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Learning to Select MCP Algorithms: From Traditional ML to Dual-Channel GAT-MLP

Xiang Li, Shanshan Wang, Chenglong Xiao

TL;DR

This work tackles instance-aware solver selection for the Maximum Clique Problem by combining traditional ML with a dual-channel GNN. It constructs a labeled dataset by running four exact MCP solvers on a diverse set of graphs and extracting 12 global/local features, training various models and introducing GAT-MLP to fuse local and global information. Empirical results show GAT-MLP achieves 90.43% accuracy, outperforming classical classifiers and other GNN baselines, and ablation confirms the complementary value of the two channels and simple concatenation fusion. The framework demonstrates the promise of graph neural networks for combinatorial algorithm selection and provides a benchmark and code for future work.

Abstract

The Maximum Clique Problem (MCP) is a foundational NP-hard problem with wide-ranging applications, yet no single algorithm consistently outperforms all others across diverse graph instances. This underscores the critical need for instance-aware algorithm selection, a domain that remains largely unexplored for the MCP. To address this gap, we propose a novel learning-based framework that integrates both traditional machine learning and graph neural networks. We first construct a benchmark dataset by executing four state-of-the-art exact MCP solvers on a diverse collection of graphs and extracting their structural features. An evaluation of conventional classifiers establishes Random Forest as a strong baseline and reveals that connectivity and topological features are key predictors of performance. Building on these insights, we develop GAT-MLP, a dual-channel model that combines a Graph Attention Network (GAT) to encode local graph structure with a Multilayer Perceptron (MLP) to model global features. Extensive experiments demonstrate that GAT-MLP achieves superior and consistent performance, significantly outperforming all baseline methods. Our results highlight the effectiveness of the dual-channel architecture and the promise of graph neural networks for combinatorial algorithm selection, achieving 90.43% accuracy in choosing the optimal solver. Code and models are available at: https://anonymous.4open.science/r/GAT-MLP-7E5F.

Learning to Select MCP Algorithms: From Traditional ML to Dual-Channel GAT-MLP

TL;DR

This work tackles instance-aware solver selection for the Maximum Clique Problem by combining traditional ML with a dual-channel GNN. It constructs a labeled dataset by running four exact MCP solvers on a diverse set of graphs and extracting 12 global/local features, training various models and introducing GAT-MLP to fuse local and global information. Empirical results show GAT-MLP achieves 90.43% accuracy, outperforming classical classifiers and other GNN baselines, and ablation confirms the complementary value of the two channels and simple concatenation fusion. The framework demonstrates the promise of graph neural networks for combinatorial algorithm selection and provides a benchmark and code for future work.

Abstract

The Maximum Clique Problem (MCP) is a foundational NP-hard problem with wide-ranging applications, yet no single algorithm consistently outperforms all others across diverse graph instances. This underscores the critical need for instance-aware algorithm selection, a domain that remains largely unexplored for the MCP. To address this gap, we propose a novel learning-based framework that integrates both traditional machine learning and graph neural networks. We first construct a benchmark dataset by executing four state-of-the-art exact MCP solvers on a diverse collection of graphs and extracting their structural features. An evaluation of conventional classifiers establishes Random Forest as a strong baseline and reveals that connectivity and topological features are key predictors of performance. Building on these insights, we develop GAT-MLP, a dual-channel model that combines a Graph Attention Network (GAT) to encode local graph structure with a Multilayer Perceptron (MLP) to model global features. Extensive experiments demonstrate that GAT-MLP achieves superior and consistent performance, significantly outperforming all baseline methods. Our results highlight the effectiveness of the dual-channel architecture and the promise of graph neural networks for combinatorial algorithm selection, achieving 90.43% accuracy in choosing the optimal solver. Code and models are available at: https://anonymous.4open.science/r/GAT-MLP-7E5F.

Paper Structure

This paper contains 18 sections, 8 equations, 8 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Exact Algorithms for the Maximum Clique Problem
  4. Algorithm Selection for Combinatorial Problems
  5. Methodology
  6. Dataset Preparation and Classical Machine Learning Models
  7. Dual-Channel Architecture
  8. Baselines
  9. Experiments
  10. Experiment Settings
  11. Experimental Environment
  12. Datasets
  13. Evaluation Metrics
  14. Hyperparameter Settings
  15. Experimental Results
  16. ...and 3 more sections

Figures (8)

  • Figure 1: Win-rate of four state-of-the-art solvers across graph families.
  • Figure 2: The proposed framework for algorithm selection in the MCP.
  • Figure 3: Overview of the three methods for handling multi-label samples.
  • Figure 4: Architecture of the proposed dual-channel GAT model, consisting of a structure encoder (graph-based) and a statistical encoder (global features), followed by feature fusion and classification.
  • Figure 5: Accuracy of four classifiers under three feature-engineering methods (mean $\pm$ std; *: Mann--Whitney U test vs. best, $p<0.05$).
  • ...and 3 more figures