Neuro-Symbolic Constrained Optimization for Cloud Application Deployment via Graph Neural Networks and Satisfiability Modulo Theory

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.