An improved discrete migrating birds optimization (IDMBO) algorithm is presented in this work to solve the no-wait flow shop scheduling problem (NWFSSP) with makespan criterion. In the algorithm, all of the solutions in population are treated as birds aligned in a V formation named the leader and followers. To guarantee the quality and the diversity of initial population, the leader is provided by the standard deviation heuristic (SDH) algorithm, and the rest (the followers) are generated randomly. Given that IDMBO is a neighborhood-based search algorithm, the quality of algorithm depends heavily on the neighborhood structures, where the two variants of the hybrid multi-neighborhood strategy, which are multiply neighborhood structures are embedded in variable neighborhood search (VNS) in different forms, are performed to generate the neighborhood solutions for leader and followers, respectively. Furthermore, the population reset mechanism is performed after a given number iterations without improving the current solution. The local search (LS) method can further ameliorate the quality of solutions. The computational study is conducted to analyze the efficiency of IDMBO algorithm on benchmarks designed by Reeve and Taillard. And the comparison results are shown that the presented algorithm is superior to several existing algorithms for NWFFSP.

A discrete whale optimization algorithm (DWOA) is presented to solve the no-wait flow shop scheduling problem (NWFSSP) with the optimization objective makespan. An effective combination of nearest neighbor (NN) and standard deviation heuristics (SDH) is used to acquire initial solutions of the population. After that, three crossover operators, the two-point crossover (TPX), multiple-point crossover (MPX) and job-based crossover (JBX) operators, are designed to mimics the humpback whales hunting process. Moreover, the dynamic transform mechanism of search process is designed to better balance the exploration and exploitation ability of DWOA. In order to further improve the optimization effect of DWOA, the parallel neighborhood search (PNS) and the serial neighborhood search (SNS) are selected to execute the local search and promoting global search scheme, respectively. Finally, to test the performance of DWOA, extensive experiments are conducted on benchmarks designed by Reeves and Taillard, which contain parameters tuning, effectiveness of the improvement strategies in the DWOA and comparison with several existing algorithms. From the experimental results, it is validated that the effectiveness of the improved mechanisms and the performance of the DWOA which can find better makespan values compared with other algorithms for solving NWFSSP.