{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,5]],"date-time":"2026-06-05T05:25:40Z","timestamp":1780637140607,"version":"3.54.1"},"reference-count":54,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2024,3,30]],"date-time":"2024-03-30T00:00:00Z","timestamp":1711756800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001602","name":"Science Foundation Ireland","doi-asserted-by":"publisher","award":["12\/RC\/2289-P2"],"award-info":[{"award-number":["12\/RC\/2289-P2"]}],"id":[{"id":"10.13039\/501100001602","id-type":"DOI","asserted-by":"publisher"}]},{"name":"European Regional Development Fund","award":["12\/RC\/2289-P2"],"award-info":[{"award-number":["12\/RC\/2289-P2"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>In a multi-objective optimization problem, a decision maker has more than one objective to optimize. In a bilevel optimization problem, there are the following two decision-makers in a hierarchy: a leader who makes the first decision and a follower who reacts, each aiming to optimize their own objective. Many real-world decision-making processes have various objectives to optimize at the same time while considering how the decision-makers affect each other. When both features are combined, we have a multi-objective bilevel optimization problem, which arises in manufacturing, logistics, environmental economics, defence applications and many other areas. Many exact and approximation-based techniques have been proposed, but because of the intrinsic nonconvexity and conflicting multiple objectives, their computational cost is high. We propose a hybrid algorithm based on batch Bayesian optimization to approximate the upper-level Pareto-optimal solution set. We also extend our approach to handle uncertainty in the leader\u2019s objectives via a hypervolume improvement-based acquisition function. Experiments show that our algorithm is more efficient than other current methods while successfully approximating Pareto-fronts.<\/jats:p>","DOI":"10.3390\/a17040146","type":"journal-article","created":{"date-parts":[[2024,3,31]],"date-time":"2024-03-31T13:28:00Z","timestamp":1711891680000},"page":"146","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Multi-Objective BiLevel Optimization by Bayesian Optimization"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3807-5425","authenticated-orcid":false,"given":"Vedat","family":"Dogan","sequence":"first","affiliation":[{"name":"Insight Centre for Data Analytics, School of Computer Science and Information Technology, University College Cork, T12 XF62 Cork, Ireland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6218-9158","authenticated-orcid":false,"given":"Steven","family":"Prestwich","sequence":"additional","affiliation":[{"name":"Insight Centre for Data Analytics, School of Computer Science and Information Technology, University College Cork, T12 XF62 Cork, Ireland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,3,30]]},"reference":[{"key":"ref_1","unstructured":"Stackelberg, H.v. 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