A hash map-based memetic algorithm for the distributed permutation flowshop scheduling problem with preventive maintenance to minimize total flowtime

Abstract

Distributed scheduling problems have been an active research topic due to their close connection with the multifactory production environment in today’s decentralized economy. In this paper, the distributed permutation flowshop scheduling problem with preventive maintenance is studied with the goal of minimizing the total flowtime. A mathematical model and a hash map-based algorithm are presented to tackle the problem. The Nawaz–Enscore–Ham heuristic is improved and incorporated with the distributed Liu–Reeves heuristic to provide a promising initial solution in a finite number of steps. The proposed algorithm employs the data structure of the hash map to store all the candidate solutions in the form of key–value pairs. The selection, crossover, and mutation operators are also modified to expand the scope of exploration in the discrete domain. The local search hybridizes the job insertion operator and the job swap operator to further improve the obtained offspring solutions and utilizes the characteristic of the population hash map to reduce the efforts of solution evaluations. The candidate solution obtained by the local search is hashed by a rotating hash method and then placed at the node with the corresponding hash code. A series of experiments were conducted to verify the effectiveness of the hybrid local search operators and hash map strategy. Computational results indicate that the multiple strategies not only help to escape from the local optimization but also improve the computational efficiency. When compared with 10 state-of-the-art algorithms, the proposed algorithm generates an average relative percentage deviation of 0.134%, which is significant improvement.