M2NGT-QL-OA: A Q-learning-based hybrid modified nutcracker and modified gorilla troops optimization algorithm for autonomic placement of IoT Services in fog platform

Metaheuristic optimization algorithms are widely used to solve complex engineering and real-world problems; however, no single algorithm can efficiently address all problem types. To overcome this limitation, this paper proposes M 2 NGT-QL-OA, a novel hybrid metaheuristic algorithm designed to solve the complex Autonomic Placement Problem of IoT Services in Fog Platforms (APPSF). The methodology integrates a Modified Nutcracker Optimizer (MNO) and a Modified Artificial Gorilla Troops Optimizer (MGTO) within a Q-learning (QL) framework, which dynamically selects the optimal sub-algorithm during the search process to balance exploration and exploitation. Key refinements include a Novel Nonlinear Parameter Control Strategy (N 2 PCS) for the Nutcracker component and the integration of nine chaotic maps and a nonlinear Exponential Factor (EF) for the Gorilla Troops component. The performance of M 2 NGT-QL-OA was rigorously validated against the CEC2017, CEC2019, and CEC2020 benchmark suites and six constrained engineering design problems. Statistical results using Friedman and Wilcoxon rank-sum tests demonstrate that the proposed algorithm significantly outperforms 17 recent and CEC-winning algorithms in terms of convergence speed, stability, and solution accuracy. When applied to the APPSF problem, M 2 NGT-QL-OA successfully optimized the trade-off between energy consumption and service throughput, proving its effectiveness for real-world IoT-Fog scenarios.