{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,13]],"date-time":"2026-05-13T18:39:27Z","timestamp":1778697567210,"version":"3.51.4"},"reference-count":36,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2020,12,30]],"date-time":"2020-12-30T00:00:00Z","timestamp":1609286400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002858","name":"China Postdoctoral Science Foundation","doi-asserted-by":"publisher","award":["2018M642635"],"award-info":[{"award-number":["2018M642635"]}],"id":[{"id":"10.13039\/501100002858","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Science Foundation of China","doi-asserted-by":"publisher","award":["61972226, 31872242, 61872220, and 61902216"],"award-info":[{"award-number":["61972226, 31872242, 61872220, and 61902216"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Community detection is a hot research direction of network science, which is of great importance to complex system analysis. Therefore, many community detection methods have been developed. Among them, evolutionary computation based ones with a single-objective function are promising in either benchmark or real data sets. However, they also encounter resolution limit problem in several scenarios. In this paper, a Multi-Objective Pigeon-Inspired Optimization (MOPIO) method is proposed for community detection with Negative Ratio Association (NRA) and Ratio Cut (RC) as its objective functions. In MOPIO, the genetic operator is used to redefine the representation and updating of pigeons. In each iteration, NRA and RC are calculated for each pigeon, and Pareto sorting scheme is utilized to judge non-dominated solutions for later crossover. A crossover strategy based on global and personal bests is designed, in which a compensation coefficient is developed to stably complete the work transition between the map and compass operator, and the landmark operator. When termination criteria were met, a leader selection strategy is employed to determine the final result from the optimal solution set. Comparison experiments of MOPIO, with MOPSO, MOGA-Net, Meme-Net and FN, are performed on real-world networks, and results indicate that MOPIO has better performance in terms of Normalized Mutual information and Adjusted Rand Index.<\/jats:p>","DOI":"10.3390\/sym13010049","type":"journal-article","created":{"date-parts":[[2020,12,30]],"date-time":"2020-12-30T20:13:41Z","timestamp":1609359221000},"page":"49","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["MOPIO: A Multi-Objective Pigeon-Inspired Optimization Algorithm for Community Detection"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8488-2228","authenticated-orcid":false,"given":"Junliang","family":"Shang","sequence":"first","affiliation":[{"name":"School of Computer Science, Qufu Normal University, Rizhao 276826, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yiting","family":"Li","sequence":"additional","affiliation":[{"name":"School of Computer Science, Qufu Normal University, Rizhao 276826, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yan","family":"Sun","sequence":"additional","affiliation":[{"name":"School of Computer Science, Qufu Normal University, Rizhao 276826, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Feng","family":"Li","sequence":"additional","affiliation":[{"name":"School of Computer Science, Qufu Normal University, Rizhao 276826, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuanyuan","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Information and Control Engineering, Qingdao University of Technology, Qingdao 266000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6104-2149","authenticated-orcid":false,"given":"Jin-Xing","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Computer Science, Qufu Normal University, Rizhao 276826, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,12,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"440","DOI":"10.1016\/j.compbiolchem.2018.11.031","article-title":"HC-HDSD: A method of hypergraph construction and high-density subgraph detection for inferring high-order epistatic interactions","volume":"78","author":"Ding","year":"2019","journal-title":"Comput. 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