Cloud manufacturing (CMfg) is a new network manufacturing mode, where one of the essential issues is service composition and optimal selection (SCOS), attracting a wide range of scholars' attention and research. At present, scholars at home and abroad mainly focus on studying the SCOS model in a single type of cloud environment, which integrates and optimizes large group enterprises' internal resources and capabilities. However, since the characteristics and objectives of the SCOS problem are different in different cloud environments (private, public, and hybrid cloud), there are many dynamic switching scenarios of manufacturing resources in different cloud environments. At this time, SCOS models in a single type of cloud environment are no longer applicable. Thus, how to realize the maximization of multi-stakeholder benefits through the adaptive partitioning of manufacturing resources in different cloud environments is an urgent problem to be solved. To fill the gap, a multi-objective service composition optimization method considering multi-user benefit and adaptive resource partitioning (SCOS-MUB-ARP) is proposed for quickly obtaining the optimal service composition that maximizes the benefits of multi-stakeholder in hybrid cloud manufacturing. To address the SCOS-MUB-ARP, a multi-objective optimization algorithm based on a combination of the NSGA-II algorithm and the mayfly algorithm (MMA-NSGA2) with several optimization strategies is presented, which contains several problem-specific optimization strategies. Numerical experiments and application cases show the effectiveness of the proposed MMA-NSGA2 in optimizing and balancing multi-objectives, compared with some well-known algorithms.

云制造（CMfg）是一种新型网络制造模式，其本质问题之一是服务组合与优化选择（SCOS），引起了学者的广泛关注和研究。目前国内外学者主要研究单一类型云环境下的SCOS模型，对大型集团企业内部资源和能力进行整合和优化。然而，由于SCOS问题在不同云环境（私有云、公有云、混合云）下的特点和目标不同，导致制造资源在不同云环境下的动态切换场景较多。此时，单一类型云环境中的SCOS模型已不再适用。因此，如何通过不同云环境下制造资源的自适应划分，实现多方利益最大化是亟待解决的问题。为了填补这一空白，提出了一种考虑多用户利益和自适应资源划分的多目标服务组合优化方法（SCOS-MUB-ARP），以快速获得混合云制造中多利益相关者利益最大化的最优服务组合。针对SCOS-MUB-ARP问题，提出了一种基于NSGA-II算法和蜉蝣算法相结合的具有多种优化策略的多目标优化算法（MMA-NSGA2），其中包含多种针对特定问题的优化策略。数值实验和应用案例表明，与一些知名算法相比，所提出的MMA-NSGA2在优化和平衡多目标方面的有效性。