Nature-inspired Metaheuristic Algorithm Research Articles

Applications of nature-inspired metaheuristic algorithms for tackling optimization problems across disciplines

Nature-inspired metaheuristic algorithms are important components of artificial intelligence, and are increasingly used across disciplines to tackle various types of challenging optimization problems. This paper demonstrates the usefulness of such algorithms for solving a variety of challenging optimization problems in statistics using a nature-inspired metaheuristic algorithm called competitive swarm optimizer with mutated agents (CSO-MA). This algorithm was proposed by one of the authors and its superior performance relative to many of its competitors had been demonstrated in earlier work and again in this paper. The main goal of this paper is to show a typical nature-inspired metaheuristic algorithmi, like CSO-MA, is efficient for tackling many different types of optimization problems in statistics. Our applications are new and include finding maximum likelihood estimates of parameters in a single cell generalized trend model to study pseudotime in bioinformatics, estimating parameters in the commonly used Rasch model in education research, finding M-estimates for a Cox regression in a Markov renewal model, performing matrix completion tasks to impute missing data for a two compartment model, and selecting variables optimally in an ecology problem in China. To further demonstrate the flexibility of metaheuristics, we also find an optimal design for a car refueling experiment in the auto industry using a logistic model with multiple interacting factors. In addition, we show that metaheuristics can sometimes outperform optimization algorithms commonly used in statistics.

A Review On Early Detection Of Chronic Kidney Disease

Early detection of Chronic Kidney Disease (CKD) is critical for timely intervention and effective treatment. Deep learning algorithms have demonstrated promise in medical applications, including disease detection. In this study, we propose a deep learning-based system for early CKD detection using the Chronic Kidney Disease dataset from Kaggle. Additionally, we incorporate the Grasshopper Optimization Algorithm (GOA) for feature selection to enhance the system's performance and interpretability. Our system employs a convolutional neural network (CNN) architecture to analyze clinical and laboratory attributes from the CKD dataset, obtained from Kaggle, consisting of 4,000 instances with 25 attributes. These attributes encompass patient demographics, blood tests, and medical history, providing a comprehensive representation of CKD-related factors. To improve the system's performance, we integrate the GOA for feature selection. The GOA is a nature-inspired metaheuristic optimization algorithm that mimics the foraging behavior of grasshoppers. It aims to identify the most relevant attributes associated with CKD from the dataset. By selecting a subset of informative features, we enhance the model's predictive accuracy and reduce overfitting. During the training phase, the CNN learns to automatically extract relevant features and patterns associated with CKD from the selected attributes. Additionally, data preprocessing techniques such as normalization and feature scaling are applied to further improve the model's performance and generalizability. To evaluate the system's performance, we conduct experiments using a separate test dataset comprising 1,000 instances from the CKD dataset. The incorporation of the GOA for feature selection in our deep learning system not only improves its performance but also enhances interpretability. By identifying the most relevant attributes associated with CKD, we focus on key biomarkers and risk factors, enhancing the system's accuracy and providing valuable insights into the disease. Our research showcases the potential of deep learning algorithms, coupled with GOA-based feature selection, for early CKD detection. By leveraging the Kaggle CKD dataset and incorporating the GOA, we contribute to improving the accuracy and applicability of the system in real-world clinical settings. To handle Big data we are proposing to implement this problem on Pyspark one of the Big data computational environments for effective learning. In this platform, we can dynamically scale the infrastructure as per the demand of the data. Ultimately, our work aims to advance the early detection and management of CKD, leading to improved patient outcomes and more effective healthcare interventions.

A Communication-Efficient Federated Learning Framework for Sustainable Development Using Lemurs Optimizer

The pressing need for sustainable development solutions necessitates innovative data-driven tools. Machine learning (ML) offers significant potential, but faces challenges in centralized approaches, particularly concerning data privacy and resource constraints in geographically dispersed settings. Federated learning (FL) emerges as a transformative paradigm for sustainable development by decentralizing ML training to edge devices. However, communication bottlenecks hinder its scalability and sustainability. This paper introduces an innovative FL framework that enhances communication efficiency. The proposed framework addresses the communication bottleneck by harnessing the power of the Lemurs optimizer (LO), a nature-inspired metaheuristic algorithm. Inspired by the cooperative foraging behavior of lemurs, the LO strategically selects the most relevant model updates for communication, significantly reducing communication overhead. The framework was rigorously evaluated on CIFAR-10, MNIST, rice leaf disease, and waste recycling plant datasets representing various areas of sustainable development. Experimental results demonstrate that the proposed framework reduces communication overhead by over 15% on average compared to baseline FL approaches, while maintaining high model accuracy. This breakthrough extends the applicability of FL to resource-constrained environments, paving the way for more scalable and sustainable solutions for real-world initiatives.

