{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:41:27Z","timestamp":1760150487321,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2023,12,1]],"date-time":"2023-12-01T00:00:00Z","timestamp":1701388800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001807","name":"Sao Paulo Research Foundation (FAPESP)","doi-asserted-by":"publisher","award":["2018\/23139-8"],"award-info":[{"award-number":["2018\/23139-8"]}],"id":[{"id":"10.13039\/501100001807","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["MAKE"],"abstract":"<jats:p>A Bayesian network (BN) is a probabilistic graphical model that can model complex and nonlinear relationships. Its structural learning from data is an NP-hard problem because of its search-space size. One method to perform structural learning is a search and score approach, which uses a search algorithm and structural score. A study comparing 15 algorithms showed that hill climbing (HC) and tabu search (TABU) performed the best overall on the tests. This work performs a deeper analysis of the application of the adaptive genetic algorithm with varying population size (AGAVaPS) on the BN structural learning problem, which a preliminary test showed that it had the potential to perform well on. AGAVaPS is a genetic algorithm that uses the concept of life, where each solution is in the population for a number of iterations. Each individual also has its own mutation rate, and there is a small probability of undergoing mutation twice. Parameter analysis of AGAVaPS in BN structural leaning was performed. Also, AGAVaPS was compared to HC and TABU for six literature datasets considering F1 score, structural Hamming distance (SHD), balanced scoring function (BSF), Bayesian information criterion (BIC), and execution time. HC and TABU performed basically the same for all the tests made. AGAVaPS performed better than the other algorithms for F1 score, SHD, and BIC, showing that it can perform well and is a good choice for BN structural learning.<\/jats:p>","DOI":"10.3390\/make5040090","type":"journal-article","created":{"date-parts":[[2023,12,1]],"date-time":"2023-12-01T04:12:56Z","timestamp":1701403976000},"page":"1877-1887","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Bayesian Network Structural Learning Using Adaptive Genetic Algorithm with Varying Population Size"],"prefix":"10.3390","volume":"5","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9616-2738","authenticated-orcid":false,"given":"Rafael","family":"Rodrigues Mendes Ribeiro","sequence":"first","affiliation":[{"name":"Department of Electrical and Computing Engineering, University of S\u00e3o Paulo, S\u00e3o Carlos 13566-590, SP, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0137-6678","authenticated-orcid":false,"given":"Carlos","family":"Dias Maciel","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computing Engineering, University of S\u00e3o Paulo, S\u00e3o Carlos 13566-590, SP, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,12,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"101224","DOI":"10.1016\/j.swevo.2022.101224","article-title":"An efficient Bayesian network structure learning algorithm based on structural information","volume":"76","author":"Fang","year":"2023","journal-title":"Swarm Evol. Comput."},{"doi-asserted-by":"crossref","unstructured":"Tian, T., Kong, F., Yang, R., Long, X., Chen, L., Li, M., Li, Q., Hao, Y., He, Y., and Zhang, Y. (2023). A Bayesian network model for prediction of low or failed fertilization in assisted reproductive technology based on a large clinical real-world data. Reprod. Biol. Endocrinol., 21.","key":"ref_2","DOI":"10.1186\/s12958-023-01065-x"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"117209","DOI":"10.1016\/j.jenvman.2022.117209","article-title":"A probabilistic decision support tool for prediction and management of rainfall-related poor water quality events for a drinking water treatment plant","volume":"332","author":"Bertone","year":"2023","journal-title":"J. Environ. Manag."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"3103","DOI":"10.5194\/hess-26-3103-2022","article-title":"Seasonal forecasting of lake water quality and algal bloom risk using a continuous Gaussian Bayesian network","volume":"26","author":"Clayer","year":"2022","journal-title":"Hydrol. Earth Syst. Sci."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"8641","DOI":"10.1007\/s10489-021-02362-x","article-title":"Transfer learning of Bayesian network for measuring QoS of virtual machines","volume":"51","author":"Hao","year":"2021","journal-title":"Appl. Intell."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1007\/s10489-018-1274-3","article-title":"Causal inference and Bayesian network structure learning from nominal data","volume":"49","author":"Luo","year":"2019","journal-title":"Appl. Intell."},{"unstructured":"Koller, D., and Friedman, N. (2009). Probabilistic Graphical Models: Principles and Techniques, MIT Press.","key":"ref_7"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1007\/s12243-022-00940-9","article-title":"A novel network traffic prediction method based on a Bayesian network model for establishing the relationship between traffic and population","volume":"78","author":"Shiomoto","year":"2023","journal-title":"Ann. Telecommun."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"104961","DOI":"10.1016\/j.jlp.2022.104961","article-title":"Dynamic risk assessment for underground gas storage facilities based on Bayesian network","volume":"82","author":"Xu","year":"2023","journal-title":"J. Loss Prev. Process. Ind."