{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,8]],"date-time":"2026-05-08T14:11:02Z","timestamp":1778249462210,"version":"3.51.4"},"reference-count":53,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2022,11,26]],"date-time":"2022-11-26T00:00:00Z","timestamp":1669420800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>Bayesian Optimization (BO) with Gaussian process regression is a popular framework for the optimization of time-consuming cost functions. However, the joint exploitation of BO and parallel processing capabilities remains challenging, despite intense research efforts over the last decade. In particular, the choice of a suitable batch-acquisition process, responsible for selecting promising candidate solutions for batch-parallel evaluation, is crucial. Even though some general recommendations can be found in the literature, many of its hyperparameters remain problem-specific. Moreover, the limitations of existing approaches in terms of scalability, especially for moderately expensive objective functions, are barely discussed. This work investigates five parallel BO algorithms based on different batch-acquisition processes, applied to the optimal scheduling of Underground Pumped Hydro-Energy Storage stations and classical benchmark functions. Efficient management of such energy-storage units requires parallel BO algorithms able to find solutions in a very restricted time to comply with the responsive energy markets. Our experimental results show that for the considered methods, a batch of four candidates is a good trade-off between execution speed and relevance of the candidates. Analysis of each method\u2019s strengths and weaknesses indicates possible future research directions.<\/jats:p>","DOI":"10.3390\/a15120446","type":"journal-article","created":{"date-parts":[[2022,11,28]],"date-time":"2022-11-28T04:56:25Z","timestamp":1669611385000},"page":"446","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Batch Acquisition for Parallel Bayesian Optimization\u2014Application to Hydro-Energy Storage Systems Scheduling"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4925-4995","authenticated-orcid":false,"given":"Maxime","family":"Gobert","sequence":"first","affiliation":[{"name":"Mathematics and Operational Research, University of Mons, 7000 Mons, Belgium"},{"name":"BONUS Team, Inria Lille-Nord Europe, 59600 Villeneuve d\u2019Ascq, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9635-4396","authenticated-orcid":false,"given":"Jan","family":"Gmys","sequence":"additional","affiliation":[{"name":"BONUS Team, Inria Lille-Nord Europe, 59600 Villeneuve d\u2019Ascq, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9853-2694","authenticated-orcid":false,"given":"Jean-Fran\u00e7ois","family":"Toubeau","sequence":"additional","affiliation":[{"name":"Power Systems and Markets Research, University of Mons, 7000 Mons, Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nouredine","family":"Melab","sequence":"additional","affiliation":[{"name":"BONUS Team, Inria Lille-Nord Europe, 59600 Villeneuve d\u2019Ascq, France"},{"name":"CNRS\/CRIStAL, University of Lille, 59600 Lille, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Daniel","family":"Tuyttens","sequence":"additional","affiliation":[{"name":"Mathematics and Operational Research, University of Mons, 7000 Mons, Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2409-2128","authenticated-orcid":false,"given":"Fran\u00e7ois","family":"Vall\u00e9e","sequence":"additional","affiliation":[{"name":"Power Systems and Markets Research, University of Mons, 7000 Mons, Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,11,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2815","DOI":"10.1109\/TPWRS.2020.3046710","article-title":"Data-Driven Scheduling of Energy Storage in Day-Ahead Energy and Reserve Markets With Probabilistic Guarantees on Real-Time Delivery","volume":"36","author":"Toubeau","year":"2021","journal-title":"IEEE Trans. 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