A DE Based Variable Iterated Greedy Algorithm for the No-Idle Permutation Flowshop Scheduling Problem with Total Flowtime Criterion

In this paper, we present a variable iterated greedy (vIGP_DE) algorithm where its parameters (basically destruction size and cooling parameter for the simulated annealing type of acceptance criterion) are optimized by the differential evolution algorithm. A unique multi-chromosome solution representation is presented such that first chromosome represents the destruction size and cooling parameter of the iterated greedy algorithm while second chromosome is simply a permutation assigned to each individual in the population randomly. As an application area, we choose to solve the no-idle permutation flowshop scheduling problem with the total flowtime criterion. To the best of our knowledge, the no-idle permutation flowshop problem hasn’t yet been studied thought it’s a variant of the well-known permutation flowshop scheduling problem. The performance of the vIGP_DE algorithm is tested on the Taillard’s benchmark suite and compared to a very recent variable iterated greedy algorithm from the existing literature. The computational results show its highly competitive performance and ultimately, we provide the best known solutions for the total flowtime criterion for the Taillard’s benchmark suit.