{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:47:06Z","timestamp":1760240826107,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2019,9,24]],"date-time":"2019-09-24T00:00:00Z","timestamp":1569283200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61663046","61876166"],"award-info":[{"award-number":["61663046","61876166"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Open Foundation of Key Laboratory of Software Engineering of Yunnan Province","award":["2015SE204"],"award-info":[{"award-number":["2015SE204"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Information"],"abstract":"<jats:p>Since the beginning of the 21st century, research on artificial intelligence has made great progress. Bayesian networks have gradually become one of the hotspots and important achievements in artificial intelligence research. Establishing an effective Bayesian network structure is the foundation and core of the learning and application of Bayesian networks. In Bayesian network structure learning, the traditional method of utilizing expert knowledge to construct the network structure is gradually replaced by the data learning structure method. However, as a result of the large amount of possible network structures, the search space is too large. The method of Bayesian network learning through training data usually has the problems of low precision or high complexity, which make the structure of learning differ greatly from that of reality, which has a great influence on the reasoning and practical application of Bayesian networks. In order to solve this problem, a hybrid optimization artificial bee colony algorithm is discretized and applied to structure learning. A hybrid optimization technique for the Bayesian network structure learning method is proposed. Experimental simulation results show that the proposed hybrid optimization structure learning algorithm has better structure and better convergence.<\/jats:p>","DOI":"10.3390\/info10100294","type":"journal-article","created":{"date-parts":[[2019,9,25]],"date-time":"2019-09-25T03:51:18Z","timestamp":1569383478000},"page":"294","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Hybrid Optimization Algorithm for Bayesian Network Structure Learning"],"prefix":"10.3390","volume":"10","author":[{"given":"Xingping","family":"Sun","sequence":"first","affiliation":[{"name":"Software School, Yunnan University, Kunming 650091, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chang","family":"Chen","sequence":"additional","affiliation":[{"name":"Software School, Yunnan University, Kunming 650091, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lu","family":"Wang","sequence":"additional","affiliation":[{"name":"Software School, Yunnan University, Kunming 650091, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5466-7092","authenticated-orcid":false,"given":"Hongwei","family":"Kang","sequence":"additional","affiliation":[{"name":"Software School, Yunnan University, Kunming 650091, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yong","family":"Shen","sequence":"additional","affiliation":[{"name":"Software School, Yunnan University, Kunming 650091, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qingyi","family":"Chen","sequence":"additional","affiliation":[{"name":"Software School, Yunnan University, Kunming 650091, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,9,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1023\/A:1007465528199","article-title":"Bayesian Network Classifiers","volume":"29","author":"Friedman","year":"1997","journal-title":"Mach. Learn."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"931","DOI":"10.1007\/s11590-014-0803-1","article-title":"Structure Learning of Bayesian Networks using Global Optimization with Applications in Data Classification","volume":"9","author":"Taheri","year":"2015","journal-title":"Optim. Lett."},{"key":"ref_3","first-page":"434","article-title":"Probabilistic reasoning in intelligent systems: Networks of plausible inference","volume":"88","author":"Pearl","year":"1988","journal-title":"J. Philos."},{"key":"ref_4","first-page":"121","article-title":"Learning Bayesian Networks is NP-Hard","volume":"112","author":"Chickering","year":"1994","journal-title":"Networks"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"767","DOI":"10.1109\/TEVC.2009.2024142","article-title":"Using a local discovery ant algorithm for Bayesian network structure learning","volume":"13","author":"Pinto","year":"2009","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1145\/1282427.1282422","article-title":"DTN routing as a resource allocation problem","volume":"37","author":"Balasubramanian","year":"2007","journal-title":"ACM Sigcomm Comput. Commun. Rev."},{"key":"ref_7","first-page":"112","article-title":"Energy-efficient Intra-domain Routing Algorithm Based on Directed Acyclic Graph","volume":"45","author":"Geng","year":"2018","journal-title":"Comput. Sci."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1111\/j.2517-6161.1988.tb01721.x","article-title":"Local Computations with Probabilities on Graphical Structures and their Application to Expert Systems","volume":"50","author":"Lauritzen","year":"1988","journal-title":"J. R. Stat. Soc."},{"key":"ref_9","unstructured":"Robinson, R.W. (1976, January 24\u201326). Counting unlabeled acyclic digraphs. Proceedings of the Fifth Australian Conference on Combinatorial Mathematics V, Melbourne, Australia."