Solving flow shop scheduling problems by quantum differential evolutionary algorithm

This paper proposed a novel quantum differential evolutionary algorithm (QDEA) based on the basic quantum-inspired evolutionary algorithm (QEA) for permutation flow shop scheduling problem (PFSP). In this QDEA, the quantum chromosomes are encoded and decoded by using the quantum rotating angle and a simple strategy named largest rotating angle value rule to determine job sequence based on job's quantum information is proposed for the representation of PFSP, firstly. Then, we merge the advantages of differential evolution strategy, variable neighborhood search and QEA by adopting the differential evolution to perform the updating of quantum gate and variable neighborhood search to raise the performance of the local search. We adopted QDEA to minimize the makespan, total flowtime and the maximum lateness of jobs and make the simulations. The results and comparisons with other algorithms based on famous benchmarks demonstrated the effectiveness of the proposed QDEA. Another contribution of this paper is to report new absolute values of total flowtime and maximum lateness for various benchmark problem sets.