Exact Methods for Solving Multi-Objective Problem on Single Machine Scheduling

Hanan Ali Chachan; Alaa Sabah Hameed

doi:10.24996/ijs.2019.60.8.17

Authors

Hanan Ali Chachan Department of Mathematics, College of Sciences, Al-Mustansireyah University, Baghdad, Iraq
Alaa Sabah Hameed Department of Mathematics, College of Sciences, Al-Mustansireyah University, Baghdad, Iraq

DOI:

https://doi.org/10.24996/ijs.2019.60.8.17

Keywords:

Multi-Objective Problem (MOP), Branch and Bound (BAB) method, Genetic Algorithm (GA), Particle Swarm Optimization (PSO)

Abstract

In this paper, one of the Machine Scheduling Problems is studied, which is the problem of scheduling a number of products (n-jobs) on one (single) machine with the multi-criteria objective function. These functions are (completion time, the tardiness, the earliness, and the late work) which formulated as . The branch and bound (BAB) method are used as the main method for solving the problem, where four upper bounds and one lower bound are proposed and a number of dominance rules are considered to reduce the number of branches in the search tree. The genetic algorithm (GA) and the particle swarm optimization (PSO) are used to obtain two of the upper bounds. The computational results are calculated by coding (programing) the algorithms using (MATLAP) and the final results up to (18) product (jobs) in a reasonable time are introduced by tables and added at the end of the research.