The Steiner Tree Problem (STP) is a fundamental NP-hard problem with widespread applications in network optimization and social network analysis (SNA). This paper introduces Fusion Ant Optimization (FAO), a novel metaheuristic framework based on Ant Colony Optimization (ACO), designed to improve solution quality and convergence for STP in SNA. Unlike conventional ACO approaches, FAO integrates multiple heuristic functions–terminal proximity, global topological influence, and node visitation frequency–with a dynamic local penalty mechanism to achieve a balanced exploration-exploitation trade-off. This multi-heuristic approach, combined with adaptive penalization, constitutes a significant advancement over existing ACO methods by leveraging SNA-specific graph properties, such as node centrality and dynamic topologies, to enhance scalability and solution quality. We evaluate FAO on benchmark instances derived from the SNAP Facebook Ego Network, modeled as an undirected and unweighted graph. Experimental results demonstrate that FAO achieves optimal solutions in over 80% of cases for small terminal sets ( \(k \le 10\) ), with minimal deviation in others, and consistently outperforms greedy baselines for larger cases ( \(k > 10\) ), remaining below the theoretical \(1.39 \cdot k\) approximation ratio. These results highlight FAO’s robustness across configurations, while underscoring the importance of hyperparameter tuning. FAO provides a scalable and adaptive solution for STP in complex networks, laying a strong foundation for future extensions to weighted graphs and learning-guided optimization.

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Fusion Ant Optimization: A Multi-heuristic Ant Colony Optimization for Steiner Tree Problem in Social Network Analysis

  • Lam Nguyen Phan Binh,
  • Anh Nguyen Thai

摘要

The Steiner Tree Problem (STP) is a fundamental NP-hard problem with widespread applications in network optimization and social network analysis (SNA). This paper introduces Fusion Ant Optimization (FAO), a novel metaheuristic framework based on Ant Colony Optimization (ACO), designed to improve solution quality and convergence for STP in SNA. Unlike conventional ACO approaches, FAO integrates multiple heuristic functions–terminal proximity, global topological influence, and node visitation frequency–with a dynamic local penalty mechanism to achieve a balanced exploration-exploitation trade-off. This multi-heuristic approach, combined with adaptive penalization, constitutes a significant advancement over existing ACO methods by leveraging SNA-specific graph properties, such as node centrality and dynamic topologies, to enhance scalability and solution quality. We evaluate FAO on benchmark instances derived from the SNAP Facebook Ego Network, modeled as an undirected and unweighted graph. Experimental results demonstrate that FAO achieves optimal solutions in over 80% of cases for small terminal sets ( \(k \le 10\) ), with minimal deviation in others, and consistently outperforms greedy baselines for larger cases ( \(k > 10\) ), remaining below the theoretical \(1.39 \cdot k\) approximation ratio. These results highlight FAO’s robustness across configurations, while underscoring the importance of hyperparameter tuning. FAO provides a scalable and adaptive solution for STP in complex networks, laying a strong foundation for future extensions to weighted graphs and learning-guided optimization.