In population-based optimization methods, the process typically starts by generating an initial set of candidate solutions. Let n denote the total number of barnacles, and let the initial position of the i-th individual be defined as follows [62]:(1)Xi,j=rand×(ubj−lbj)+lbj,i=1,2,⋯,n,j=1,2,⋯,dwhere Xi,j represents the j-th coordinate of the i-th barnacle’s position, while d represents the number of dimensions in the problem. Additionally, ubj and lbj correspond to the upper and lower bounds of the j-th dimension, as defined by the problem constraints. Finally, rand is a random variable drawn from a uniform distribution on [0, 1].

In the next phase of BMO, two parents (Dad and Mum) are selected to generate offspring. The selection process is primarily based on the length of their reproductive organs, denoted by pl, with individuals having longer pl values being more likely to be chosen. To promote exploitation, the algorithm randomly selects one barnacle as a parent based on its pl, ensuring that fertilization occurs with only a single partner at a time. Diversity is preserved through the sperm release mechanism, which is triggered whenever a barnacle selects a mating partner whose position index exceeds its own pl. The following equations mathematically describe this process [62].(2)bM=rand(n) (3)bD=rand(n)where bM and bD represent the selected parents for reproduction within the population X, which consists of n individuals.

In the final stage of the BMO mating process, the selected Dad and Mum produce offspring. The genetic contribution of each parent is evaluated using the Hardy–Weinberg principle. For the parental alleles D and M, the expected frequencies are f(DD)=p2 and f(MM)=q2 for the homozygous types, and f(DM)=2pq for the heterozygous type. These frequencies guide the determination of the genetic composition of the resulting offspring. The creation of a new barnacle, denoted Xit+1, is formally expressed by the following equation [62].(4)Xit+1=p×XbDt+q×XbMtwhere p is a random value selected from the interval [0,1], and q is defined as equal to 1−p. These parameters represent the proportion of characteristics inherited by the new offspring Xit+1 from the paternal barnacle (bD) and the maternal barnacle (bM). For example, if p=0.4, the offspring inherits 40% of its traits from the father and the remaining 60% from the mother.

BMO shifts its search behavior into a more exploratory mode, referred to as the sperm-casting phase, when a specific condition is met in which both selected parents must have index values exceeding the predefined parameter pl. The mathematical operator describing this exploration mechanism is given in the following equation [62].(5)Xit+1=rand×XbMtwhere rand denotes a random variable uniformly distributed over the interval [0,1].

The time complexity of the BMO algorithm depends on several key factors, including the population size (n, i.e., the number of barnacles), the problem dimension (d), the maximum number of iterations (T), and the computational cost of evaluating the fitness function (f). During the initialization phase, the computational complexity is O(n), while the sorting operation also contributes O(n). Evaluating the fitness function over all iterations adds O(T×n×f) to the time complexity, and updating the population’s positions contributes O(T×n×d). The overall computational complexity of the BMO algorithm can be expressed as O(n×(2+T×(f+d))).

This subsection examines the space complexity, focusing on the memory required to store variables, population data, and intermediate computations. Evaluating space complexity is essential for determining the algorithm’s feasibility on systems with limited memory. The BMO algorithm has a space complexity of O(n×d), primarily due to the memory required to store the population’s positions and fitness values across all dimensions. This storage allows the algorithm to track the locations of individual barnacles and their corresponding fitness evaluations within the search space.

To mitigate stagnation and enhance exploration of the search space, the pl parameter is employed in the BMO. In the original study, pl is recommended to be set to 50%–70% of the population size to achieve an effective balance between exploration and exploitation. This heuristic guideline is supported by empirical analyses of benchmark functions, such as the two-dimensional unimodal sphere function, in which intermediate values of pl (e.g., 5 to 7 for a population size of 10) promote convergence toward the global optimum. Such values enable sufficient local refinement through direct mating while introducing occasional randomization via sperm casting to preserve population diversity. Nevertheless, the optimal setting of pl remains problem-dependent. It requires further empirical tuning or sensitivity analysis for specific optimization scenarios to avoid excessive exploration, which may lead to inefficient dispersion, or over-exploitation, which can result in premature convergence to suboptimal regions.

