{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,26]],"date-time":"2026-07-26T02:18:10Z","timestamp":1785032290711,"version":"3.55.0"},"reference-count":31,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2023,4,19]],"date-time":"2023-04-19T00:00:00Z","timestamp":1681862400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Princess Nourah bint Abdulrahman University Researchers","award":["PNURSP2023R195"],"award-info":[{"award-number":["PNURSP2023R195"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This article addresses the problem of converting a single-objective combinatorial problem into a multi-objective one using the Pareto front approach. Although existing algorithms can identify the optimal solution in a multi-objective space, they fail to satisfy constraints while achieving optimal performance. To address this issue, we propose a multi-objective artificial bee colony optimization algorithm with a classical multi-objective theme called fitness sharing. This approach helps the convergence of the Pareto solution set towards a single optimal solution that satisfies multiple objectives. This article introduces multi-objective optimization with an example of a non-dominated sequencing technique and fitness sharing approach. The experimentation is carried out in MATLAB 2018a. In addition, we applied the proposed algorithm to two different real-time datasets, namely the knapsack problem and the nurse scheduling problem (NSP). The outcome of the proposed MBABC-NM algorithm is evaluated using standard performance indicators such as average distance, number of reference solutions (NRS), overall count of attained solutions (TNS), and overall non-dominated generation volume (ONGV). The results show that it outperforms other algorithms.<\/jats:p>","DOI":"10.3390\/axioms12040395","type":"journal-article","created":{"date-parts":[[2023,4,20]],"date-time":"2023-04-20T02:01:11Z","timestamp":1681956071000},"page":"395","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Multi-Objective ABC-NM Algorithm for Multi-Dimensional Combinatorial Optimization Problem"],"prefix":"10.3390","volume":"12","author":[{"given":"Muniyan","family":"Rajeswari","sequence":"first","affiliation":[{"name":"Department of Computer Science and Engineering, Sri Manakula Vinayagar Engineering College, Pondicherry 605107, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0734-3423","authenticated-orcid":false,"given":"Rajakumar","family":"Ramalingam","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Technology, Madanapalle Institute of Technology and Science, Madanapalle 517325, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9032-9560","authenticated-orcid":false,"given":"Shakila","family":"Basheer","sequence":"additional","affiliation":[{"name":"Department of Information Systems, College of Computer and Information Science, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Keerthi Samhitha","family":"Babu","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Information Technology, KL Deemed to be University, Guntur District, Vaddeswaram 522302, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8302-4571","authenticated-orcid":false,"given":"Mamoon","family":"Rashid","sequence":"additional","affiliation":[{"name":"Department of Computer Engineering, Faculty of Science and Technology, Vishwakarma University, Pune 411048, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ramar","family":"Saranya","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Engineering, Manonmaniam Sundaranar University, Tirunelveli 627012, India"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,4,19]]},"reference":[{"key":"ref_1","first-page":"493","article-title":"Messy genetic algorithms: Motivation, analysis, and first results","volume":"3","author":"Goldberg","year":"1989","journal-title":"Complex Syst."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2268","DOI":"10.1007\/s10489-017-1074-1","article-title":"MOGOA algorithm for constrained and unconstrained multi-objective optimization problems","volume":"48","author":"Tharwat","year":"2018","journal-title":"Appl. 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