Collaborative variable neighborhood search for multi-objective distributed scheduling in two-stage hybrid flow shop with sequence-dependent setup times

Distributed scheduling is seldom investigated in hybrid flow shops. In this study, distributed two-stage hybrid flow shop scheduling problem (DTHFSP) with sequence-dependent setup times is considered. A collaborative variable neighborhood search (CVNS) is proposed to simultaneously minimize total tardiness and makespan. DTHFSP is simplified by incorporating factory assignment into machine assignment of a prefixed stage, and its solution is newly represented with a machine assignment string and a scheduling string. CVNS consists of two cooperated variable neighborhood search (VNS) algorithms, and neighborhood structures and global search have collaborated in each VNS. Eight neighborhood structures and two global search operators are defined to produce new solutions. The current solution is periodically replaced with a member of the archive farthest from it. Experiments are conducted , and the computational results validate that CVNS has good advantages over the considered DTHFSP.