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The first algorithm proposes improvements to an existing algorithm employing a decomposition and search procedure in finding a new point. Differently, the second algorithm maximizes one of the criteria throughout the algorithm and generates new points by setting bounds on the linear function value. The decomposition and search procedure in the algorithms is accompanied by problem\u2010specific mechanisms in order to explore the objective function space efficiently. The algorithms are designed to produce solutions that meet a prespecified accuracy level. We conduct experiments on multiobjective combinatorial optimization problems and show that the algorithms work\u00a0well.<\/jats:p>","DOI":"10.1111\/itor.12627","type":"journal-article","created":{"date-parts":[[2019,1,21]],"date-time":"2019-01-21T05:20:03Z","timestamp":1548048003000},"page":"2248-2267","update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Optimizing a linear function over the nondominated set of multiobjective integer programs"],"prefix":"10.1111","volume":"28","author":[{"ORCID":"http:\/\/orcid.org\/0000-0002-6664-9430","authenticated-orcid":false,"given":"Banu","family":"Lokman","sequence":"first","affiliation":[{"name":"Portsmouth Business School University of Portsmouth Richmond Building, Portland Street Portsmouth PO1 3DE UK"}]}],"member":"311","published-online":{"date-parts":[[2019,1,20]]},"reference":[{"key":"e_1_2_6_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2005.02.072"},{"key":"e_1_2_6_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(84)90269-5"},{"key":"e_1_2_6_4_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02196590"},{"key":"e_1_2_6_5_1","doi-asserted-by":"publisher","DOI":"10.1007\/s12532-015-0093-3"},{"key":"e_1_2_6_6_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2016.02.037"},{"key":"e_1_2_6_7_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10898-014-0205-z"},{"key":"e_1_2_6_8_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02207641"},{"key":"e_1_2_6_9_1","doi-asserted-by":"publisher","DOI":"10.1007\/b101915"},{"key":"e_1_2_6_10_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02578918"},{"key":"e_1_2_6_11_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4939-3094-4_19"},{"key":"e_1_2_6_12_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10898-003-3784-7"},{"key":"e_1_2_6_13_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2008.02.005"},{"key":"e_1_2_6_14_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2013.08.001"},{"key":"e_1_2_6_15_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10898-014-0227-6"},{"key":"e_1_2_6_16_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10898-014-0212-0"},{"key":"e_1_2_6_17_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10898-012-9955-7"},{"key":"e_1_2_6_18_1","volume-title":"An algorithm for optimizing a linear function over the integer efficient set","author":"Nguyen N.C.","year":"1992"},{"key":"e_1_2_6_19_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2008.10.023"},{"key":"e_1_2_6_20_1","doi-asserted-by":"publisher","DOI":"10.1016\/0377-2217(95)00184-0"},{"key":"e_1_2_6_21_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2013.09.001"}],"container-title":["International Transactions in Operational Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1111%2Fitor.12627","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1111\/itor.12627","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1111\/itor.12627","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1111\/itor.12627","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,2]],"date-time":"2023-09-02T06:12:15Z","timestamp":1693635135000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1111\/itor.12627"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,1,20]]},"references-count":20,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2021,7]]}},"alternative-id":["10.1111\/itor.12627"],"URL":"https:\/\/doi.org\/10.1111\/itor.12627","archive":["Portico"],"relation":{},"ISSN":["0969-6016","1475-3995"],"issn-type":[{"value":"0969-6016","type":"print"},{"value":"1475-3995","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,1,20]]},"assertion":[{"value":"2018-03-23","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2018-12-28","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2019-01-20","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}