An efficient quantum immune algorithm to minimize mean flow time for hybrid flow shop problems

Hybrid flow shop problem (HFSP) can be regarded as a generalized flow shop with multiple processing stages, of which at least one consists of parallel machines. HFSP is fairly common in flexible manufacturing and in process industry. This paper presents an efficient quantum immune algorithm (QIA) for HFSP. The objective is to find an optimal job sequence that minimize the mean flow time. Since HFSP has been proved to be NP-hard in a strong sense even in case of two stages, immune algorithm (IA) and quantum algorithm (QA) are used to solve the problem, respectively. To improve the performance of IA, an effective IA with new adaptive crossover and fractional parts mutation operators is proposed, which is called AIA. A randomly replacing strategy is employed to promote population diversity of QA, namely RRQA. In order to achieve better results, the paper proposes a quantum immune algorithm (QIA), which combines IA with QA to optimize the HFSP. Furthermore, all the improvements are added into QIA to be ARRQIA, which possesses the merits of global exploration, fast convergence, and robustness. The simulation results show that the proposed AIA significantly enhances the performance of IA. RRQA also produces more efficient and more stable results than QA. So far as ARRQIA is concerned, it outperforms the other algorithms in the paper and the average solution quality has increased by 3.37% and 6.82% compared with IA and QA on the total 60 instances.