A Novel Cuckoo Search Algorithm for Solving Permutation Flowshop Scheduling Problems

The permutation flowshop scheduling problem (PFSP) is a classical optimization problem in the field of system engineering. In this paper, different from the traditional PFSP, we take into account the fact that all jobs in PFSPs may have different velocity degrees, i.e., each job can use its own velocity degree on all machines and its processing time is changed, accordingly. A novel cuckoo search algorithm is proposed to solve this PFSP with the purpose of jointly minimizing the total flow time and the total energy consumption, by means of achieving a Pareto-optimal solution set. Our proposed algorithm establishes a new movement strategy to increase the multiformity of scheduling solutions so that local optimization can be avoided. In addition, we propose a novel local search method that is capable of expanding the Pareto-optimal solution set. In order to evaluate the proposed algorithm comprehensively, extensive simulations were performed, showing that our proposed algorithm outperforms the best existing algorithm for the considered problem in the state-of-the-art, in terms of both the effectiveness and the efficiency. Furthermore, the proposed new movement strategy and the novel local search method are also verified to be effective, and make contributions to the high effectiveness of the proposed algorithm.