A factorial based particle swarm optimization with a population adaptation mechanism for the no-wait flow shop scheduling problem with the makespan objective

Abstract

The no-wait flow shop scheduling problem (NWFSP) performs an essential role in the manufacturing industry. In this paper, a factorial based particle swarm optimization with a population adaptation mechanism (FPAPSO) is implemented for solving the NWFSP with the makespan criterion. The nearest neighbor mechanism and NEH method are employed to generate a potential initial population. The factorial representation, which uniquely represents each number as a string of factorial digits, is designed to transfer the permutation domain to the integer domain. A variable neighbor search strategy based on the insert and swap neighborhood structure is introduced to perform a local search around the current best solution. A population adaptation (PA) mechanism is designed to control the diversity of the population and to avoid the particles being trapped into local optima. Furthermore, a runtime analysis of FPAPSO is performed with the level-based theorem. The computational results and comparisons with other state-of-the-art algorithms based on the Reeve's and Taillard's instances demonstrate the efficiency and performance of FPAPSO for solving the NWFSP.