Reconfigurable distributed flowshop group scheduling with a nested variable neighborhood descent algorithm

Abstract

Inspired by a real-world cellular manufacturing system for processing printed circuit boards (PCBs), this study addresses a reconfigurable distributed flowshop scheduling problem (RDFGSP), where the flowline is considered as a cell and a complete process includes two flows through the flowlines. The characteristics of the RDFGSP lie in the reconfigurability of the flowlines and the families with grouped jobs. To solve this problem, at the two flows the family assignment part and sequence part (including family sequence and job sequence) are all required to be addressed. To solve the problem, a mixed integer linear programming (MILP) model is first developed, which can solve the small-scaled instances to optimality. Since the NP-hard property of the problem, a nested variable neighborhood descent (NVND) algorithm is developed. Its core ideas lie in the dynamic solution encoding and decoding strategies and the specially designed nested loops, including the external and internal loops. In the external loop, the solution encoding and decoding only consider the sequence part, and the family assignment part is conceived using the machine property in the decoding process. The internal loop is triggered when a decoding process in the external loop is completed, where the family assignment part and sequence part are all considered. In addition, a collaborative process and a restart strategy are employed to guarantee the global search capability. In the experimental study, the iterated F-Race (I/F-Race) is used to help determine the algorithm parameters with minimum user intervention. Comprehensive computational results demonstrate that the proposed algorithm outperforms the math solver CPLEX and other state-of-the-art metaheuristics.