{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,3]],"date-time":"2026-03-03T02:14:03Z","timestamp":1772504043663,"version":"3.50.1"},"reference-count":97,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2021,10,28]],"date-time":"2021-10-28T00:00:00Z","timestamp":1635379200000},"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>In this paper, a discrete moth\u2013flame optimization algorithm for community detection (DMFO-CD) is proposed. The representation of solution vectors, initialization, and movement strategy of the continuous moth\u2013flame optimization are purposely adapted in DMFO-CD such that it can solve the discrete community detection. In this adaptation, locus-based adjacency representation is used to represent the position of moths and flames, and the initialization process is performed by considering the community structure and the relation between nodes without the need of any knowledge about the number of communities. Solution vectors are updated by the adapted movement strategy using a single-point crossover to distance imitating, a two-point crossover to calculate the movement, and a single-point neighbor-based mutation that can enhance the exploration and balance exploration and exploitation. The fitness function is also defined based on modularity. The performance of DMFO-CD was evaluated on eleven real-world networks, and the obtained results were compared with five well-known algorithms in community detection, including GA-Net, DPSO-PDM, GACD, EGACD, and DECS in terms of modularity, NMI, and the number of detected communities. Additionally, the obtained results were statistically analyzed by the Wilcoxon signed-rank and Friedman tests. In the comparison with other comparative algorithms, the results show that the proposed DMFO-CD is competitive to detect the correct number of communities with high modularity.<\/jats:p>","DOI":"10.3390\/a14110314","type":"journal-article","created":{"date-parts":[[2021,10,28]],"date-time":"2021-10-28T23:50:28Z","timestamp":1635465028000},"page":"314","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":40,"title":["DMFO-CD: A Discrete Moth-Flame Optimization Algorithm for Community Detection"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0135-1115","authenticated-orcid":false,"given":"Mohammad H.","family":"Nadimi-Shahraki","sequence":"first","affiliation":[{"name":"Faculty of Computer Engineering, Najafabad Branch, Islamic Azad University, Najafabad 1584743311, Iran"},{"name":"Big Data Research Center, Najafabad Branch, Islamic Azad University, Najafabad 1584743311, Iran"}]},{"given":"Ebrahim","family":"Moeini","sequence":"additional","affiliation":[{"name":"Faculty of Computer Engineering, Najafabad Branch, Islamic Azad University, Najafabad 1584743311, Iran"},{"name":"Big Data Research Center, Najafabad Branch, Islamic Azad University, Najafabad 1584743311, Iran"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8872-8455","authenticated-orcid":false,"given":"Shokooh","family":"Taghian","sequence":"additional","affiliation":[{"name":"Faculty of Computer Engineering, Najafabad Branch, Islamic Azad University, Najafabad 1584743311, Iran"},{"name":"Big Data Research Center, Najafabad Branch, Islamic Azad University, Najafabad 1584743311, Iran"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1443-9458","authenticated-orcid":false,"given":"Seyedali","family":"Mirjalili","sequence":"additional","affiliation":[{"name":"Centre for Artificial Intelligence Research and Optimisation, Torrens University Australia, Fortitude Valley, QLD 4006, Australia"},{"name":"Yonsei Frontier Lab, Yonsei University, Seoul 03722, Korea"}]}],"member":"1968","published-online":{"date-parts":[[2021,10,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"194","DOI":"10.1016\/j.asoc.2016.11.025","article-title":"Community detection from biological and social networks: A comparative analysis of metaheuristic algorithms","volume":"50","author":"Atay","year":"2017","journal-title":"Appl. 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