Optimizing Patient Recruitment in Global Clinical Trials using Nature-Inspired Metaheuristics

A common problem seen in the ineffective execution of global multicenter trials is the frequent inability to recruit a sufficient number of patients. A myriad of barriers to recruiting enough patients timely exist and may include practical limits on the number of recruiting sites imposed by the various countries, as well as administrative, cost and unanticipated issues. The Poisson-gamma recruitment model is a widely accepted statistical tool used to predict and track recruitment at different levels of a trial and make inference. An optimal recruitment plan can be designed using mathematical optimization, however, the search is complicated with multiple nonlinear objectives and constraints that arise from regulatory and budgetary considerations. We review nature-inspired metaheuristic algorithms which are powerful, flexible, general purpose optimization tools and demonstrate their capability and utility in optimizing complex recruitment designs for global clinical trials using the Poisson-gamma model as an exemplary model. This research opens up new avenues for improving the efficiency and effectiveness of patient recruitment in clinical trials, thereby potentially accelerating the development of new medical treatments.

Optimised deep k-nearest neighbour's based diabetic retinopathy diagnosis(ODeep-NN) using retinal images.

Diabetes mellitus has been regarded as one of the prime health issues in present days, which can often lead to diabetic retinopathy, a complication of the disease that affects the eyes, causing loss of vision. For precisely detecting the condition's existence, clinicians are required to recognise the presence of lesions in colour fundus images, making it an arduous and time-consuming task. To deal with this problem, a lot of work has been undertaken to develop deep learning-based computer-aided diagnosis systems that assist clinicians in making accurate diagnoses of the diseases in medical images. Contrariwise, the basic operations involved in deep learning models lead to the extraction of a bulky set of features, further taking a long period of training to predict the existence of the disease. For effective execution of these models, feature selection becomes an important task that aids in selecting the most appropriate features, with an aim to increase the classification accuracy. This research presents an optimised deep k-nearest neighbours'-based pipeline model in a bid to amalgamate the feature extraction capability of deep learning models with nature-inspired metaheuristic algorithms, further using k-nearest neighbour algorithm for classification. The proposed model attains an accuracy of 97.67 and 98.05% on two different datasets considered, outperforming Resnet50 and AlexNet deep learning models. Additionally, the experimental results also portray an analysis of five different nature-inspired metaheuristic algorithms, considered for feature selection on the basis of various evaluation parameters.

Elk herd optimizer: a novel nature-inspired metaheuristic algorithm

This paper proposes a novel nature-inspired swarm-based optimization algorithm called elk herd optimizer (EHO). It is inspired by the breeding process of the elk herd. Elks have two main breeding seasons: rutting and calving. In the rutting season, the elk herd splits into different families of various sizes. This division is based on fighting for dominance between bulls, where the stronger bull can form a family with large numbers of harems. In the calving season, each family breeds new calves from its bull and harems. This inspiration is set in an optimization context where the optimization loop consists of three operators: rutting season, calving season, and selection season. During the selection season, all families are merged, including bulls, harems, and calves. The fittest elk herd will be selected for use in the upcoming rutting and calving seasons. In simple words, EHO divides the population into a set of groups, each with one leader and several followers in the rutting season. The number of followers is determined based on the fitness value of its leader group. Each group will generate new solutions based on its leader and followers in the calving season. The members of all groups including leaders, followers, and new solutions are combined and the fittest population is selected in the selection season. The performance of EHO is assessed using 29 benchmark optimization problems utilized in the CEC-2017 special sessions on real-parameter optimization and four traditional real-world engineering design problems. The comparative results were conducted against ten well-established metaheuristic algorithms and showed that the proposed EHO yielded the best results for almost all the benchmark functions used. Statistical testing using Friedman’s test post-hocked by Holm’s test function confirms the superiority of the proposed EHO when compared to other methods. In a nutshell, EHO is an efficient nature-inspired swarm-based optimization algorithm that can be used to tackle several optimization problems.

