Collaborative multi-CP model and meta-feedback learning-assisted matheuristic for solving the flexible job shop scheduling problem with sequence-dependent setup times

Abstract

The flexible job shop scheduling problem with sequence-dependent setup times (FJSP-SDST) is a crucial challenge in modern manufacturing, where varying setup times significantly impact scheduling performance. This challenge has motivated significant research interest in solving FJSP-SDST through both exact and approximate methods. Although existing exact methods, such as mixed-integer linear programming and constraint programming (CP) have been explored, they remain inefficient in solving large-scale instances. To address this limitation, this paper proposes a collaborative multi-CP model, inspired by the collaborative optimization paradigm, which integrates global and local optimization stages to effectively solve large instances. Due to the NP-hard nature of FJSP-SDST, an approximate method, the meta-feedback learning-assisted matheuristic (MFLA-MH) algorithm, is proposed. The algorithm adopts collaborative variable neighborhood search as its main framework and incorporates meta-feedback learning to adaptively guide search operator selection. Additionally, two mathematical neighborhood structures and a mathematical evolution operator, as matheuristic techniques, are designed to optimize the subproblem solutions and overcome the limitations of traditional encoding-decoding methods. Experimental results on 20 real-world cases demonstrate that the collaborative multi-CP model and MFLA-MH efficiently generate high-quality solutions, and outperform state-of-the-art methods.