A Discrete Electromagnetism-Like Mechanism Algorithm for Solving Distributed Permutation Flowshop Scheduling Problem

A distributed permutation flow shop scheduling problem (DPFSP) is an NP-hard problem recently put forward in shop scheduling sphere. Exact algorithms for a DPFSP's solution can be extremely computationally costly. This paper proposes to apply an electromagnetism-like mechanism (EM) algorithm as a heuristic solution method to a DPFSP. To fit into the discrete domain of a DPFSP, modifications to the original EM algorithm, including redefinition of distance and movement and of charge and force calculation, have been made, to improve the performance of the proposed algorithm, a VNS local search mechanism employing the concept of the critical factory has been devised. The experimental results show the superiority of the proposed algorithm over the original EM algorithm. New best known solutions have been found to the Naderi's DPFSP benchmark suite adapted from Tail lard instances.