A NOVEL HYBRID HARMONY SEARCH (HS) WITH WAR STRATEGY OPTIMIZATION (WSO) FOR SOLVING OPTIMIZATION PROBLEMS

The usage of nature-inspired meta-heuristic algorithms is increasing due to their simplicity and versatility. These algorithms are widely used in numerous domains, especially in scientific fields such as operations research, computer science, artificial intelligence, and mathematics. Based on the core principles of exploration and exploitation, they provide flexible problem-solving abilities. This study presents a novel method to improve the effectiveness of the War Strategy Optimization (WSO) algorithm for optimization issues. The suggested approach combines the WSO technique with the Harmony Search (HS) algorithm, resulting in a hybrid algorithm called H-WSO. The aim is to enhance the overall optimization performance by leveraging the capabilities of both algorithms through the integration of swarm intelligence approaches. In order to assess the effectiveness of the recently suggested H-WSO algorithm, a set of experiments was carried out on 50 benchmark test functions. These functions included both unimodal and multimodal functions and spanned across different dimensions. The findings from these studies clearly showed a notable enhancement in the efficiency of the H-WSO algorithm when compared to the original WSO algorithm. Various metrics were utilized to evaluate the effectiveness of the proposed algorithm, including the optimal fitness function value (Mean), Standard Deviation (St.d), and Median. The H-WSO algorithm regularly shows higher efficiency than the WSO algorithm, making it a promising and practical approach for addressing complicated optimization challenges

Enhancing network stability in VANETs using nature inspired algorithm for intelligent transportation system.

The Internet of Vehicles (IoV) is one of the developing paradigms that integrates the automotive industry with the Internet of Things (IoT). The evolution of traditional Vehicular Ad-hoc Networks (VANETs), which are a layered framework for Intelligent Transportation Systems (ITS), is employed to provide Quality of Service (QoS) to end users in hazardous situations. VANETs can set up ad-hoc networks and share information among themselves using Peer-to-Peer (P2P) communication. Dynamic properties in VANETs such as dynamic topology, node mobility, sparse vehicle distribution, and bandwidth constraints can have an impact on scalability, routing, and security. This can result in frequent link failures, instability, reliability, and QOS concerns, as well as the inherent complexity of NP-hard problems. Researchers have proposed several techniques to achieve stability; the most prominent one is clustering, which relies on mobility metrics. However, existing clustering techniques generate overwhelming clusters, resulting in greater resource consumption, communication overhead, and hop count, which may lead to increased latency. Therefore, the primary objective is to achieve stability by increasing cluster lifetime, which is accomplished by generating optimal clusters. A nature-inspired meta-heuristic algorithm titled African Vulture Optimization Based Clustering Algorithm (AVOCA) is implemented to achieve it. The proposed algorithm can achieve load optimization with efficient resource utilization by mitigating hidden node challenges and ensuring communication proficiency. By maintaining an equilibrium state between the exploration and exploitation phases, AVOCA avoids local optima. The paper explores a taxonomy of the techniques used in Cluster Head (CH) selection, coordination, and maintenance to achieve stability with lower communication costs. We evaluated the effectiveness of AVOCA using various network grid sizes, transmission ranges, and network nodes. The results show that AVOCA generates 40% less clusters when compared to the Clustering Algorithm Based on Moth-Flame Optimization for VANETs (CAMONET). AVOCA generates 45% less clusters when compared to Self-Adaptive Multi-Kernel Clustering for Urban VANETs (SAMNET), AVOCA generates 43% less clusters when compared to Intelligent Whale Optimization Algorithm (i-WOA) and AVOCA generates 38% less clusters when compared to Harris Hawks Optimization (HHO). The results show that AVOCA outperforms state-of-the-art algorithms in generating optimal clusters.

Nature-Inspired Metaheuristic Algorithm with deep learning for Healthcare Data Analysis

<abstract> <p>Cardiovascular disease (CVD) detection using deep learning (DL) includes leveraging advanced neural network (NN) models to analyze medical data, namely imaging, electrocardiograms (ECGs), and patient records. This study introduces a new Nature Inspired Metaheuristic Algorithm with Deep Learning for Healthcare Data Analysis (NIMADL-HDA) technique. The NIMADL-HDA technique examines healthcare data for the recognition and classification of CVD. In the presented NIMADL-HDA technique, Z-score normalization was initially performed to normalize the input data. In addition, the NIMADL-HDA method made use of a barnacle mating optimizer (BMO) for the feature selection (FS) process. For healthcare data classification, a convolutional long short-term memory (CLSTM) model was employed. At last, the prairie dog optimization (PDO) algorithm was exploited for the optimal hyperparameter selection procedure. The experimentation outcome analysis of the NIMADL-HDA technique was verified on a benchmark healthcare dataset. The obtained outcomes stated that the NIMADL-HDA technique reached an effectual performance over other models. The NIMADL-HDA method provides an adaptable and sophisticated solution for healthcare data analysis, aiming to improve the interpretability and accuracy of the algorithm in terms of medical applications.</p> </abstract>

