Solution Techniques for Fuzzy Graph Partitioning Based on Heuristic Optimization
نویسندگان
1 Faculty of Mathematical Sciences, Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran.
2 Faculty of Mathematical Sciences, Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran.
3 Mosaheb Institute of Mathematics, Kharazmi University, Tehran, Iran.
4 Faculty of Mathematical Sciences, Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran.
5 Faculty of Mathematical Sciences, Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran.
doi
10.30473/coam.2025.74009.1296چکیده
In this study, we proposed a novel graph partitioning problem where the edges are characterized by trapezoidal fuzzy numbers. A linear ranking function is employed to establish an order among these fuzzy numbers. We derive the necessary conditions for the existence of an optimal solution to this problem. To address the fuzzy graph partitioning problem, we implement and compare the performance of three algorithms: Genetic Algorithm, Tabu Search, and Sequential Least Squares Programming. The algorithms are evaluated based on objective values, computational time, and the number of iterations across multiple numerical examples. Utilizing Dolan-Moré performance profiles, we demonstrate the superiority of our proposed approach relative to existing methods. The findings highlight the robustness and computational efficiency of our methodology, making a meaningful contribution to the advancement of fuzzy graph algorithms and their practical applications.
