Tabu Search Algorithm Based on Lower Bound and Exact Algorithm Solutions for Minimizing the Makespan in Non-Identical Parallel Machines Scheduling

Recently, several heuristics have been interested in scheduling problems, especially those that are difficult to solve via traditional methods, and these are called NP-hard problems. As a result, many methods have been proposed to solve the difficult scheduling problems; among those, effective methods are the tabu search algorithm (TS), which is characterized by its high ability to adapt to problems of the large size scale and ease of implementation and gives solution closest to the optimum, but even though those difficult problems are common in many industries, there are only a few numbers of previous studies interested in the scheduling of jobs on unrelated parallel machines. In this paper, a developed TS algorithm based on lower bound (LB) and exact algorithm (EA) solutions is proposed with the objective of minimizing the total completion time (makespan) of jobs on nonidentical parallel machines. The given solution via EA was suggested to enhance and assess the solution obtained from TS. Moreover, the LB algorithm was developed to evaluate the quality of the solution that is supposed to be obtained by the developed TS algorithm and, in addition, to reduce the period for searching for the optimal solution. Two numerical examples from previous studies from the literature have been solved using the developed TS algorithm. Findings show that the developed TS algorithm proved its superiority and speed in giving it the best solution compared to those solutions previously obtained from the literature.