METASEZGİSEL ALGORİTMALARIN FARKLI PERFORMANS KRİTERLERİ İLE KARŞILAŞTIRILMASI

Nature-inspired metaheuristic algorithms are widely used because they achieve successful results in difficult optimization problems. Their popularity has led to the development of new metaheuristics for solving different engineering problems. New metaheuristics lead scientific research by providing faster and more efficient results. In this study, Artificial Rabbit Algorithm (ARO), Dwarf Mongoose Algorithm (DMO) and Genetic Algorithm (GA), which are recently developed metaheuristics, are compared. According to the literature review, the performances of these three algorithms are compared for the first time. Single and multi-modal standard quality test functions were used to evaluate the algorithms. The results of the algorithms were checked by t-test to see if there is a significant difference in terms of the functions used. According to the results obtained, it was observed that ARO produced more successful results than the other algorithms compared. This shows that the newly developed metaheuristics can be used in many engineering problems.

Yellow Ground Squirrel Algorithm (YGSA): A Novel Metaheuristic Algorithm for Global Optimization

In recent years, numerous methods have emerged for optimizing problems inspired by nature. Each of these methods, according to their nature, has applications for solving specific problems with unique characteristics. Given the wide array of optimization problems across various fields, introducing novel algorithms with distinct behaviors can be both appealing and practical. In this article, a nature-inspired meta-heuristic optimization algorithm called Yellow Ground Squirrel Algorithm (YGSA) is introduced. The main idea behind YGSA is to simulate the natural behavior of a yellow ground squirrel in terms of pursuit and evasion from a farmer (the predator) and reaching the nest. The objective of the proposed algorithm is to enhance and attain a more equitable equilibrium between the fundamental stages of exploration and exploitation in contrast to preceding approaches. This balance arises from the fact that the yellow ground squirrel, during its escape, simultaneously tries to increase the distance from the farmer (the predator) and decrease the distance to its nest (burrow). To validate the proposed algorithm, 56 benchmark evaluation functions from various unimodal and multimodal types have been evaluated. The evaluation results are compared with the HBO, EBO-CMAR, FO, SCA, PSO, CS, GSA, MVO, and WSO algorithms. The optimization results for unimodal test functions demonstrate the high exploitation capability of YGSA in approaching the optimal solution, while the optimization results for multimodal test functions indicate the strong exploration ability of YGSA in finding the main optimal region in the search space.

Metaheuristic Solutions to Order-of-Addition Design Problems

There is increasing recognition that the order of administration of drugs in drug combination studies can markedly affect the outcome. Similarly, manufactured products are often sequentially produced and the final quality frequently depends on the order of assembly. Order-of-addition designs account for the order of administration of the components, and they are quite prevalent, yet research in this area is quite limited. Because of the large dimension of such optimization problems, analytical approaches are invariably very limited and apply to simple setups only. Numerical approaches are also seriously underdeveloped. To this end, we employ two exemplary nature-inspired metaheuristic algorithms, Differential Evolution (DE) and Particle Swarm Optimization (PSO), to search for efficient order-of-addition designs for two classes of important inferential problems: (a) estimating parameters in an imprecisely specified model, and (b) constructing space-filling designs without specifying a model. We evaluate the capability of DE and PSO to solve the two classes of order-of-addition design problems and compare their performance with other algorithms that have been used to tackle somewhat similar problems. Using different criteria, we demonstrate that DE and PSO clearly outperform current algorithms by a wide margin. Supplementary materials containing codes to generate all results in this article are available online.

An interactive tool for designing efficient toxicology experiments.