The population size plays a critical role in determining the performance of population-based metaheuristic algorithms. In the original BMO study, the population size (n) was fixed at 30 across all benchmark problems. However, subsequent studies have demonstrated that adopting a fixed population size, regardless of problem characteristics or dimensionality, lacks scientific justification. The existing literature indicates that dynamically adjusting the population size constitutes an effective adaptive strategy for achieving a more appropriate balance between exploration and exploitation. Consequently, the development of mechanisms for automatically identifying an optimal, problem-dependent population size (n) represents a challenging yet promising avenue for future research.

The maximum number of iterations significantly influences the performance of population-based metaheuristic algorithms. In the original BMO study, the maximum number of iterations (T) was fixed at 500 for all experiments. However, similar to the population size issue, employing a fixed iteration limit without accounting for problem complexity may lead to inefficiencies. For relatively simple problems, convergence may occur prematurely, resulting in unnecessary computational effort, whereas more complex search landscapes may require additional iterations to escape local optima and achieve higher-quality solutions. Prior studies have demonstrated that adaptive strategies for controlling the iteration limit based on convergence rate, fitness stagnation, or composite stopping criteria such as function evaluation budgets, can enhance both computational efficiency and solution quality. Consequently, developing adaptive mechanisms to determine the maximum number of iterations in BMO represents a promising research direction to improve its adaptability and performance across diverse optimization problems.

Purusothaman and Gopalakrishnan [81] introduced a Self-Adaptive BMO (SA-BMO) for node localization in wireless sensor networks. The method addresses challenges such as random node placement, fixed costs, and energy limitations through a two-phase strategy: first, optimal selection of target nodes based on inter-node displacement, and second, localization of remaining nodes using anchor nodes weighted by a recurrent neural network. The SA-BMO algorithm optimizes the localization process by minimizing an objective function that combines distances and anchor weights. Simulation results demonstrated that SA-BMO improves localization accuracy and network efficiency, making it a robust solution for wireless sensor network deployment and management.

Nasir et al. [82] developed an elitism-crossover BMO (ECBMO), a modified variant of the original BMO, to overcome issues with local optima and improve solution accuracy. The algorithm incorporates an elitism-crossover strategy, in which superior features from the best-so-far agent are inherited by newly generated offspring, while communication between the best agent and others is strengthened. ECBMO was evaluated on IEEE and CEC2014 benchmark functions, achieving higher accuracy and more precise convergence than the original BMO. The algorithm was also applied to optimize PID parameters for a buck converter, yielding superior voltage responses with reduced steady-state error and overshoot, demonstrating its effectiveness in both numerical benchmarks and real-world engineering applications.

Li et al. [83] introduced a variant of BMO called Converged BMO (CBMO) to optimize the sizing and control of fuel cell and battery systems in hybrid electric vehicles. This approach incorporates quasi-oppositional learning to accelerate convergence and a logistic chaotic map to maintain population diversity and avoid local optima. CBMO was applied to determine an optimal configuration that balances cost, reliability, and performance of the hybrid motor system. Simulation results highlighted the trade-offs between battery size, fuel cell lifetime, and fuel consumption, demonstrating that CBMO effectively improves optimization in complex energy management problems for hybrid electric vehicles.

In another study, Selim et al. [84] designed an enhanced version of BMO to solve the optimal allocation problem of distributed generators in radial distribution systems. To overcome issues such as local optima and slow convergence, the algorithm was improved by incorporating quasi-oppositional learning and chaotic maps, forming CQOBMO. The improved method was validated on 23 benchmark functions and then applied to minimize power and energy losses in distribution systems with uncertainties in distributed generator output and time-varying loads. Case studies on IEEE 33-bus and 69-bus systems demonstrated significant reductions in losses, with up to 68.86% loss reduction using photovoltaic distributed generators and up to 67.80% reduction when combined with battery energy storage.

Similarly, Mohammadnejad et al. [85] developed an Amended BMO (ABMO) for optimal base-station placement and transmission-power allocation in 5G wireless networks. The modified algorithm incorporates quasi-oppositional learning and a chaotic mapping strategy to enhance population diversity, avoid local optima, and improve convergence speed. By optimizing both the number of connected users and power efficiency, ABMO demonstrates superior performance compared to the original BMO and other state-of-the-art algorithms such as DE and RGA. Simulation results confirmed that ABMO effectively identifies the optimal base station locations and adjusts power levels, achieving statistically significant improvements in network coverage and energy efficiency.

