# A Distributed Energy-Throughput Efficient Cross-Layer Framework Using Hybrid Optimization Algorithm
###### Abstract
Addressing these challenges will pave the way for more efficient and robust MI-WUSNs that can be deployed for a wide range of applications, including environmental monitoring, structural health monitoring, and navigation in challenging underground environments. As research in this field progresses, it is expected that innovative solutions and approaches will be developed to overcome these challenges and unlock the full potential of MI-WUSNs. In this article, we propose a distributed cross-layer solution specifically designed for WUSNs that utilize MI communication using MPNMRA. Our solution addresses the quality requirements of diverse applications while simultaneously achieving optimal energy efficiency, low computational complexity, and higher throughput. These distinctive characteristics make the proposed protocol practical and applicable in real-world scenarios. The marine predator naked mole rat algorithm (MPNMRA) is a recently introduced nature-inspired optimization algorithm to mitigate the drawbacks of both the marine predator algorithm (MPA) and the naked mole-rat algorithm (NMRA) while retaining the benefits of the respective algorithms. This algorithm is suitable for unimodal, multimodal, and complex engineering design problems. In this study, we present a distributed energy-throughput efficient cross-layer network utilizing a hybrid marine predator naked mole rat algorithm (DECMN) protocol framework. The DECMN protocol is designed to achieve a predefined quality of service (QoS) while considering the interactions between different layers, thereby optimizing resource utilization and enhancing overall system performance. DECMN offers significant improvements in energy efficiency and throughput gains with low computing complexity. Initially, we analyze the interference effects of the MI channel model both with and without relay coils, as well as the impact of path loss and bandwidth on the physical layer functionality. We propose a cross-layer solution within the DECMN framework that addresses the performance requirements of diverse applications. Specifically, we consider the objective functions, namely energy consumption and packet transmission rate, and assign weights to these objectives. Through the use of specific weight vectors, we transform the optimization problem into a single objective function using a weighted sum method. Overall, the DECMN protocol framework provides a comprehensive and efficient solution for achieving energy efficiency, high throughput, and satisfying the performance needs of different applications. The main contribution of the proposed cross-layer solution can be summarized as follows:  
* A comprehensive study has been conducted to investigate the interactions between different underground communication functions and the QoS requirements of various applications. * A cross-layer framework that efficiently utilizes the limited bandwidth of the MI communication channel and integrates the functionalities of MI relay coils (referred to as MI waveguide) has been developed. * The DECMN framework is designed to distribute the cross-layer solution, ensuring statistical QoS guarantees and achieving optimal throughput gains while simultaneously saving energy. Simulation results demonstrate that DECMN outperforms layered protocols and DEAP in terms of energy savings and throughput improvements. The proposed solution adopts a two-stage per-node decision-making process, which only requires information from neighboring nodes and reduces computational complexity compared with centralized cross-layer designs. The rest of the paper is organized as follows: The hybrid marine predator naked mole-rat algorithm (MPNMRA), which is utilized in the proposed solution, is described comprehensively in Section 2. The DECMN framework is introduced in Section 3 as a cross-layer optimization problem. The framework is designed to achieve optimal energy throughput, and its components and functionalities are discussed. An evaluation of the performance of the proposed cross-layer solution is provided in Section 4.