Vol. 5 No. 2 (2025): July−December 2025
Articles

Deep Reinforcement Learning Approach for Maximum Clique Problem: A Graph Neural Network Enhanced Q-Learning Framework

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  • Toan Khang Trinh,
  • Zhuxuanzi Wang
Toan Khang Trinh
Computer Science, California State University Long Beach, CA, USA
Zhuxuanzi Wang
Information Systems, Cornell Tech, NY, USA

Published 2025-07-10

Keywords

  • Deep Reinforcement Learning,
  • Maximum Clique Problem,
  • Graph Neural Networks,
  • Q-Learning

How to Cite

Trinh, T. K., & Wang, Z. (2025). Deep Reinforcement Learning Approach for Maximum Clique Problem: A Graph Neural Network Enhanced Q-Learning Framework. Spectrum of Research, 5(2). Retrieved from https://spectrumofresearch.com/index.php/sr/article/view/35

Copyright (c) 2025 Spectrum of Research

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

The Maximum Clique Problem (MCP) represents one of the fundamental NP-hard optimization challenges in graph theory with widespread applications in bioinformatics, social network analysis, and resource allocation systems. Traditional heuristic approaches often struggle with scalability and solution quality trade-offs when addressing large-scale graph instances. This paper presents a novel deep reinforcement learning framework that integrates Graph Neural Networks (GNN) with Q-learning for solving the Maximum Clique Problem. The proposed approach employs a sophisticated state representation mechanism that captures both local and global graph structural information through multi-layer graph convolutional operations. The Q-learning agent learns optimal node selection policies through iterative interaction with graph environments, while the GNN component provides enhanced feature extraction capabilities. Experimental validation on standard benchmark datasets demonstrates significant improvements over conventional heuristic methods, achieving an average solution quality improvement of 15.3% and computational efficiency gains of 23.7% compared to state-of-the-art algorithms. The framework exhibits robust performance across diverse graph topologies, including sparse and dense networks, with particular effectiveness on graphs containing 500 to 5000 vertices. The integration of attention mechanisms within the GNN architecture enables dynamic focus on promising graph regions during the solution construction process. Performance analysis reveals consistent convergence behavior and stable learning dynamics across multiple experimental configurations, establishing the framework's reliability for practical applications in computational optimization.

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