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

Abstract

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.

DOI: 10.5281/zenodo.16734145