Improved Whale Optimization Algorithm Research Articles

Time-Optimized Robot Trajectory Based on Improved Whale Optimization Algorithm in Intelligent Manufacturing

Abstract To discuss the low convergence accuracy of whale optimization algorithm (WOA) and the problem of converging to local optima, we proposed using nonlinear convergence factors and introducing nonlinear inertia weights in the WOA. The modified WOA was used to optimize the trajectory of a six-degrees-of-freedom (6DOF) industrial robot. To improve the convergence accuracy and the local and global search ability of the WOA, we first replaced the convergence factor with a nonlinear convergence factor and added a nonlinear inertia weight. The algorithm was used along with a quintic polynomial equation to develop a time-optimal trajectory, for the robot, for use in practical application scenarios. Simulation experiment results showed that the duration of a complete loading–unloading process was reduced by 30% after robot motion trajectory optimization compared with that before optimization, indicating the effectiveness of the improved WOA and its suitability for robot trajectory optimization.

Voltage sag source location based on power polarity and twin characteristics matching

AbstractPrecisely locating the voltage sag sources is significant for improving power quality and clarifying the responsibilities of both power supply and consumption. However, the existing location models are complex, computationally intensive, and influenced by the measurement error and fault type, which have low positioning efficiency and large errors. Therefore, this paper proposes a method for locating voltage sag sources based on power polarity and twin characteristics matching. The method firstly uses the polarity of the sequence sag component disturbance reactive power at the monitoring point to determine the sag line. Secondly, the basic realization method of the twin power system is discussed, and the twin characteristics are defined by combining the positive and negative sequence sag component disturbance reactive power and the twin database is established. Thirdly, the spectral norm and Pearson product‐moment correlation coefficient are used to define the data matching degree, and the precise location model of the sag source is established with the objective function of maximizing the data matching between the twin characteristics of the preset and actual sag. Finally, the Improved Whale Optimization Algorithm is used to solve the location model. The correctness and superiority of the proposed method is verified based on IEEE33 node modelling.

Debris flow volume prediction model based on back propagation neural network optimized by improved whale optimization algorithm.

Debris flow is a sudden natural disaster in mountainous areas, which seriously threatens the lives and property of nearby residents. Therefore, it is necessary to predict the volume of debris flow accurately and reliably. However, the predictions of back propagation neural networks are unstable and inaccurate due to the limited dataset. In this study, the Cubic map optimizes the initial population position of the whale optimization algorithm. Meanwhile, the adaptive weight adjustment strategy optimizes the weight value in the shrink-wrapping mechanism of the whale optimization algorithm. Then, the improved whale optimization algorithm optimizes the final weights and thresholds in the back propagation neural network. Finally, to verify the performance of the final model, sixty debris flow gullies caused by earthquakes in Longmenshan area are selected as the research objects. Through correlation analysis, 4 main factors affecting the volume of debris flow are determined and inputted into the model for training and prediction. Four methods (support vector machine regression, XGBoost, back propagation neural network optimized by artificial bee colony algorithm, back propagation neural network optimized by grey wolf optimization algorithm) are used to compare the prediction performance and reliability. The results indicate that loose sediments from co-seismic landslides are the most important factor influencing the flow of debris flows in the earthquake area. The mean absolute percentage error, mean absolute error and R2 of the final model are 0.193, 29.197 × 104 m3 and 0.912, respectively. The final model is more accurate and stable when the dataset is insufficient and under complexity. This is attributed to the optimization of WOA by Cubic map and adaptive weight adjustment. In general, the model of this paper can provide reference for debris flow prevention and machine learning algorithms.

An Efficient Metaheuristic Technique for Wireless Sensor Network Integrated Micro Grid Environment Using Improved Whale Optimization Algorithm (Iwoa)

Wireless Sensor Network (WSN) nodes require careful power management to maintain long term operation without regular battery changes. Battery replacement can be challenging and expensive in a microgrid scenario where sensors may be installed in remote or i naccessible areas. To extend the life of WSN nodes, energy efficient design and power management strategies should be used. A potential strategy for effectively monitoring, controlling, and managing the distributed energy resources (DERs) inside a microgri d is theincorporation of WSNs with microgrids. This research work uses Improved Whale Optimization Algorithm (WOA) for optimizing the routing and performance. The humpback whale's hunting style served as the inspiration for the WOA, a metaheuristic optimization algorithm. WOA is an optimization technique that is used with MG and WSNs. During the optimization phase, WOA establishes a balance between exploitation and exploration. To increase the lifespan of a WSN in a microgrid, effective energy management i s frequently needed. When considering the dynamic energy availability from renewable sources and the energy requirements of the microgrid components, WOA is used to optimise energy allocation and routing in WSNs. This may lead to increased energy efficiency and longer network longevity. The IWOA attains 97.5% PDR that is higher than the existing state of art techniques.

