Payame Noor University (PNU) Control and Optimization in Applied Mathematics 2383-3130 10 2 2025 07 01 Solution Techniques for Fuzzy Graph Partitioning Based on Heuristic Optimization 273 293 12021 10.30473/coam.2025.74009.1296 EN Mohammad Alsaeedi Faculty of Mathematical Sciences‎, ‎Department of Applied Mathematics‎, ‎Ferdowsi University of Mashhad‎, ‎Mashhad‎, ‎Iran. Mostafa Tavakolli Faculty of Mathematical Sciences‎, ‎Department of Applied Mathematics‎, ‎Ferdowsi University of Mashhad‎, ‎Mashhad‎, ‎Iran. Ahmad Abouyee Faculty of Mathematical Sciences‎, ‎Department of Applied Mathematics‎, ‎Ferdowsi University of Mashhad‎, ‎Mashhad‎, ‎Iran. Khatere Ghorbani Moghadam Mosaheb Institute of Mathematics‎, ‎Kharazmi University‎, ‎Tehran‎, ‎Iran‎. Reza Ghanbari Faculty of Mathematical Sciences‎, ‎Department of Applied Mathematics‎, ‎Ferdowsi University of Mashhad‎, ‎Mashhad‎, ‎Iran. Journal Article 2025 03 13 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. https://mathco.journals.pnu.ac.ir/article_12021_6f19abc98599517a9fe5b178969d3b80.pdf