{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,24]],"date-time":"2025-11-24T07:10:08Z","timestamp":1763968208074,"version":"build-2065373602"},"reference-count":59,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2017,2,22]],"date-time":"2017-02-22T00:00:00Z","timestamp":1487721600000},"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>Control of gene regulatory networks is one of the fundamental topics in systems biology. In the last decade, control theory of Boolean networks (BNs), which is well known as a model of gene regulatory networks, has been widely studied. In this review paper, our previously proposed methods on optimal control of probabilistic Boolean networks (PBNs) are introduced. First, the outline of PBNs is explained. Next, an optimal control method using polynomial optimization is explained. The finite-time optimal control problem is reduced to a polynomial optimization problem. Furthermore, another finite-time optimal control problem, which can be reduced to an integer programming problem, is also explained.<\/jats:p>","DOI":"10.3390\/a10010031","type":"journal-article","created":{"date-parts":[[2017,2,22]],"date-time":"2017-02-22T11:36:58Z","timestamp":1487763418000},"page":"31","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Optimization-Based Approaches to Control of Probabilistic Boolean Networks"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3358-0254","authenticated-orcid":false,"given":"Koichi","family":"Kobayashi","sequence":"first","affiliation":[{"name":"Graduate School of Information Science and Technology, Hokkaido University, Kita 14, Nishi 9, Kita-ku, Sapporo 060-0814, Hokkaido, Japan"}]},{"given":"Kunihiko","family":"Hiraishi","sequence":"additional","affiliation":[{"name":"School of Information Science, Japan Advanced Institute of Science and Technology, 1-1 Asahidai, Nomi, Ishikawa 923-1292, Japan"}]}],"member":"1968","published-online":{"date-parts":[[2017,2,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1662","DOI":"10.1126\/science.1069492","article-title":"Systems biology: A brief overview","volume":"295","author":"Kitano","year":"2002","journal-title":"Science"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"206","DOI":"10.1038\/nature01254","article-title":"Computational systems biology","volume":"420","author":"Kitano","year":"2002","journal-title":"Nature"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"2381","DOI":"10.1016\/j.ejca.2005.08.010","article-title":"Chromatin modifier enzymes, the histone code and cancer","volume":"41","author":"Caldas","year":"2005","journal-title":"Eur. 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