{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T04:04:16Z","timestamp":1776657856149,"version":"3.51.2"},"reference-count":25,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2019,1,10]],"date-time":"2019-01-10T00:00:00Z","timestamp":1547078400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Foundation of Liaoning Educational Committee","award":[".L2015265"],"award-info":[{"award-number":[".L2015265"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>Quality of service multicast routing is an important research topic in networks. Research has sought to obtain a multicast routing tree at the lowest cost that satisfies bandwidth, delay and delay jitter constraints. Due to its non-deterministic polynomial complete problem, many meta-heuristic algorithms have been adopted to solve this kind of problem. The paper presents a new hybrid algorithm, namely ACO&amp;CM, to solve the problem. The primary innovative point is to combine the solution generation process of ant colony optimization (ACO) algorithm with the Cloud model (CM). Moreover, within the framework structure of the ACO, we embed the cloud model in the ACO algorithm to enhance the performance of the ACO algorithm by adjusting the pheromone trail on the edges. Although a high pheromone trail intensity on some edges may trap into local optimum, the pheromone updating strategy based on the CM is used to search for high-quality areas. In order to avoid the possibility of loop formation, we devise a memory detection search (MDS) strategy, and integrate it into the path construction process. Finally, computational results demonstrate that the hybrid algorithm has advantages of an efficient and excellent performance for the solution quality.<\/jats:p>","DOI":"10.3390\/a12010018","type":"journal-article","created":{"date-parts":[[2019,1,11]],"date-time":"2019-01-11T04:10:16Z","timestamp":1547179816000},"page":"18","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["A Novel Hybrid Ant Colony Optimization for a Multicast Routing Problem"],"prefix":"10.3390","volume":"12","author":[{"given":"Xiaoxia","family":"Zhang","sequence":"first","affiliation":[{"name":"College of Software Engineering, University of Science and Technology LiaoNing, Anshan 114051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xin","family":"Shen","sequence":"additional","affiliation":[{"name":"College of Software Engineering, University of Science and Technology LiaoNing, Anshan 114051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ziqiao","family":"Yu","sequence":"additional","affiliation":[{"name":"College of Software Engineering, University of Science and Technology LiaoNing, Anshan 114051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,1,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1953","DOI":"10.1016\/j.cor.2003.12.007","article-title":"A survey of combinatorial optimization problems in multicast routing","volume":"32","author":"Oliveira","year":"2005","journal-title":"Comput. 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