In another work, Hai et al. [86] formulated a Converged BMO (CBMO) to optimize the operation of a microgrid with high penetration of renewable energy sources and plug-in hybrid electric vehicles. The study developed a single-objective model to minimize the total operating cost, leveraging a CBMO enhanced with quasi-oppositional and chaotic optimization strategies. Simulation results showed that CBMO outperformed conventional methods such as GA, PSO, and ICA in both cost reduction and convergence speed, achieving lower operating costs across different scenarios and significantly shorter mean simulation times.

Likewise, Hai et al. [87] designed a Converged BMO (CBMO) enhanced with quasi-oppositional and chaotic optimization strategies for the day-ahead scheduling of electric vehicles and responsive loads in a microgrid with wind and solar generation. The study formulated a two-stage optimization model to minimize generation, reserve, and startup costs while addressing fluctuations from renewable energy sources. Simulation results across three scenarios showed that CBMO significantly reduced operational costs compared to other methods.

In addition, Rawa et al. [88] developed a Converged BMO (CBMO) for seasonal short-term scheduling of a microgrid integrating energy storage and solar photovoltaic systems. The study defined a single-objective optimization problem to minimize the total operating cost while accounting for the effects of varying climatic conditions. To enhance CBMO’s performance, quasi-oppositional and chaotic optimization strategies were incorporated. Simulation results demonstrated that CBMO not only outperformed several well-known algorithms in reducing cost across different weather scenarios but also achieved shorter mean simulation times.

Lastly, Hai et al. [89] designed a Converged BMO (CBMO) to address the day-ahead stochastic operation of a renewable energy-powered microgrid with high penetration of plug-in electric vehicles and plug-in hybrid electric vehicles. The study formulated the problem as a stochastic programming model to minimize the total operating and reliability costs, leveraging the unscented transform to capture system uncertainties. To enhance the performance of CBMO, quasi-oppositional and chaotic optimization strategies were incorporated. Simulation results demonstrated that the method efficiently manages the scheduling of distributed generation units and electric vehicles, reduces operating costs through V2G technology, and achieves superior performance compared to several well-known optimization algorithms.

Yang et al. [90] developed an improved BMO (IBMO) to optimally identify unknown parameters in proton exchange membrane fuel cell models. This variant enhances the original BMO by incorporating Lévy flights to improve exploration and a logistic chaotic map to increase population diversity and prevent premature convergence. IBMO was employed to minimize the sum of squared errors between experimental and estimated output voltages, and its performance was validated on Horizon 500W and NedSstack PS6 PEMFC stacks. Comparative results with other metaheuristic methods, including EPO, EHO, and WCO, showed that IBMO achieved the lowest error values, demonstrating superior accuracy, robustness, and reliability in modeling proton exchange membrane fuel cell systems.

In another work, Rizk-Allah and El-Fergany [91] proposed a novel BMO variant, named the Neighborhood Laplacian BMO (NLBMO), to enhance parameter optimization in solar cell diode models. NLBMO integrates two new search strategies including Laplacian-based crossover search for diversification and neighborhood-based wandering search for intensification to improve solution quality and balance global and local exploration. The algorithm was employed to optimize single-diode and double-diode models of various photovoltaic modules. Comparative results demonstrated that NLBMO significantly outperformed the original BMO and other state-of-the-art methods, achieving markedly lower RMSE across multiple PV models.

In another study, Li et al. [92] introduced an enhanced version of BMO that combines a logistic model and a chaotic mapping to improve optimization performance. This variant, known as LCBMO, dynamically adjusts algorithm parameters to balance exploration and exploitation and leverages chaotic sequences to strengthen local search. Subsequent studies have developed multiple derivatives of LCBMO and evaluated them on standard benchmark functions to identify the most effective configuration. Beyond numerical optimization, LCBMO has been successfully applied to complex real-world problems, such as multilevel color image segmentation, using Masi entropy as the objective function. Comparative analyses with alternative optimization methods and objective functions demonstrate the robustness and efficiency of this approach, with statistical tests confirming the significance of its performance improvements.

