工业互联网平台是智能制造的关键推动者，能够允许各类物理制造资源虚拟封装后以制造服务的形式进行协作。制造服务协作优化是工业互联网平台的核心功能，其目的在于针对制造任务构建高质量的服务协作方案。在对服务协作方案进行优化时，必须同时满足制造任务的制造功能需求以及制造数量需求。然而，现有的制造服务协作优化研究主要关注面向功能需求的横向服务协作，针对面向数量需求的纵向服务协作鲜有涉及。因此，本文提出了一种同时考虑制造任务功能需求和数量需求的双维度服务协作方法。首先，提出了一种多粒度的制造服务建模方法，并在此基础上建立了双维度制造服务协作优化（DMSCO）模型。在纵向维度上，多个功能相似的制造服务组成一个服务集群以共同完成一个子任务；在横向维度上，多个功能互补的服务集群协作完成整个任务。其中，制造服务的选择和所选服务之间的制造数量分配是模型中的关键问题。针对该问题，本文设计了一种具有多种局部搜索算子的多目标模因算法，并在算法中构建竞争机制以动态调整每个局部搜索算子的选择概率。实验结果表明，与常用算法相比，本文所提算法在收敛性、质量性指标和综合指标等方面均具有优势。

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.