Renewable energy hosting capacity assessment in distribution networks based on multi‐strategy improved whale optimization algorithm

AbstractThe increasing penetration of distributed renewable energy poses significant challenges to the safety and stability of distribution system, rendering the renewable energy hosting capacity of distribution networks a major concern. To effectively evaluate the renewable energy hosting capacity in distribution networks, this paper introduces a comprehensive hosting capacity assessment model considering various safety and stability constraints. Given the numerous non‐linear constraints inherent in the hosting capacity assessment model for distribution networks, a multi‐strategy improved Whale Optimization Algorithm is proposed. Improvements are made to the population initialization and population position update strategies, and a mutation strategy is introduced to prevent premature convergence, thereby enhancing the algorithm's performance. Finally, the effectiveness of the proposed model and the method is validated through the utilization of three distribution systems. Moreover, the key factors that restrict the improvement of hosting capacity are revealed from the perspective of distribution network topology.

Study of flow stress in Mg-Gd-Y-Nd-Zr alloys based on IWOA-BPNN model

This study investigates the compression deformation behavior of an Mg-Gd-Y-Nd-Zr alloy at temperatures ranging from 293 K to 573 K and strain rates ranging from 293K to 573K and strain rates ranging from 1000 s−1 to 2100 s−1 using a split Hopkinson pressure bar. A modified Johnson-Cook (JC) constitutive model and a backpropagation neural network (BPNN) model based on the improved whale optimization algorithm (IWOA) are established. Four statistical metrics, including correlation coefficient (R), mean absolute error (MAE), mean absolute percentage error (MAPE), and root mean square error (RMSE), are employed to evaluate the predictive accuracy of the two models. The findings indicate that the flow stress of the alloy is sensitive to strain, strain rate, and temperature. Increasing strain and strain rate or decreasing deformation temperature results in higher flow stress. Error calculations revealed that the modified Johnson-Cook constitutive model has an R of 0.98731, a MAPE of 7.3653%, a MAE of 19.6305 MPa, and a RMSE of 26.5704 MPa. In contrast, the model established using the IWOA-BPNN has an R of 0.99996, a MAPE of 0.58894%, a MAE of 1.2671 MPa, and a RMSE of 1.7709 MPa. The IWOA-BPNN model demonstrates higher accuracy and accurately predicts the flow stress of the alloy.

Thermal Management of Proton‐Exchange Membrane Fuel Cells with Enhanced Fuzzy Control via an Improved Whale Optimization Algorithm

Proton exchange membrane fuel cells (PEMFCs) require an appropriate operating temperature to achieve high performance and longevity. In addressing the critical need for effective thermal management in PEMFCs for vehicle propulsion systems, this study has developed and introduced a novel thermal management system model equipped with dual‐cooling loops. Addressing the issues of slow response and poor dynamic performance inherent in traditional control strategies, as well as the computational complexity that hinders the practical application of existing advanced control strategies, this research proposes a fuzzy proportional‐integral‐derivative (PID) controller optimizing the improved whale optimization algorithm (IWOA‐FPID) aimed at enhancing fan side control. By simulating step changes in current load and designing dynamic operating conditions based on the most basic and simple energy management system, the performance of IWOA‐FPID in temperature control is validated. The final results indicate that the IWOA‐FPID strategy significantly outperforms existing control methods, notably reducing adjustment time and minimizing temperature overshoot to ≈0.5 K. The proposed framework achieves efficient temperature control, highlighting its potential for broader application in vehicular fuel cells and offering a promising solution to the challenges of PEMFC thermal management.

