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For problems whose optimal solutions cannot be obtained, precision is traded with speed through substituting the integrality constrains in a binary integer program with a penalty. In this way, instead of constraining a variable <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:mi>u<\/mml:mi><\/mml:mrow><\/mml:math> with binary restriction, <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mrow><mml:mi>u<\/mml:mi><\/mml:mrow><\/mml:math> is considered as real number between 0 and 1, with the penalty of <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mi>M<\/mml:mi><mml:mi>u<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mn fontstyle=\"italic\">1<\/mml:mn><mml:mo>-<\/mml:mo><mml:mi>u<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>, in which <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\"><mml:mrow><mml:mi>M<\/mml:mi><\/mml:mrow><\/mml:math> is a large number. Values not near to the boundary extremes of 0 and 1 make the component of <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M5\"><mml:mi>M<\/mml:mi><mml:mi>u<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mn fontstyle=\"italic\">1<\/mml:mn><mml:mo>-<\/mml:mo><mml:mi>u<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math> large and are expected to be avoided implicitly. The nonbinary values are then converted to priorities, and a genetic algorithm can use these priorities to fill its initial pool for producing feasible solutions. The presented framework can be applied to many combinatorial optimization problems. Here, a procedure based on this framework has been applied to a scheduling problem, and the results of computational experiments have been discussed, emphasizing the knowledge generated and inefficiencies to be circumvented with this framework in future.<\/jats:p>","DOI":"10.1155\/2017\/7048042","type":"journal-article","created":{"date-parts":[[2017,10,17]],"date-time":"2017-10-17T19:32:15Z","timestamp":1508268735000},"page":"1-10","source":"Crossref","is-referenced-by-count":0,"title":["Towards Merging Binary Integer Programming Techniques with Genetic Algorithms"],"prefix":"10.1155","volume":"2017","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7948-5500","authenticated-orcid":true,"given":"Reza","family":"Zamani","sequence":"first","affiliation":[{"name":"School of Computing and Information Technology, Wollongong University, Wollongong, NSW 2522, 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