An effective shuffled frog-leaping algorithm for hybrid flow-shop scheduling with multiprocessor tasks

As a strongly NP-hard problem, the hybrid flow-shop problem with multiprocessor tasks (HFSPMT) has gained increasing attention due to its academic significance and application value. In this paper, an effective algorithm based on the shuffled frog leaping algorithm (SFLA) is proposed for solving the HFSPMT. First, three decoding methods are used together to decode a solution to a better schedule. Especially, the forward scheduling decoding method is employed, aiming at narrowing the idle time between consecutive operations in the processor as well as increasing the flexibility in selecting processors to schedule the following operations. Second, a bilevel crossover is designed to make each individual share the good “meme” within each memeplex and exchange the good “meme” between different memeplexes. Third, multiple local search operators are used in an effective way by employing the meta-Lamarckian learning strategy to enhance the local exploitation ability. Meanwhile, the use of crossover and local search together in the SFLA can enrich the memetic search behavior and balance the exploration and exploitation abilities. In addition, the effect of parameter setting of the algorithm is investigated based on the Taguchi method of design of experiment, and suitable values are suggested for the parameters. Extensive testing results based on two types of well-known benchmarks are provided. And the effectiveness of the proposed algorithm is demonstrated by the comparisons with some existing algorithms.