This paper proposes a novel hybrid neuro-symbolic framework for the optimal and scalable deployment of component-based applications in the Cloud. The challenge of efficiently mapping application components to virtual machines (VMs) across diverse VM Offers from Cloud Providers is formalized as a constrained optimization problem (COP), considering both general and application-specific constraints. Due to the NP-hard nature and scalability limitations of exact solvers, we introduce a machine learning-enhanced approach where graph neural networks (GNNs) are trained on small-scale deployment instances and their predictions are used as soft constraints within the Z3 SMT solver. The deployment problem is recast as a graph edge classification task over a heterogeneous graph, combining relational embeddings with constraint reasoning. Our framework is validated through several realistic case studies, each highlighting different constraint profiles. Experimental results confirm that incorporating GNN predictions improves solver scalability and often preserves or even improves cost-optimality. This work demonstrates the practical benefits of neuro-symbolic coupling for Cloud infrastructure planning and contributes a reusable methodology for general NP-hard problems.

翻译：本文提出了一种新颖的混合神经符号框架，用于在云环境中实现组件化应用的最优且可扩展部署。将应用组件高效映射到云提供商提供的多样化虚拟机（VM）供应方案中的挑战，被形式化为一个约束优化问题（COP），同时考虑通用约束与应用特定约束。鉴于精确求解器的NP难特性及可扩展性限制，我们引入了一种机器学习增强方法：在图神经网络（GNNs）上训练小规模部署实例，并将其预测结果作为软约束集成到Z3 SMT求解器中。该部署问题被重构为在异质图上的图边分类任务，结合了关系嵌入与约束推理。通过多个现实案例研究验证了本框架的有效性，每个案例均突显了不同的约束配置。实验结果表明，融入GNN预测能提升求解器的可扩展性，并常保持甚至改善成本最优性。本研究展示了神经符号耦合在云基础设施规划中的实际优势，并为一般NP难问题贡献了一种可复用的方法论。