The constrained permutation Flowshop problem: An effective two-stage iterated greedy algorithm to minimize weighted tardiness

In the domain of just-in-time permutation flowshop scheduling, most studies typically assume that all jobs either have their own soft due date or none of them do. However, in practice, scheduling a combination of hard and soft due date jobs, particularly with the context of emergency order insertion, remains a significant research topic. This paper addresses a constrained permutation flowshop scheduling problem with a mix of hard and soft due date jobs under total weighted tardiness criterion (CPFSP-TWT). We establish a mathematical model and propose an effective Two-Stage Iterated Greedy (ETSIG) algorithm tailored to the problem's characteristics, incorporating a two-stage constructive heuristic to generate a high-quality initial solution. We introduce problem-specific acceleration mechanisms based on position-bound considerations to enhance operational efficiency. We propose three knowledge-based repair strategies for handling infeasible solutions, along with a dynamic self- adjustment mechanism. Additionally, three efficient local search procedures integrate several specific perturbation operators to balance algorithmic exploitation and exploration abilities. Experimental evaluations affirm ETSIG's superiority over five state-of-the-art metaheuristics from closely related literature, establishing its efficacy in addressing CPFSP-TWT.