A Comparative Analysis of Heuristic Metaheuristic and Exact Approach to Minimize Make Span of Permutation Flow Shop Scheduling

Abstract

The study of permutation flow shop scheduling issues has proved fascinating. Make span reduction has been explored extensively throughout the years as one of the many factors. If there are more than two machines, finding a schedule that optimizes total completion times for Permutation Flow Shop issues is NP Hard. The well-known Nawaz–Enscore–Ham (NEH) heuristic is acknowledged as the top performing approach for the permutation flow shop scheduling issue till now, according to the make span minimization criteria. For large-scale problems, however, the NEH approach takes a long time to discover an estimated optimum solution. Many researchers have offered heuristics and meta-heuristics as the time it takes to compute grows exponentially in proportion to the size of the problem. For the permutation flow shop scheduling problem, we proposed a genetic algorithm with the criterion of minimizing make span as the criteria. The method's performance is compared to that of the well-known NEH algorithm. Computational experiments on benchmark data sets revealed that the proposed approach produces satisfactory solutions in short computational cycles. Furthermore, it just requires a few user-defined parameters, making it relevant to real-world flow shop scheduling challenges. The findings reveal that, when compared to an exact technique, the proposed genetic algorithm (GA) is capable of rapidly seeking optimal solutions for most small-sized instances. Furthermore, the proposed GA continues to function satisfactorily for medium and large-scale instances and generates solutions in a reasonable period.