Deep Learning-Based Stock Market Prediction and Investment Model for Financial Management

This study explores the potential application of deep learning techniques in stock market prediction and investment decision-making. The authors used multi-temporary stock data (MTS) for effective multi-scale feature extraction in reverse cross attention (RCA), combined with improved whale optimization algorithm (IWOA) to select the optimal parameters for the bidirectional long short-term memory network (BiLSTM) and constructed an innovative RCA-BiLSTM stock intelligent trend prediction model. At the same time, a complete RCA-BiLSTM-DQN stock intelligent prediction and investment model was established by combining the deep Q network (DQN) investment strategy. The research results indicate that the model has excellent sequence modeling and decision learning capabilities, which can capture the nonlinear characteristics and complex correlations of the market and provide more accurate prediction results. It can continuously improve the robustness and stability of the model through adaptive learning and automatic optimization.

IWO-IGA—A Hybrid Whale Optimization Algorithm Featuring Improved Genetic Characteristics for Mapping Real-Time Applications onto 2D Network on Chip

Network on Chip (NoC) has emerged as a potential substitute for the communication model in modern computer systems with extensive integration. Among the numerous design challenges, application mapping on the NoC system poses one of the most complex and demanding optimization problems. In this research, we propose a hybrid improved whale optimization algorithm with enhanced genetic properties (IWOA-IGA) to optimally map real-time applications onto the 2D NoC Platform. The IWOA-IGA is a novel approach combining an improved whale optimization algorithm with the ability of a refined genetic algorithm to optimally map application tasks. A comprehensive comparison is performed between the proposed method and other state-of-the-art algorithms through rigorous analysis. The evaluation consists of real-time applications, benchmarks, and a collection of arbitrarily scaled and procedurally generated large-task graphs. The proposed IWOA-IGA indicates an average improvement in power reduction, improved energy consumption, and latency over state-of-the-art algorithms. Performance based on the Convergence Factor, which assesses the algorithm’s efficiency in achieving better convergence after running for a specific number of iterations over other efficiently developed techniques, is introduced in this research work. These results demonstrate the algorithm’s superior convergence performance when applied to real-world and synthetic task graphs. Our research findings spotlight the superior performance of hybrid improved whale optimization integrated with enhanced GA features, emphasizing its potential for application mapping in NoC-based systems.

A new strategy for groundwater level prediction using a hybrid deep learning model under Ecological Water Replenishment.

Accurate prediction of the groundwater level (GWL) is crucial for sustainable groundwater resource management. Ecological water replenishment (EWR) involves artificially diverting water to replenish the ecological flow and water resources of both surface water and groundwater within the basin. However, fluctuations in GWLs during the EWR process exhibit high nonlinearity and complexity in their time series, making it challenging for single data-driven models to predict the trend of groundwater level changes under the backdrop of EWR. This study introduced a new GWL prediction strategy based on a hybrid deep learning model, STL-IWOA-GRU. It integrated the LOESS-based seasonal trend decomposition algorithm (STL), improved whale optimization algorithm (IWOA), and Gated recurrent unit (GRU). The aim was to accurately predict GWLs in the context of EWR. This study gathered GWL, precipitation, and surface runoff data from 21 monitoring wells in the Yongding River Basin (Beijing Section) over a period of 731days. The research results demonstrate that the improvement strategy implemented for the IWOA enhances the convergence speed and global search capabilities of the algorithm. In the case analysis, evaluation metrics including the root mean square error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE), and Nash-Sutcliffe efficiency (NSE) were employed. STL-IWOA-GRU exhibited commendable performance, with MAE achieving the best result, averaging at 0.266. When compared to other models such as Variance Mode Decomposition-Gated Recurrent Unit (VMD-GRU), Ant Lion Optimizer-Support Vector Machine (ALO-SVM), STL-Particle Swarm Optimization-GRU (STL-PSO-GRU), and STL-Sine Cosine Algorithm-GRU (STL-SCA-GRU), MAE was reduced by 18%, 26%, 11%, and 29%, respectively. This indicates that the model proposed in this study exhibited high prediction accuracy and robust versatility, making it a potent strategic choice for forecasting GWL changes in the context of EWR.

