Abstract: To solve the hybrid flow shop scheduling problem with the identical parallel machine,an improved grey wolf optimization was proposed to minimize the makespan.A mathematical model of the problem was established according its characteristics.A new calculation formula was proposed for the important parameter  in grey wolf algorithm to improve the global exploration capability at early stage and the local search ability at late.Meanwhile,as the wolves gathered toward decision-making wolves,for maintaining the diversity of wolves,a plane-mirror imaging learning strategy was proposed to avoid the algorithm falling into local optimization.Moreover,considering the unbalance of machine at each stage,the forward decoding and reverse decoding strategy was used to improve the probability of finding the optimal solution.The proposed algorithm was compared with other algorithms on the benchmark cases and an actual enterprise case,and the effectiveness and reliability of the algorithm were verified.

Key words: hybrid flow shop scheduling, grey wolf optimization, plane-mirror imaging, reverse decoding

摘要： 针对带有相同并行机的混合流水车间调度问题,以最小化最大完工时间为研究目标,提出一种改进灰狼优化算法。根据问题特征建立了数学模型;对灰狼算法中的重要控制参数C提出一种新的计算公式,保证了算法的初期全局勘探能力和后期局部搜索能力。随着狼群向决策狼聚集,为了保持狼群的多样性,提出一种基于平面镜成像学习策略,以避免算法陷入局部最优。鉴于混合流水车间每个阶段加工设备的配置不均衡,采用正序和逆序解码策略,从而提高找到问题最优解的概率。将所提算法和其他算法应用于某企业实际案例与benchmark案例进行对比,验证了算法的有效性和可靠性。

关键词: 混合流水车间调度, 灰狼算法, 平面镜成像, 逆序解码