Local search metaheuristic for solving hybrid flow shop problem in slabs and beams manufacturing

Abstract

Solving optimization problems in the modern manufacturing industry is one of the most attractive areas of operational research. In this paper, we propose an industrial optimization case of slabs and beams production problem. The suggested approach consists in modeling the process as a hybrid flow shop with unrelated parallel machines under constraints of sequence dependent setup time. Jobs launched in production are of different characteristics and require a machine preparation time at each phase during their production cycle. The goal is to minimize the total tardiness of all jobs when they are completed on the last stage. The hybrid flow shop problem is considered as one of the NP-hard issues since it consists of at least two stages. To solve numerically this problem, we propose two methods, the iterative local search (ILS) and the iterated greedy (IG) metaheuristics. In addition, we suggest two new improvements, the first relates to the initial step while the second concerns the steps of the neighborhood exploration. In the initial phase, we consider an initial solution set generated from the priority rules whose scheduling is ensured by the Nawaz-Enscore-Ham (NEH) algorithm and the greedy randomized adaptive search procedure (GRASP). In the second phase, we suggest a new version of exploration of the neighborhood. In fact, from a single solution, we will generate a set of neighboring solutions and we will choose the best solution. In this new resolution approach, we develop a total of twelve algorithms based on neighborhood exploration. We note that the proposed algorithms are hybrid metaheuristics and are among the most powerful optimization algorithms in local search. A simulation study is conducted to verify the effectiveness of the suggested algorithms.This simulation is performed on a set of instances by varying the number of jobs, the number of machines per stage and the number of stages. We find that the IG algorithm based on NEH initialization heuristic gives good results in terms of quality and convergence time to the best solution.