{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:53:58Z","timestamp":1777704838528,"version":"3.51.4"},"reference-count":14,"publisher":"SAGE Publications","issue":"6","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IFS"],"published-print":{"date-parts":[[2023,12,2]]},"abstract":"<jats:p>Bandwidth consecutive multicoloring problem is also known as a b-coloring problem. Let G\u00a0=\u00a0(V, E) be a graph where V is the set of vertices and E is the set of edges. Let each vertex v of V has a positive integer weight b\u00a0(v) and each edge (v, w) of E has a non-negative integer weight b\u00a0(v, w). A bandwidth consecutive multicoloring of a graph is a problem of assigning b\u00a0(v) consecutive positive integers to each vertex v of V in such a manner that the difference between all the integers of vertex v and all the integers of vertex w is greater than b\u00a0(v, w). The maximum integer assigned in this coloring is called the span of the coloring. The b-coloring is the problem of minimizing this span. No metaheuristic is proposed for general graphs so far for this problem till date as it is strongly NP-hard. In this paper, we proposed three heuristics for the problem including a greedy randomized adaptive search procedure (GRASP). The efficiency of these algorithms is tested on benchmark graphs and their performance is compared among themselves. Experimental results showed that among all three proposed heuristics, GRASP performed well for the given problem.<\/jats:p>","DOI":"10.3233\/jifs-224242","type":"journal-article","created":{"date-parts":[[2023,9,15]],"date-time":"2023-09-15T11:11:27Z","timestamp":1694776287000},"page":"9991-10002","source":"Crossref","is-referenced-by-count":0,"title":["Heuristic approach for bandwidth consecutive multi-coloring problem"],"prefix":"10.1177","volume":"45","author":[{"given":"Stuti","family":"Srivastava","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Dayalbagh Educational Institute, Agra, U.P., India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Richa","family":"Bansal","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Dayalbagh Educational Institute, Agra, U.P., India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Antika","family":"Thapar","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Dayalbagh Educational Institute, Agra, U.P., India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","reference":[{"issue":"1","key":"10.3233\/JIFS-224242_ref1","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/j.swevo.2011.02.002","article-title":"A practicaltutorial on the use of non-parametricstatistical tests as a methodology for comparing evolutionary andswarm intelligence algorithms","volume":"1","author":"Derrac","year":"2011","journal-title":"Swarm and EvolutionaryComputation"},{"key":"10.3233\/JIFS-224242_ref2","doi-asserted-by":"crossref","first-page":"1949","DOI":"10.1051\/ro\/2020065","article-title":"Integer and constraint programming approach for providing optimality to the bandwidth multicoloring problem","volume":"55","author":"Dias","year":"2021","journal-title":"RAIRO-Oper. 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Algorithms for Bandwidth Consecutive Multicolorings of Graphs. In: Snoeyink J., Lu P., Su K. and Wang L. (eds) Frontiers in Algorithmics and Algorithmic Aspects in Information and Management. Lecture Notes in Computer Science, vol 7285. (2012), Springer, Berlin, Heidelberg.","DOI":"10.1007\/978-3-642-29700-7_11"},{"key":"10.3233\/JIFS-224242_ref13","doi-asserted-by":"crossref","first-page":"6472","DOI":"10.1016\/j.tcs.2013.02.015","article-title":"Bandwidth consecutive multicolorings of graphs","volume":"532","author":"Nishikawa","year":"2014","journal-title":"Theoretical Computer Science"},{"key":"10.3233\/JIFS-224242_ref14","doi-asserted-by":"crossref","first-page":"208220","DOI":"10.1016\/j.tcs.2015.07.052","article-title":"Efficient approximation algorithms for bandwidth consecutive multicolorings of graphs","volume":"607","author":"Obata","year":"2015","journal-title":"Theoretical Computer Science"},{"issue":"2","key":"10.3233\/JIFS-224242_ref15","first-page":"309","article-title":"Scheduling: Theory, Algorithms and Systems","volume":"14","author":"Pinedo","year":"2008","journal-title":"Springer Science, New York"}],"container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"original-title":[],"link":[{"URL":"https:\/\/content.iospress.com\/download?id=10.3233\/JIFS-224242","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T09:42:08Z","timestamp":1777455728000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/full\/10.3233\/JIFS-224242"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,12,2]]},"references-count":14,"journal-issue":{"issue":"6"},"URL":"https:\/\/doi.org\/10.3233\/jifs-224242","relation":{},"ISSN":["1064-1246","1875-8967"],"issn-type":[{"value":"1064-1246","type":"print"},{"value":"1875-8967","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,12,2]]}}}