Similarly, Li et al. [93] designed an improved BMO (IBMO) for precise parameter identification in lithium-ion battery models and sensors. The study introduces an improved second-order RC model that incorporates battery hysteresis voltage to better capture dynamic behavior. To enhance convergence, IBMO integrates tent chaos mapping, a cosine control factor, and Lévy flight strategies. The approach is validated against standard benchmark functions and applied to two real battery operating conditions, achieving low root-mean-square errors (0.0431 and 0.0483) and minimal mean absolute percentage errors (0.38% and 0.56%).

Furthermore, Al-Qaness et al. [94] introduced a Dynamic Opposition-Based BMO with Triangular Mutation (DBMT) to enhance exploration and prevent premature convergence in high-dimensional Social IoT (SIoT) applications. Applied to resource allocation and decision-making tasks, DBMT demonstrated superior predictive accuracy and convergence stability on UCI and SIoT datasets, showing that opposition-based learning and mutation strategies significantly improve BMO’s adaptability and robustness for large-scale heterogeneous IoT data.

Additionally, Zamli et al. [95] proposed the Elitist BMO (eBMO) to address the slow convergence and limited search efficiency of the original BMO. The eBMO enhances exploration and exploitation by using an elite exponential probability to guide the search between intensification via swap operations and diversification into new regions, while replacing random number generation with a Chebyshev map to improve solution quality. Applied to the generation of 8×8 substitution boxes, eBMO demonstrated competitive performance compared to existing methods.

Another example is provided by Ai et al. [96], who developed a Modified BMO (MBMO) to improve parameter estimation from self-potential anomalies in geophysical studies. MBMO incorporates a variable-genital-length strategy, an improved offspring evolution method, and an out-of-bounds correction mechanism, thereby enhancing its global exploration and local exploitation capabilities. Tested on both theoretical models and real self-potential datasets from Türkiye, Canada, India, and Germany, MBMO outperformed the original BMO in accurately estimating model parameters. Further validation on 11 challenging benchmark functions confirmed its effectiveness, highlighting MBMO as a reliable and robust tool for parameter estimation in complex geophysical and optimization problems.

Also, Jena et al. [97] designed an Enhanced BMO (EBMO) using an exponential information gain function for entropy-based multilevel thresholding in image segmentation. By incorporating Gaussian mutation and a random flow toward the best solution, EBMO balances exploration and exploitation, preventing premature convergence. Evaluated on benchmark functions and the CEC 2014 test suite, the method outperformed several algorithms, and in image segmentation, EBMO-EE improved PSNR, SSIM, FSIM, and UM values by 2%–4% over existing metaheuristics.

Lastly, Ai et al. [98] introduced a Modified BMO (MBMO) for joint inversion of active Rayleigh wave dispersion, refraction travel times, and vertical electrical sounding data to achieve reliable near-surface geophysical parameter estimation. MBMO enhances the standard BMO by incorporating variable genital length, improved offspring evolution, and boundary-handling mechanisms, enabling a better balance between global exploration and local exploitation. Tested on synthetic models and four real-world datasets from Türkiye, MBMO outperformed both the original BMO and PSO, providing more accurate and robust inversion results.

The literature indicates that BMO has been integrated with various other metaheuristic algorithms to enhance its effectiveness and robustness. Table 4 summarizes the reported hybrid variants of BMO combined with different meta-heuristic methods. The following discussion offers a detailed examination of these hybrid BMO combinations.

Devarapalli et al. [100] proposed a hybrid Barnacles Mating–Cuckoo Search algorithm (BMO-CS) to address global optimization problems by enhancing the intensification capabilities of the original BMO through features from the CS algorithm. The method was first validated on standard benchmark functions, demonstrating efficient convergence to optimal solutions. BMO-CS was then applied to a complex electrical power system stability problem using a multi-objective formulation, outperforming traditional approaches and other metaheuristics, including HHO, BMO, and BMOPSO. The algorithm effectively improved system stability by shifting poles left in the s-plane and enhancing damping under fault conditions, highlighting its potential for solving challenging engineering optimization tasks.

