An Industrial Internet platform is acknowledged to be a requisite promoter for smart manufacturing, enabling physical manufacturing resources to be virtualized and permitting resources to collaborate in the form of services. As a central function of the platform, manufacturing service collaboration optimization is dedicated to establishing high-quality service collaboration solutions for manufacturing tasks. Such optimization is inseparable from the functional and amount requirements of a task, which must be satisfied when orchestrating services. However, existing manufacturing service collaboration optimization methods mainly focus on horizontal collaboration among services for functional demands and rarely consider vertical collaboration to cover the needed amounts. To address this gap, this paper proposes a dual-dimensional service collaboration methodology that combines functional and amount collaboration. First, a multi-granularity manufacturing service modeling method is presented to describe services. On this basis, a dual-dimensional manufacturing service collaboration optimization (DMSCO) model is formulated. In the vertical dimension, multiple functionally equivalent services form a service cluster to fulfill a subtask; in the horizontal dimension, complementary service clusters collaborate for the entire task. Service selection and amount distribution to the selected services are critical issues in the model. To solve the problem, a multi-objective memetic algorithm with multiple local search operators is tailored. The algorithm embeds a competition mechanism to dynamically adjust the selection probabilities of the local search operators. The experimental results demonstrate the superiority of the algorithm in terms of convergence, solution quality, and comprehensive metrics, in comparison with commonly used algorithms.

工业互联网平台被公认为是智能制造不可或缺的助推器，能够让实体制造资源虚拟化，让资源以服务的形式协同。制造服务协同优化作为平台的核心功能，致力于为制造任务建立优质的服务协同解决方案。这种优化离不开任务的功能和数量需求，在编排服务时必须满足这些需求。然而，现有的制造服务协同优化方法主要集中在服务之间针对功能需求的横向协同，很少考虑纵向协同来覆盖需求量。为了弥补这一差距，本文提出了一种将功能协作和数量协作相结合的二维服务协作方法论。首先，提出了一种多粒度的制造服务建模方法来描述服务。在此基础上，制定了二维制造服务协同优化（DMSCO）模型。在垂直维度上，多个功能等价的服务组成一个服务集群来完成一个子任务；在横向维度上，互补的服务集群协作完成整个任务。服务选择和所选服务的数量分配是模型中的关键问题。为了解决这个问题，定制了具有多个局部搜索算子的多目标模因算法。该算法嵌入了一种竞争机制来动态调整本地搜索算子的选择概率。实验结果表明，与常用算法相比，该算法在收敛性、求解质量和综合指标方面具有优越性。