A Hybrid PSO and Kruskal Approach for Neutrosophic Trapezoidal Minimum Spanning Tree Problem

The goal of the Minimum Spanning Tree Problem (Min-STP) is to build a spanning tree (ST) in a network or graph while minimising the overall edge cost. Logistics, interaction, mobility, and scheduling are just a few of the many real-world applications of this simple combinatorial optimisation problem. However, in real life Min-STP circumstances, uncertainty due to inconsistent, ambiguous, or missing information makes accurate estimation of edge weights difficult. The neutrosophic set is a useful tool to manage these types of problems. In this manuscript, trapezoidal neutrosophic sets are used to describe the edge weights of the neutrosophic graph. We define this problem as Neutrosophic trapezoidal Min-STP (NTMin-STP). Using trapezoidal neutrosophic sets to describe edge cost uncertainty, this paper presents a particle swarm optimisation (PSO) technique for solving NTMin-STP in a neutrosophic environment. We also modify Kruskal’s technique to solve the NTMin STP. In contrast to conventional methods, PSO provides flexibility in managing dynamic and sizable networks, which makes it especially appropriate for real-world scenarios where edge weights fluctuate. PSO’s population based search effectively explores the solution space, reducing the risk of local optima. We provide numerical examples to demonstrate the efficacy of the suggested PSO-based Min-STP technique. The findings show that PSO is a viable substitute for managing Min-STP uncertainty, providing a reliable and flexible solution.