},{"key":"e_1_3_2_64_1","doi-asserted-by":"publisher","DOI":"10.1080\/00401706.1987.10488205"},{"key":"e_1_3_2_65_1","doi-asserted-by":"publisher","DOI":"10.1117\/12.148698"},{"key":"e_1_3_2_66_1","doi-asserted-by":"publisher","DOI":"10.1109\/CEC.2019.8789910"},{"key":"e_1_3_2_67_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2021.03.002"},{"key":"e_1_3_2_68_1","doi-asserted-by":"publisher","DOI":"10.1145\/3321707.3321715"},{"key":"e_1_3_2_69_1","doi-asserted-by":"publisher","DOI":"10.1007\/s12530-020-09345-2"},{"key":"e_1_3_2_70_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10462-021-10011-5"},{"key":"e_1_3_2_71_1","unstructured":"Hao Wang. 2018. Stochastic and Deterministic Algorithms for Continuous Black-Box Optimization. Ph.D. Dissertation. Leiden University."},{"key":"e_1_3_2_72_1","doi-asserted-by":"publisher","DOI":"10.1109\/SMC.2017.8122656"},{"key":"e_1_3_2_73_1","doi-asserted-by":"publisher","DOI":"10.1145\/3510426"},{"key":"e_1_3_2_74_1","unstructured":"Ziyu Wang and Nando de Freitas. 2014. Theoretical analysis of Bayesian optimisation with unknown Gaussian process hyper-parameters. arXiv:1406.7758. Retrieved from https:\/\/arxiv.org\/abs\/1406.7758"},{"key":"e_1_3_2_75_1","first-page":"3627","volume-title":"Proceedings of the 34th International Conference on Machine Learning","volume":"70","author":"Wang Zi","year":"2017","unstructured":"Zi Wang and Stefanie Jegelka. 2017. Max-value entropy search for efficient Bayesian optimization. In Proceedings of the 34th International Conference on Machine Learning, Vol. 70. PMLR, 3627\u20133635."},{"key":"e_1_3_2_76_1","doi-asserted-by":"publisher","DOI":"10.1108\/03321641211248291"},{"key":"e_1_3_2_77_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00158-022-03256-3"},{"key":"e_1_3_2_78_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10898-020-00923-x"},{"key":"e_1_3_2_79_1","doi-asserted-by":"publisher","DOI":"10.1145\/279232.279236"}],"container-title":["ACM Transactions on Evolutionary Learning and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3716504","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3716504","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T01:19:10Z","timestamp":1750295950000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3716504"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,5,15]]},"references-count":78,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2025,6,30]]}},"alternative-id":["10.1145\/3716504"],"URL":"https:\/\/doi.org\/10.1145\/3716504","relation":{},"ISSN":["2688-3007"],"issn-type":[{"value":"2688-3007","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,5,15]]},"assertion":[{"value":"2023-09-27","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-01-14","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-05-15","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}