},{"unstructured":"Neapolitan, R. (2003). Learning Bayesian Networks, Pearson Prentice Hall.","key":"ref_10"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1016\/j.knosys.2019.03.014","article-title":"An analytical threshold for combining Bayesian Networks","volume":"175","author":"Gross","year":"2019","journal-title":"Knowl. Based Syst."},{"unstructured":"Little, C.H.C. (1977). Combinatorial Mathematics V, Proceedings of the Fifth Australian Conference, Melbourne, Australia, 24\u201326 August 1976, Springer.","key":"ref_12"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"012179","DOI":"10.1088\/1742-6596\/1818\/1\/012179","article-title":"The Applications of NP-hardness optimizations problem","volume":"1818","author":"Alridha","year":"2021","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1016\/j.ijar.2021.01.001","article-title":"Large-scale empirical validation of Bayesian Network structure learning algorithms with noisy data","volume":"131","author":"Constantinou","year":"2021","journal-title":"Int. J. Approx. Reason."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1007\/s10462-018-9615-5","article-title":"Bayesian network hybrid learning using an elite-guided genetic algorithm","volume":"52","author":"Contaldi","year":"2019","journal-title":"Artif. Intell. Rev."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"8721","DOI":"10.1007\/s10462-022-10351-w","article-title":"A survey of Bayesian Network structure learning","volume":"56","author":"Kitson","year":"2023","journal-title":"Artif. Intell. Rev."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1095","DOI":"10.1007\/s11222-019-09857-1","article-title":"Learning Bayesian networks from big data with greedy search: Computational complexity and efficient implementation","volume":"29","author":"Scutari","year":"2021","journal-title":"Stat. Comput."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"108426","DOI":"10.1016\/j.knosys.2022.108426","article-title":"A novel discrete firefly algorithm for Bayesian network structure learning","volume":"242","author":"Wang","year":"2022","journal-title":"Knowl. Based Syst."},{"doi-asserted-by":"crossref","unstructured":"Yu, Y., Luo, S., He, Y., Huang, H., and Zhang, W. (2022, January 30\u201331). A Prufer-leaf Coding Genetic Algorithm for Bayesian Network Structure Learning. Proceedings of the 2022 Global Conference on Robotics, Artificial Intelligence and Information Technology (GCRAIT), Chicago, IL, USA.","key":"ref_19","DOI":"10.1109\/GCRAIT55928.2022.00044"},{"doi-asserted-by":"crossref","unstructured":"Ribeiro, R.R.M., and Maciel, C.D. (2022, January 18\u201323). AGAVaPS\u2014Adaptive Genetic Algorithm with Varying Population Size. Proceedings of the 2022 IEEE Congress on Evolutionary Computation (CEC), Padua, Italy.","key":"ref_20","DOI":"10.1109\/CEC55065.2022.9870394"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1007\/s10928-006-9004-6","article-title":"A Genetic Algorithm-Based, Hybrid Machine Learning Approach to Model Selection","volume":"33","author":"Bies","year":"2006","journal-title":"J. Pharmacokinet. Pharmacodyn."},{"key":"ref_22","first-page":"2149","article-title":"A Scoring Function for Learning Bayesian Networks Based on Mutual Information and Conditional Independence Tests","volume":"7","year":"2006","journal-title":"J. Mach. Learn. Res."},{"doi-asserted-by":"crossref","unstructured":"Ankan, A., and Panda, A. (2015, January 6\u201312). pgmpy: Probabilistic graphical models using python. Proceedings of the 14th Python in Science Conference (SCIPY 2015), Austin, TX, USA.","key":"ref_23","DOI":"10.25080\/Majora-7b98e3ed-001"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1","DOI":"10.18637\/jss.v035.i03","article-title":"Learning Bayesian Networks with the bnlearn R Package","volume":"35","author":"Scutari","year":"2010","journal-title":"J. Stat. Softw."},{"doi-asserted-by":"crossref","unstructured":"Chicco, D., and Jurman, G. (2020). The advantages of the Matthews correlation coefficient (MCC) over F1 score and accuracy in binary classification evaluation. BMC Genom., 21.","key":"ref_25","DOI":"10.1186\/s12864-019-6413-7"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1007\/s10994-006-6889-7","article-title":"The max-min hill-climbing Bayesian network structure learning algorithm","volume":"65","author":"Tsamardinos","year":"2006","journal-title":"Mach. Learn."},{"unstructured":"Constantinou, A.C. (2020). Evaluating structure learning algorithms with a balanced scoring function. arXiv.","key":"ref_27"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"103384","DOI":"10.1016\/j.engappai.2019.103384","article-title":"Uncertainties in conditional probability tables of discrete Bayesian Belief Networks: A comprehensive review","volume":"88","author":"Rohmer","year":"2020","journal-title":"Eng. Appl. Artif. Intell."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"396","DOI":"10.1016\/j.procs.2019.08.231","article-title":"The Comparison Firebase Realtime Database and MySQL Database Performance using Wilcoxon Signed-Rank Test","volume":"157","author":"Ohyver","year":"2019","journal-title":"Procedia Comput. Sci."}],"container-title":["Machine Learning and Knowledge Extraction"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2504-4990\/5\/4\/90\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T21:35:47Z","timestamp":1760132147000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2504-4990\/5\/4\/90"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,12,1]]},"references-count":29,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2023,12]]}},"alternative-id":["make5040090"],"URL":"https:\/\/doi.org\/10.3390\/make5040090","relation":{},"ISSN":["2504-4990"],"issn-type":[{"type":"electronic","value":"2504-4990"}],"subject":[],"published":{"date-parts":[[2023,12,1]]}}}