The design of dose-response experiments is an important part of toxicology research. Efficient design of these experiments requires choosing optimal doses and assigning the correct number of subjects to those doses under a given criterion. Optimal design theory provides the tools to find the most efficient experimental designs in terms of cost and statistical efficiency. However, the mathematical details can be distracting and make these designs inaccessible to many toxicologists. To facilitate use of these designs, we present an easy to use web-app for finding two types of optimal designs for models commonly used in toxicology. We include tools for checking the optimality of a given design and for assessing efficiency of any user-supplied design. Using state-of-the-art nature-inspired metaheuristic algorithms, the web-app allows the user to quickly find optimal designs for estimating model parameters or the benchmark dose.

Snow Geese Algorithm: A novel migration-inspired meta-heuristic algorithm for constrained engineering optimization problems

This paper proposes a novel nature-inspired meta-heuristic algorithm, named Snow Geese Algorithm. It is inspired by the migratory behavior of snow geese and emulates the distinctive “Herringbone” and “Straight Line” shaped flight patterns observed during their migration. The algorithm is structured into three main phases for benchmark testing. In the first phase, the Snow Geese Algorithm's numerical results are compared with those of several classical meta-heuristic algorithms using the same test functions and original data from these algorithms. In the second phase, in order to minimize potential variations during the comparison, all algorithms undergo evaluation on a standardized testing platform. In the third phase, this paper applies the Snow Geese Algorithm to solve four widely recognized engineering optimization problems: the tubular column design, piston lever optimization design, reinforced concrete beam design and car side impact design. These real-world engineering problems serve as test cases to assess Snow Geese Algorithm problem-solving capabilities. The primary objective of the Snow Geese Algorithm is to provide an alternative perspective for tackling complex optimization problems. Please note that the complete source code for the Snow Geese Algorithm is publicly available at https://github.com/stones3421/SGA-project.

A nature-inspired meta-heuristic knowledge-based algorithm for solving multiobjective optimization problems

A nature-inspired meta-heuristic knowledge-based algorithm for solving multiobjective optimization problems

Walrus optimizer: A novel nature-inspired metaheuristic algorithm

Metaheuristic algorithms are intelligent optimization approaches that lead the searching procedure through utilizing exploitation and exploration. The increasing complexity of real-world optimization problem has prompted the development of more metaheuristic algorithms. Hence, this work proposes a novel swarm intelligence algorithm, Walrus optimizer (WO). It is inspired by the behaviors of walruses that choose to migrate, breed, roost, feed, gather and escape by receiving key signals (danger signals and safety signals). To test the capability of the proposed algorithm, 23 standard functions and the benchmark suite from the IEEE (Institute of Electrical and Electronics Engineers) Congress on Evolutionary Computation (CEC) 2021 are used. In addition, to evaluate the practicability of the proposed algorithm to solve various real-world optimization problems, 6 standard classical engineering optimization problems are examined and compared. For statistical purposes, 100 independent optimization runs are conducted to determine the statistical measurements, including the mean, standard deviation, and the computation time of the program, by considering a predefined stopping criterion. Some well-known statistical analyses are also used for comparative purposes, including the Friedman and Wilcoxon analysis. The results demonstrate that the proposed algorithm can provide special stability features and very competitive performance in dealing with high-dimensional benchmarks and real-world problems. The proposal of WO promotes the continuous development and application expansion of artificial intelligence, improves the efficiency of optimization calculation, and provides powerful tools for solving complex problems in the real world. The source code of WO is publicly availabe at https://ww2.mathworks.cn/matlabcentral/fileexchange/154702-walrus-optimizer-wo.

3EDANFIS: Three Channel EEG-Based Depression Detection Technique with Hybrid Adaptive Neuro Fuzzy Inference System

