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The algorithm is based on the \u201cBranch and Cut\u201d principle, which combines the <jats:italic>branching process<\/jats:italic> to ensure decision variables\u2019 integrity and <jats:italic>efficient cuts<\/jats:italic> built off the non-increasing gradients\u2019 directions of objective functions to eliminate inefficient integer solutions. The proposed approach accelerates the convergence to the efficient solution that optimizes the utility function. After presenting and describing the algorithm, a detailed didactic example is illustrated, followed by an experimental study to validate our approach and show computational costs.<\/jats:p>","DOI":"10.1051\/ro\/2024003","type":"journal-article","created":{"date-parts":[[2024,1,3]],"date-time":"2024-01-03T19:50:21Z","timestamp":1704311421000},"page":"741-758","source":"Crossref","is-referenced-by-count":1,"title":["Linear fractional optimization over the efficient set of multi-objective integer quadratic problem"],"prefix":"10.1051","volume":"58","author":[{"given":"Ali","family":"Bencheikh","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2013-356X","authenticated-orcid":false,"given":"Mustapha","family":"Moula\u00ef","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"250","published-online":{"date-parts":[[2024,2,22]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","first-page":"1140","DOI":"10.1016\/j.ejor.2005.02.072","volume":"174","author":"Abbas","year":"2006","journal-title":"Eur. 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