Research on Parameter Inversion of Coal Mining Subsidence Prediction Model Based on Improved Whale Optimization Algorithm

Rapid coal mining results in a series of mining subsidence damages. Predicting surface movement and deformation accurately is essential to reducing mining damage. The accurate determination of parameters for a mining subsidence prediction model is crucial for accurately predicting mining subsidence. In this research, with the incorporation of the Sobol sequence and Lévy flight strategy, we propose an improved whale optimization algorithm (IWOA), thereby enhancing its global optimization capability and mitigating local optimization issues. Our simulation experiment results demonstrate that the IWOA achieved a root mean square error and relative error of less than 0.42 and 0.27%, respectively, indicating its superior accuracy compared to a basic algorithm. The IWOA inversion model also exhibits superior performance compared to a basic algorithm in mitigating gross error interference, Gaussian noise interference, and missing observation point interference. Additionally, it demonstrates enhanced global search capabilities. The IWOA was employed to perform parameter inversion for the working face 1414(1) in Guqiao Coal Mine. The root mean square error of the inversion results did not exceed 6.03, while the subsidence coefficient q, tangent of the main influence angle tanβ, horizontal movement coefficient b, and mining influence propagation angle θ were all below 0.32. The average value of the fitted root mean square error for the subsidence value’s fitted root mean square error and horizontal movement value’s fitted root mean square error of the IWOA was 91.51 mm, which satisfies the accuracy requirements for general engineering applications.

[Research on emotion recognition method based on IWOA-ELM algorithm for electroencephalogram].

Emotion is a crucial physiological attribute in humans, and emotion recognition technology can significantly assist individuals in self-awareness. Addressing the challenge of significant differences in electroencephalogram (EEG) signals among different subjects, we introduce a novel mechanism in the traditional whale optimization algorithm (WOA) to expedite the optimization and convergence of the algorithm. Furthermore, the improved whale optimization algorithm (IWOA) was applied to search for the optimal training solution in the extreme learning machine (ELM) model, encompassing the best feature set, training parameters, and EEG channels. By testing 24 common EEG emotion features, we concluded that optimal EEG emotion features exhibited a certain level of specificity while also demonstrating some commonality among subjects. The proposed method achieved an average recognition accuracy of 92.19% in EEG emotion recognition, significantly reducing the manual tuning workload and offering higher accuracy with shorter training times compared to the control method. It outperformed existing methods, providing a superior performance and introducing a novel perspective for decoding EEG signals, thereby contributing to the field of emotion research from EEG signal.

A Novel Improved Whale Optimization Algorithm for Global Optimization and Engineering Applications

The Whale Optimization Algorithm (WOA) is a swarm intelligence algorithm based on natural heuristics, which has gained considerable attention from researchers and engineers. However, WOA still has some limitations, including limited global search efficiency and a slow convergence rate. To address these issues, this paper presents an improved whale optimization algorithm with multiple strategies, called Dynamic Gain-Sharing Whale Optimization Algorithm (DGSWOA). Specifically, a Sine–Tent–Cosine map is first adopted to more effectively initialize the population, ensuring a more uniform distribution of individuals across the search space. Then, a gaining–sharing knowledge based algorithm is used to enhance global search capability and avoid falling into a local optimum. Finally, to increase the diversity of solutions, Dynamic Opposition-Based Learning is incorporated for population updating. The effectiveness of our approach is evaluated through comparative experiments on blackbox optimization benchmarking and two engineering application problems. The experimental results suggest that the proposed method is competitive in terms of solution quality and convergence speed in most cases.

Ensemble 3D CNN and U-Net-based brain tumour classification with MKKMC segmentation

Advanced brain cancer is the deadliest type with just a few months survival rate. Existing technologies hinder the objective of forecasting cancer.   This work aims to fulfil the pressing requirement for timely and precise identification of advanced-stage brain tumours, which are notorious for their markedly reduced life expectancy. It presents an innovative hybrid approach for predicting brain tumours and improves diagnostic capabilities. The Multiple Kernel K-Means Cluster Algorithm (MKKCA) is used to segment brain MRI images effectively, differentiating healthy and tumorous tissues. After segmentation, a hybrid approach with 3D-Convolutional Neural Network (CNN) and U-Net has been utilized for classification. The objective is to effectively and accurately distinguish normal and pathological brain images. To enhance the efficiency, we include the Improved Whale Optimization Algorithm (IWOA), which guarantees accurate and dependable performance via location updates. The methodology demonstrates outstanding precision with 98.5% accuracy rate, 98.56% specificity, 91% sensitivity, 87.45% precision and a recall rate of 96% with the F-Measure at 96.02%. These findings, obtained using MATLAB, demonstrate a substantial performance improvement compared to current approaches. This development not only represents a significant addition to diagnostic imaging but also a crucial role in the prediction and treatment of brain cancers.

