A Comparative Study of Solution Representations Using New Matrix Metaheuristic for Solving Job Shop Scheduling Problems

The JSSP is recognized as one of the most difficult combinatorial optimization problems because it as well and indeed can be classified as an NP-hard problem. This paper introduces two metaheuristic frameworks which both make use of Iterated Local Search, but differ fundamentally from each other in the way they represent solutions. The initial metaheuristic, called the Priority-based metaheuristic, creates schedules using priority dispatching rules guided by ILS. In contrast, the second metaheuristic, referred to as the Permutational coding-based metaheuristic, employs a permutation coding approach for every operation and directly implements neighborhood moves on this sequence. Both metaheuristics aim to reduce makespan. To evaluate their performance, computational experiments were performed in MATLAB on recognized benchmark datasets to analyze the quality of solutions. The main goal is to identify which representation provides a better equilibrium between exploration and exploitation abilities when combined with the same ILS methods. The JSSP is known to be one of the complex problems of combinatorial nature due to the fact that it belongs to the class of NP-hard problems. In this study, two novel methods of solving the JSSP are presented and evaluated. The two methods are that both make use of the Iterated Local Search (ILS) algorithm. The first method, termed Priority-based metaheuristic, is the one which constructs schedules according to priority scheduling rules based on ILS. On the other hand, the second method, which is termed Permutational coding-based metaheuristics, is built on the idea of coding each operation in terms of a permutation of the operation and putting the neighborhood operations directly on the short string. The two metaheuristic methods are aimed at minimizing the makespan. In order to test the performance of the two methods, computational tests are conducted in MATLAB using the standard benchmark tests to investigate the performance of the problems solved.