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<p>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<sup>2</sup>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<sup>2</sup>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<sup>2</sup>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<sup>2</sup>NGT-QL-OA successfully optimized the trade-off between energy consumption and service throughput, proving its effectiveness for real-world IoT-Fog scenarios.</p>

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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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年6月29日

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  • Eman M. El-Gendy,
  • Abdelrahman O. Ali,
  • Mahmoud M. Saafan

摘要

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 M2NGT-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 (N2PCS) 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 M2NGT-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, M2NGT-QL-OA successfully optimized the trade-off between energy consumption and service throughput, proving its effectiveness for real-world IoT-Fog scenarios.