Minimising Makespan and total tardiness for the flowshop group scheduling problem with sequence dependent setup times

The challenge of optimizing multiple objectives while considering job groups and partial due dates is prevalent in the flowshop group scheduling problem (FGSP). Despite its significance, the multi-objective FGSP with partial due dates (MFGSP) remains largely unaddressed in existing FGSP literature. In this paper, we bridge this gap by introducing a mixed integer linear programming model and an iterated greedy algorithm tailored for MFGSP with sequence-dependent group setup times, aimed at minimizing both makespan and total tardiness concurrently. Our proposed approach delves into the specific characteristics of times, acknowledging the inherent conflicts between objectives and the unique nature of each objective. We propose two novel local search operators: one inspired by the asymmetric traveling salesman problem and the other based on a domination criterion. These operators are seamlessly integrated into the iterated greedy algorithm framework, augmented with a cone-weighted scalar method as a fitness function and adaptive perturbation parameters. Extensive experimental evaluations demonstrate the efficacy and efficiency of our proposed algorithm, showcasing its capability to solve the MFGSP effectively. Through this research, we contribute a practical and versatile solution to a largely unexplored area in group scheduling optimization.