Rolling bearing fault diagnosis based on improved whale-optimization- algorithm–variational-mode-decomposition method

Rolling bearings are a key component of rotating machinery and their health directly affects the safe operation of mechanical equipment. Therefore, fault diagnose for rolling bearings is very important. The fault diagnosis process of rolling bearings includes three stages: signal decomposition, feature extraction, and pattern recognition. Variational mode decomposition (VMD) can suppress end effects, but improper parameter settings will cause information losses or excessive decomposition. In this work, an improved whale optimization algorithm (IWOA) is applied to parameter settings of VMD. Correspondingly, an IWOA-VMD signal decomposition method is proposed. The decomposed signal is combined with a Laplace score method and classifier to remove the redundancy and noise in the feature set and obtain a low-dimensional sensitive feature subset. Then, aiming at the problem of the parameter settings of a least squares support vector machine (LSSVM) affecting the recognition performance and accuracy, a salp swarm algorithm (SSA) is used to globally optimize the penalty parameter and kernel width in the LSSVM to establish an SSA-LSSVM fault recognition model. This model is applied to the fault diagnosis of rolling bearings. In particular, rolling bearing fault samples at Case Western Reserve University are used to verify the method. The results indicate that the proposed method is effective and improves the speed and accuracy of fault diagnosis.

Swarm intelligence based deep learning model via improved whale optimization algorithm and Bi-directional long short-term memory for fault diagnosis of chemical processes

The chemical production process typically possesses complexity and high risks. Effective fault diagnosis is a key technology for ensuring the reliability and safety of chemical production processes. In this study, a comprehensive fault diagnosis method based on time-varying filtering empirical mode decomposition (TVF-EMD), kernel principal component analysis (KPCA), and an improved whale optimization algorithm (WOA) to optimize bi-directional long short-term memory (BiLSTM) is proposed. This research utilizes TVF-EMD and KPCA to analyze and preprocess the raw data, eliminating noise and and reducing the dimensions of the fault data. Subsequently, BiLSTM is employed for fault data classification. To address the hyperparameters within BiLSTM, the enhanced WOA is used for optimization. Finally, the efficacy and superiority of this approach are validated through two fault diagnosis examples.

A hybrid prediction model of improved bidirectional long short-term memory network for cooling load based on PCANet and attention mechanism

Accurate and reliable cooling load forecasting is a prerequisite for air-conditioning system control and the basis for building-side energy management. Therefore, a hybrid prediction model of an improved bidirectional long short-term memory (BiLSTM) network based on principal component analysis network (PCANet) and attention mechanism (CNN-IBiLSTM-Attention) is proposed to predict the cooling load of large commercial buildings. First of all, the PCANet algorithm is used to analyze the sensitivity of the influencing factors. Then, the hybrid strategy improved whale optimization algorithm (HSIWOA) is used to optimize the hyperparameter of BiLSTM. At last, the performance of the proposed algorithm is verified by using the actual data of two commercial buildings in Xi'an. The results show that using the PCANet algorithm for sensitivity analysis avoids feature redundancy. HSIWOA is suitable for hyperparameter optimization of BiLSTM. Compared with the other three prediction models, CNN-IBiLSTM-Attention reduced the mean absolute percentage error (MAPE) of Building 1 and 2 test sets by 31.55 %, 55.59 %, and 60.58 % and 56.49 %, 60.3 %, and 67.37 %, respectively. The proposed prediction model has superior hyperparameter optimization ability, better model complexity, and stronger generalization ability. Therefore, the proposed prediction model becomes a reliable tool for predicting the cooling load of large commercial buildings.