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1290","DOI":"10.1038\/nprot.2011.308","article-title":"Quantitative prediction of cellular metabolism with constraint-based models: The COBRA Toolbox v2.0","volume":"6","author":"Schellenberger","year":"2011","journal-title":"Nat. Protoc."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Lee, C., and van Beek, P. (2017, January 16\u201319). Metaheuristics for Score-and-Search Bayesian Network Structure Learning. Proceedings of the 30th Canadian Conference on Artificial Intelligence, Canadian AI 2017, Edmonton, AB, Canada.","DOI":"10.1007\/978-3-319-57351-9_17"},{"key":"ref_12","first-page":"2149","article-title":"A Scoring Function for Learning Bayesian Networks based on Mutual Information and Conditional Independence Tests","volume":"7","author":"Campos","year":"2006","journal-title":"J. Mach. Learn. Res."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"716","DOI":"10.1109\/TAC.1974.1100705","article-title":"A New Look at the Statistical Model Identification","volume":"19","author":"Akaike","year":"1974","journal-title":"Autom. Control. IEEE Trans."},{"key":"ref_14","first-page":"514","article-title":"Estimating the dimension of a linear model","volume":"17","author":"Perez","year":"1981","journal-title":"Ann. Stat."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"975","DOI":"10.1007\/BF01009452","article-title":"Optimization by simulated annealing: Quantitative studies","volume":"34","author":"Kirkpatrick","year":"1984","journal-title":"J. Stat. Phys."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1007\/BF00994016","article-title":"Learning Bayesian Networks: The Combination of Knowledge and Statistical Data","volume":"20","author":"Heckerman","year":"1995","journal-title":"Mach. Learn."},{"key":"ref_17","first-page":"95","article-title":"Bayesian network structure learning method based on causal effect","volume":"35","author":"An","year":"2018","journal-title":"J. Comput. Appl."},{"key":"ref_18","unstructured":"Cao, J. (2019, September 22). Bayesian Network Structure Learning and Application Research. (In Chinese)."},{"key":"ref_19","first-page":"790","article-title":"Bayesian network structure learning based on fusion prior method","volume":"40","author":"Gao","year":"2018","journal-title":"Syst. Eng. Electron."},{"key":"ref_20","first-page":"2060","article-title":"Structure Learning Method of Bayesian Network with Hybrid Particle Swarm Optimization Algorithm","volume":"39","author":"Yu","year":"2018","journal-title":"Small Microcomput. Syst."},{"key":"ref_21","first-page":"124","article-title":"Ensemble learning artificial bee colony algorithm","volume":"46","author":"Du","year":"2019","journal-title":"J. Xidian Univ. (Natural Science Edition)"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"912","DOI":"10.1109\/34.537345","article-title":"Structure learning of Bayesian networks by genetic algorithms: A performance analysis of control parameters","volume":"18","author":"Larranaga","year":"1996","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_23","unstructured":"(2019, September 22). Bernoulli Process. Available online: https:\/\/link.springer.com\/referenceworkentry\/10.1007%2F978-1-4020-6754-9_1682."},{"key":"ref_24","first-page":"51","article-title":"Stochastic adaptive differential evolution algorithm","volume":"2","author":"Shen","year":"2018","journal-title":"Electron. Technol."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1023\/A:1008202821328","article-title":"Differential Evolution\u2014A Simple and Efficient Heuristic for global Optimization over Continuous Spaces","volume":"11","author":"Storn","year":"1997","journal-title":"J. Glob. Optim."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Tasgetiren, M.F., Pan, Q.K., Suganthan, P.N., Liang, Y.C., and Chua, T.J. (2009). Metaheuristics for Common due Date Total Earliness and Tardiness Single Machine Scheduling Problem, Springer.","DOI":"10.1007\/978-3-642-02836-6_10"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Beinlich, I.A., Suermondt, H.J., Chavez, R.M., and Cooper, G.F. (1989). The ALARM Monitoring System: A Case Study with Two Probabilistic Inference Techniques for Belief Networks, Springer.","DOI":"10.1007\/978-3-642-93437-7_28"},{"key":"ref_28","first-page":"325","article-title":"Bayesian Network Structure Learning Based on Artificial Bee Colony Algorithm","volume":"9","author":"Zhang","year":"2014","journal-title":"J. Intell. Syst."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"272","DOI":"10.1016\/j.ins.2016.01.090","article-title":"BNC-PSO: Structure learning of Bayesian networks by Particle Swarm Optimization","volume":"348","author":"Gheisari","year":"2016","journal-title":"Inf. Sci."},{"key":"ref_30","unstructured":"Chickering, D.M. (1996, January 1\u20134). Learning equivalence classes of Bayesian network structures. Proceedings of the Twelfth International Conference on Uncertainty in Artificial Intelligence, UAI\u201996, Portland, OR, USA."}],"container-title":["Information"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2078-2489\/10\/10\/294\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:23:37Z","timestamp":1760189017000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2078-2489\/10\/10\/294"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,9,24]]},"references-count":30,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2019,10]]}},"alternative-id":["info10100294"],"URL":"https:\/\/doi.org\/10.3390\/info10100294","relation":{},"ISSN":["2078-2489"],"issn-type":[{"type":"electronic","value":"2078-2489"}],"subject":[],"published":{"date-parts":[[2019,9,24]]}}}