Solving permutation flowshop scheduling problems with a discrete differential evolution algorithm

In this paper a new discrete Differential Evolution algorithm for the Permutation Flowshop Scheduling Problem with the total flowtime and makespan criteria is proposed. The core of the algorithm is the distance-based differential mutation operator defined by means of a new randomized bubble sort algorithm. This mutation scheme allows the Differential Evolution to directly navigate the permutations search space. Experiments were held on a well known benchmarks suite and they show that the proposal reaches very good performances compared to other state-of-the-art algorithms. The results are particularly satisfactory on the total flowtime criterion where also new upper bounds that improve on the state-of-the-art have been found.