Load Day-Ahead Automatic Generation Control Reserve Capacity Demand Prediction Based on the Attention-BiLSTM Network Model Optimized by Improved Whale Algorithm

Load forecasting is a research hotspot in academia; in the context of new power systems, the prediction and determination of load reserve capacity is also important. In order to adapt to new forms of power systems, a day-ahead automatic generation control (AGC) reserve capacity demand prediction method based on the Fourier transform and the attention mechanism combined with a bidirectional long and short-term memory neural network model (Attention-BiLSTM) optimized by an improved whale optimization algorithm (IWOA) is proposed. Firstly, based on the response time, Fourier transform is used to refine the distinction between various types of load reserve demand, and the power of the AGC reserve band is calculated using Parseval’s theorem to obtain the reserve capacity demand sequence. The maximum mutual information coefficient method is used to explore the relevant influencing factors of the AGC reserve sequence concerning the data characteristics of the AGC reserve sequence. Then, the historical daily AGC reserve demand sequences with relevant features are input into the Attention-BiLSTM prediction model, and the improved whale algorithm is used to automatically find the optimal hyperparameters to obtain better prediction results. Finally, the arithmetic simulation results show that the model proposed in this paper has the best prediction performance with the upper (0.8810) and lower (0.6651) bounds of the coefficient of determination (R2) higher than the other models, and it has the smallest mean absolute percentage error (MAPE) and root mean square error (RMSE).

Pre‐insertion resistors temperature prediction based on improved WOA‐SVR

AbstractThe pre‐insertion resistors (PIR) within high‐voltage circuit breakers are critical components and warm up by generating Joule heat when an electric current flows through them. Elevated temperature can lead to temporary closure failure and, in severe cases, the rupture of PIR. To accurately predict the temperature of PIR, this study combines finite element simulation techniques with Support Vector Regression (SVR) optimized by an Improved Whale Optimization Algorithm (IWOA) approach. The IWOA includes Tent mapping, a convergence factor based on the sigmoid function, and the Ornstein–Uhlenbeck variation strategy. The IWOA‐SVR model is compared with the SSA‐SVR and WOA‐SVR. The results reveal that the prediction accuracies of the IWOA‐SVR model were 90.2% and 81.5% (above 100°C) in the ± 3°C temperature deviation range and 96.3% and 93.4% (above 100°C) in the ± 4°C temperature deviation range, surpassing the performance of the comparative models. This research demonstrates that the method proposed can realize the online monitoring of the temperature of the PIR, which can effectively prevent thermal faults PIR and provide a basis for the opening and closing of the circuit breaker within a short period.

A self-adaptive attraction and repulsion-based naked mole-rat algorithm for energy-efficient mobile wireless sensor networks

Naked mole-rat algorithm (NMRA) is a swarm intelligence-based algorithm that draws inspiration from the mating behaviour of mole rats (workers and breeders). This approach, which is based on the ability of breeders to reproduce with the queen, has been utilized to tackle optimization problems. The algorithm, however, suffers from local optima stagnation problem and a slower rate of convergence in order to provide gobal optimal solution. This study suggests attraction and repulsion strategy based NMRA (ARNMRA) along with self-adaptive properties to avoid trapping of solution in local optima. This strategy is utilized to create new breeder rat solutions and mating factor (λ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(\\lambda )$$\\end{document} is made self-adaptive using simulated annealing (sa) based mutation operator. ARNMRA is evaluated on CEC 2005 numerical benchmark problems and found to be superior to other algorithms, including well-known ones like selective operation based GWO (SOGWO), opposition based laplacian equilibrium optimizer (OB-L-EO), improved whale optimization algorithm (IWOA), success-history based adaptive DE (SHADE) and original NMRA. Further, according to experimental results, the performance of ARNMRA is likewise superior to the NMRA for the CEC 2019 and CEC 2020 numerical problems. Convergence profiles and statistical tests (rank-sum test and Friedman test) are employed further to validate the experimental results. Moreover, this article extends the application of ARNMRA to address the data gathering aspect in mobile wireless sensor networks (MWSNs) with the goal of prolonging network lifetime and enhancing energy efficiency. In this MWSN-based protocol, a sensor node is elected as a cluster head based on factors like mobility, residual energy, and connection time. The protocol aims to maximize the system lifetime by efficiently collecting data from all sensors and transmitting it to the base station. The study emphasizes the significance of considering dynamic node densities and speed when designing effective data-gathering protocols for MWSNs.