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

Madalina Erascu

TL;DR

This work tackles the NP-hard problem of deploying component-based cloud applications by marrying graph-based learning with formal constraint solving. It introduces a neuro-symbolic pipeline where graph neural networks predict edge-type relations in a heterogeneous component–VM graph, and these predictions are integrated as soft constraints within a Z3 SMT solver to guide COP optimization. Through four diverse case studies, the approach demonstrates improved solver scalability and often maintained or enhanced cost-optimal deployments, highlighting the practical viability of neuro-symbolic methods for cloud infrastructure planning. The paper also provides a reusable methodology, datasets, and insights into how GNN architectures and training choices impact scalability and solution quality, along with directions for future enhancements (e.g., advanced GNNs, solver-initialization techniques).

Abstract

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.

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

TL;DR

This work tackles the NP-hard problem of deploying component-based cloud applications by marrying graph-based learning with formal constraint solving. It introduces a neuro-symbolic pipeline where graph neural networks predict edge-type relations in a heterogeneous component–VM graph, and these predictions are integrated as soft constraints within a Z3 SMT solver to guide COP optimization. Through four diverse case studies, the approach demonstrates improved solver scalability and often maintained or enhanced cost-optimal deployments, highlighting the practical viability of neuro-symbolic methods for cloud infrastructure planning. The paper also provides a reusable methodology, datasets, and insights into how GNN architectures and training choices impact scalability and solution quality, along with directions for future enhancements (e.g., advanced GNNs, solver-initialization techniques).

Abstract

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.

Paper Structure

This paper contains 34 sections, 6 equations, 25 figures, 8 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Neural-Symbolic Combinatorial Optimization Pipeline
  3. Problem Definition
  4. Problem Definition (as Constrained Optimization)
  5. General Constraints
  6. Application-specific Constraints
  7. Problem definition (Graph Edge Classification)
  8. Component nodes
  9. VM nodes
  10. Graph Embedding
  11. Solution Decoding
  12. Solution Search
  13. Policy Learning
  14. Constraint-Guided Solution Refinement
  15. Case Studies
  16. ...and 19 more sections

Figures (25)

  • Figure 1: Neural-symbolic optimization pipeline
  • Figure 2: Edge classification problem for Secure Web Container
  • Figure 3: Secure Web Container application ERASCU2021100664
  • Figure 4: Secure Billing Email Service
  • Figure 5: Oryx2 Application
  • ...and 20 more figures