An effective modified migrating birds optimization for hybrid flowshop scheduling problem with lot streaming

In this paper, the problem of hybrid flowshop hybridizing with lot streaming (HLFS) with the objective of minimizing the total flow time is addressed. We propose a mathematical model and an effective modified migrating birds optimization (EMBO) to solve this problem within an acceptable computational time. A so-called shortest waiting time rule (SWT) is introduced to schedule the jobs concurrently arriving at stages more reasonably. A combined neighborhood search strategy is developed that unites two different neighborhood operators during evolution, not only taking full advantage of their specializations but also promoting their joint efforts. Two competitive mechanisms are respectively used to increase the probability of locating better solutions at the front of the flock and enhance the interaction between two lines. The scout phase on the basis of the Glover operator and a well-designed local search is applied to the individuals trapped into local optimums and helps the algorithm explore potential promising domains. The dynamic solution acceptance criteria is developed to strike a compromise between intensification and diversification mechanisms. The performance of our proposed algorithm is evaluated by comparisons with seven other efficient algorithms in the literature. And the extensive numerical illustrations demonstrate that the proposed algorithm performs much more effectively for the addressed problem