Background: Depression is a mental disorder that often negatively impacts the actions and feelings of the affected person. No laboratory tests are available to detect and properly diagnose depression. Presently, the detection of depression is done based on standardized questionnaires like Diagnostic and Statistical Manual of Mental Disorders-fifth edition (DSM-V) and Hamilton Depression Rating Scale (HAM-D) which is subjective in nature. Objective: The purpose of the study is to propose a framework for more accurate detection of depression from EEG signals using only three channels, which makes the system portable as well as efficient. Methods: In this study, we propose a classification model using EEG signal with the help of Adaptive Neuro Fuzzy Inference System optimized by nature-inspired algorithm. The proposed model is efficient, accurate, and portable as the features are extracted from only three channels, namely, Fp1, Fp2, and Fz. The three Data Channel (3EDANFIS) Adaptive Neuro Fuzzy Inference System (ANFIS) for detection of depression as well as three variants of Hybrid ANFIS – Adaptive Neuro Fuzzy Inference System-Genetic Algorithm (ANFIS-GA), Adaptive Neuro Fuzzy Inference System- Particle Swam Optimization (ANFIS-PSO) and Adaptive Neuro Fuzzy Inference System- Firefly Algorithm (ANFIS-FA) has been analyzed in this study. The features extracted are delta, theta, alpha, and beta and their corresponding sub-bands delta1, delta2, theta1, theta2, alpha1, alpha2, beta1, and beta2. Genetic Algorithm (GA), Particle Swam Optimization (PSO), and Firefly Algorithm (FA) are all nature-inspired metaheuristic algorithms which are used to optimize ANFIS by adapting the premise and consequent parameters. Results: The analysis showed that the GA and FA perform equally well in optimizing ANFIS with the highest accuracy of 83.33 % using delta1 power as well as delta power. Overall accuracy of the ANFIS-GA is found to be higher than that of the ANFIS-PSO, ANFIS-FA, and ANFIS. It was also found that the sub-band classification accuracy is higher than that of the band itself for delta, theta, and alpha bands. In case of the ANFIS, ANFIS-GA, ANFIS-PSO, and ANFIS-FA, delta1 was found to be having higher accuracy than delta power, theta1 was found to be having higher accuracy than theta power, and both alpha1 and alpha2 showed higher accuracy than alpha power. Conclusion: The use of only three EEG channels for data recording makes our technique to be more feasible, portable, convenient, and faster and hence can act as an adjunct tool for psychiatrists in the future.

Grasshopper Optimization Algorithm for Multi-objective Optimization of Multi-pass Face Milling of Polyamide (PA6)

<div>Milling is a prevalent machining technique employed in various industries for the production of metallic and non-metallic components. This article focuses on the optimization of cutting parameters for polyamide (PA6) using carbide tools, utilizing a recently developed multi-objective, nature-inspired metaheuristic algorithm known as the Multi-Objective Grasshopper Optimization Algorithm (MOGOA). This optimization process’s primary objectives are minimizing surface roughness and maximizing the material removal rate. By employing the MOGOA algorithm, the study demonstrates its efficacy in successfully optimizing the cutting parameters. This research’s findings highlight the MOGOA algorithm’s capability to effectively fine-tune cutting parameters during PA6 machining, leading to improved outcomes in terms of surface roughness reduction and enhanced material removal rate.</div>

Energy management and capacity planning of photovoltaic-wind-biomass energy system considering hydrogen-battery storage

This article proposed a Salp Swarm nature-inspired metaheuristic optimization algorithm (SSA) for the energy management and capacity planning of a standalone hybrid photovoltaic wind-biomass-hydrogen-battery energy system. The SSA is used to determine the optimum system configuration that will fulfill the demand reliably considering technical (loss of power supply probability (LPSP)) and economical (annualized system cost (ASC)) aspects. The energy management system (EMS) of the energy system is implemented using a rule-based algorithm to effectively manage the power flow of the devised hybrid energy system components. The comparative evaluation of the algorithms shows that EMS-SSA produces a better result as it offers the least levelized cost of energy (LCOE), of $0.939737/kW h, as compared to the EMS-LFA, EMS-GA and HOMER, which offer LCOE of $0.949737/kW h, $0.958660/kW h and $1.075351/kW h, respectively. Similarly, for the optimal system configuration, the annualized system cost (ASC) is found to be 1.887995 M$. This research presents a viable and environmentally sustainable electrification solution, serving as a valuable reference for making electricity investments in the energy-deficient Northeastern part of Nigeria.

Leveraging Gray Wolf Optimization for Enhanced Security Management in Wireless Sensor Network

In the realm of enhancing security management systems within Wireless Sensor Network (WSNs) for Big Data applications, the role of optimization algorithms is pivotal. This chapter delves into the utilization of Gray Wolf Optimization (GWO) as a fundamental tool to achieve efficient resource allocation, node placement optimization, and the enhancement of data transmission efficiency within WSNs. A detailed exploration of the mathematical foundations of GWO is provided to foster a comprehensive understanding of its application in security enhancement.
 In this paper Gray Wolf Optimization (GWO) is a nature-inspired metaheuristic algorithm presented that draws inspiration from the social behavior of gray wolves in the wild. In our study, GWO is employed to optimize various parameters that significantly impact the efficiency and effectiveness of WSNs.