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

The proliferation of Internet of Things (IoT) devices has necessitated fog computing paradigms to address latency and bandwidth challenges. However, optimal fog node placement remains a critical NP-hard challenge requiring simultaneous optimization of network coverage and inter-node connectivity. Existing metaheuristic approaches suffer from limitations including reliance on traditional Euclidean metrics, rigid integer-order objective functions, and poor exploration-exploitation balance. This paper introduces a novel hybrid framework integrating Fractional Krawtchouk (FK) moments with the Fungal Growth Optimizer (FGO) for multi-objective fog node placement. FK moments provide sophisticated spatial representation through discrete orthogonal polynomials enhanced with fractional-order derivatives, enabling efficient encoding of global topology and local coverage patterns. The fractional-order formulation employs non-integer penalty exponents for flexible connectivity-coverage trade-offs. Comprehensive experimental evaluation demonstrates FK-FGO's superiority over state-of-the-art algorithms including Harris Hawks Optimization, Marine Predators Algorithm, and Pufferfish Optimization Algorithm. Results show 99.21% connectivity and 98.97% coverage, with 57.3%-102.5% computational speedup compared to competing methods. The algorithm achieves 31.4% faster convergence and 46.7% per-iteration speedup versus original FGO while maintaining robust scalability from 50 to 2000 fog nodes, providing a powerful solution for next-generation fog computing deployments.