The paradoxes, accelerations and heuristics for a constrained distributed flowshop group scheduling problem

• Published in: Computers & industrial engineering Vol. 196; p. 110465
• Main Authors: Wang, Bing-Tao, Pan, Quan-Ke, Gao, Liang, Li, Weimin
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.10.2024
• Subjects: Accelerated evaluation; Composite heuristics; Deadline; Distributed flowshop group scheduling; Distributed flowshop group scheduling; Composite heuristics; Accelerated evaluation; Deadline
• ISSN: 0360-8352
• DOI: 10.1016/j.cie.2024.110465

•A mixed-integer programming model on CDFGSP is built.•Three paradoxes and two bound theories are identified.•Two insertion-based accelerations to find the best insertion position are provided.•Four composite heuristics with problem-specific knowledge are proposed. In this paper, we tackle a previously unexplored challenge in contemporary manufacturing: constrained distributed flowshop group scheduling problem (CDFGSP). Different from the traditional distributed flowshop group scheduling problem (DFGSP), CDFGSP introduces a unique perspective: some job families are bounded by particular production specifications and share a common deadline, while the remaining job families are not subject to such limits. This real-world constraint complicates the problem, and often results in infeasible solutions when using existing algorithms. To address the problem, a mathematical model for CDFGSP with the objective of minimizing makespan is first established. Then, we uncover three counterintuitive paradoxes resulting in invalid searches, summarize two new bound theories to exclude infeasible insertions and provide two accelerations for evaluating constraints and computing optimization objectives. Integrating the above problem properties, we propose four composite heuristics, each of which combines an improved Nawaz, Enscore and Ham (NEH) heuristic and a cooperative local search. Finally, thoroughly computed results prove that the mathematical model and acceleration mechanism are effective. Our two top heuristics demonstrate decent improvements over the best comparative algorithm from related research. Specifically, the rating metric is lowered by 2.09% for the best heuristic and by 1.38% for the second-best heuristic.