Document Type : Research Paper

Author

• Doha Adel Abbas

Department of Mathematics, College of Science, University of Al-Mustansiriyah, Bagdad, Iraq

Abstract

Our research includes studying the case $ 1 // F(\sum U_i ,\sum Ti ,T_{max})$  minimized the cost of a three-criteria objective function on a single machine for scheduling n jobs. and divided this into several partial problems and found simple algorithms to find the solutions to these partial problems and compare them with the optimal solutions. This research focused on one of these partial problems to find minimize a function of sum cost of $ (\sum  U_i) $ sum number of late job and $ (\sum Ti) $ sum Tardiness and $ (T_{max} ) $ the Maximum Tardiness for n job on the single machine, which is NP-hard problem, first found optimal solutions for it by two methods of Complete Enumeration technique(CEM) and Branch and Bounded ((BAB)). Then use some  Local search methods(Descent technique(DM), Simulated Annealing (SA) and Genetic Algorithm (GA)), Develop algorithm called ((A)) to find a solution close to the optimal solution. Finally, compare these methods with each other.

Keywords

• Descent Method(DM)
• Genetic Algorithm(GA)
• Maximum tardiness
• Multi-objective optimization
• Simulated annealing ((SA))
• Total Number of Late job
• Total Tardiness