A Novel Hybrid Fractional Krawtchouk and Fungal Growth Optimizer for Multi-Objective Fog Node Placement in IoT Networks

Abstract

The rapid growth of Internet of Things (IoT) devices has driven the development of fog computing paradigms aimed at overcoming latency and bandwidth bottlenecks in modern networks. Despite these advances, determining the optimal placement of fog nodes remains a challenging NP-hard problem that requires the joint optimization of network coverage and inter-node connectivity. Current metaheuristic approaches are constrained by their dependence on conventional Euclidean distance metrics, inflexible integer-order objective functions, and a poor balance between exploration and exploitation. This paper proposes a new hybrid optimization framework that integrates Fractional Krawtchouk (FK) moments with the Fungal Growth Optimizer (FGO) for multi-objective fog node placement. FK moments offer advanced spatial encoding capabilities through discrete orthogonal polynomials augmented with fractional-order derivatives, enabling efficient representation of both global network topology and localized coverage characteristics. The fractional-order formulation applies non-integer penalty exponents to achieve adaptable trade-offs between connectivity and coverage objectives. Rigorous experimental evaluation confirms that FK-FGO outperforms leading benchmark algorithms, including Harris Hawks Optimization, Marine Predators Algorithm, and Pufferfish Optimization Algorithm. The proposed method achieves 99.21% connectivity and 98.97% coverage, while delivering computational speedups of 57.3%–102.5% over competing approaches. Compared to the original FGO, FK-FGO converges 31.4% faster and reduces per-iteration processing time by 46.7%, all while demonstrating reliable scalability across network configurations ranging from 50 to 2000 fog nodes, making it a robust solution for next-generation fog computing deployments.