An adaptive iterated greedy algorithm for distributed mixed no-idle permutation flowshop scheduling problems

Abstract Distributed flow shop scheduling is a very interesting research topic. This paper studies the distributed permutation flow shop scheduling problem with mixed no-idle constraints, which have important applications in practice. The optimization goal is to minimize total flowtime. A mixed-integer linear programming model is presented and an Adaptive Iterated greedy (AIG) algorithm with the sample length changing according to the search process is designed. A restart strategy is also introduced to escape from local optima. Additionally, to further improve the performance of the algorithm, swap-based local search methods and acceleration algorithms for swap neighborhoods are proposed. Referenced Local Search (RLS), which shows better performance in solving scheduling problems, is also used in our algorithm. In the destruction stage, the job to be removed is selected according to the degree of influence on the total flowtime. In the initialization and construction phase, when a job is inserted, the jobs before and after the insertion position are removed and re-inserted into a better position to improve the algorithm search performance. A detailed design experiment is carried out to determine the best parameter configuration. Finally, large-scale experiments show that the proposed AIG algorithm is the best-performing one among all the algorithms in comparison.