aspg-33-2830-1792226099 20261017083459 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group Galoitica: Journal of Mathematical Structures and Applications GJMSA 2834-5568 2024 10 2 Hussein Abdullah Jaafar Department of Mathematics, Open Educational College, Samawah, 66001 , Iraq Hanan Ali Chachan Department of Mathematics, College of Sciences, University of Mustansiriyah , Baghdad, 10001 , Iraq In this research, the issue of scheduling n-jobs on one-machine is represented to minimize Five-Objectives-Function (FOF), for finding approximation solutions for the sum of completion time, total tardiness, total earliness, number of late jobs and late work with release date, this issue denoted by: style='font-size:10.0pt;font-family:"Cambria Math",serif;mso-fareast-font-family: Calibri;mso-bidi-font-family:"Times New Roman";mso-bidi-theme-font:major-bidi; mso-bidi-language:AR-IQ'> style='mso-spacerun:yes'> 1/ style='font-size:10.0pt;mso-ansi-font-size:10.0pt;mso-bidi-font-size:10.0pt; 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Hanan and Hussein used a branch and bound technique (B-a-B) to discovery an optimal solution path. Computational results showed the (B-a-B) technique was efficient in solving issues with up to (16- jobs). Because our issue is of a very difficult type (NP-hard), we suggest local search algorithms to discovery near optimal solution. The execution of local search techniques can be tested on large group of test issues. Computational results showed with up to (30000 jobs) in acceptable time. 2024 44 51 2830 https://creativecommons.org/licenses/by/4.0/ 10.54216/GJMSA.0100204 https://americaspg.com/journal/33/article/2830 https://americaspg.com/storage/21716571327.pdf