Galoitica: Journal of Mathematical Structures and Applications GJMSA 2834-5568 10.54216/GJSMA https://www.americaspg.com/journals/show/2830 2022 2022 Department of Mathematics, Open Educational College, Samawah, 66001 , Iraq Hussein Hussein Department of Mathematics, College of Sciences, University of Mustansiriyah , Baghdad, 10001 , Iraq Hanan Ali Chachan 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:   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 2024 44 51 10.54216/GJMSA.0100204 https://www.americaspg.com/articleinfo/33/show/2830