Following this, Roslan et al. [101] introduced a Sine-based Barnacle Mating Optimization (SbBMO) algorithm, which enhances the standard BMO by introducing a sine-based position update strategy to guide barnacles toward the current best solution while dynamically adjusting step size. This modification improves the balance between exploration and exploitation in the search process. SbBMO was evaluated on 10-dimensional CEC2014 benchmark functions, showing significant gains in accuracy compared to the original BMO. Additionally, the algorithm was applied to optimize a Proportional-Derivative controller for an inverted pendulum system, where SbBMO demonstrated superior control performance, highlighting its effectiveness in both numerical optimization and engineering control applications.

Similarly, Abd Elaziz et al. [103] proposed an enhanced version of BMO to improve its optimization capability and clustering performance. The improved approach, termed BMSCD, integrates the Sine–Cosine Algorithm (SCA) and disruption operators into the traditional BMO framework to balance exploration and exploitation. The hybridization enables the algorithm to dynamically switch between BMO and SCA strategies based on the fitness value of candidate solutions, thereby reducing the risk of stagnation and premature convergence. Extensive experiments on standard benchmark functions and clustering datasets demonstrated that BMSCD outperforms several state-of-the-art algorithms in terms of accuracy, convergence speed, and robustness, confirming its efficiency in handling complex global optimization and clustering problems.

In another work, Reddy and Venkatram [104] applied a Hybrid Barnacle Mating Dingo Optimization (HBMDO) approach to enhance energy-aware routing in wireless body area networks with mobile and multiple sink nodes. The method integrates BMO with the dingo optimizer to optimally select cluster heads based on multi-objective criteria, including distance, energy, delay, transmission load, path loss, node trust, and packet delivery ratio. By leveraging this hybrid strategy, the routing protocol achieves improved energy efficiency and extended network lifetime, outperforming conventional wireless body area network routing approaches in both reliability and overall performance.

Furthermore, Sulaiman and Mustaffa [105] employed a high-level hyper-heuristic strategy that integrates BMO with the Grey Wolf Optimizer and the Whale Optimization Algorithm to solve the optimal power flow problem in power systems with renewable energy sources. The approach, called exponential Monte Carlo with counter, combines the strengths of these metaheuristic algorithms to minimize system losses. The method was validated on a modified IEEE-57 bus system, demonstrating that the hybrid hyper-heuristic strategy outperformed the individual low-level algorithms in terms of loss reduction. This study highlights the adaptability and efficiency of BMO when combined with other optimization techniques for complex power system problems involving renewable energy integration.

In another study, Razali et al. [106] introduced a hybrid optimization approach, HMVO-BMO, that combines the Multiverse Optimizer (MVO) and BMO to optimize plug-in electric vehicle charging scheduling in distribution grids. The method aims to minimize grid power losses while accounting for random plug-in electric vehicle arrival times and overnight home charging. Simulation studies on the IEEE 33-bus system under different electric vehicle penetration levels demonstrated that HMVO-BMO outperforms the individual MVO and BMO algorithms, providing more efficient and effective solutions for managing additional power demand from widespread EV adoption.

Moreover, Kasruddin et al. [107] utilized the Mating-based Manta Ray Foraging Optimization (MMRFO), an enhanced variant of the original MRFO algorithm that integrates barnacle-inspired mating strategies to improve offspring quality. By combining this mating behavior with existing Cyclone, Chain, and Somersault foraging strategies, MMRFO preserves communication between the best-performing agents and the rest of the population, enhancing exploration and exploitation. The algorithm was applied to optimize the parameters of a nonlinear fuzzy-Hammerstein model for an electric water heater, demonstrating improved dynamic modeling and more accurate output tracking compared to the standard MRFO. The study highlights MMRFO’s potential for more complex optimization tasks, including fuzzy controller design and constrained multi-objective problems, illustrating the versatility of barnacle-inspired metaheuristics in engineering applications.

Following this, Sulaiman and Mustaffa [108] developed a hyper-heuristic framework for solving optimal power flow problems in systems with FACTS devices, including SVC, TCSC, and TCPS, aiming to reduce power losses and costs. The framework used two high-level strategies, including EMCQ and Randomly Select-Only Improving, to dynamically select among low-level metaheuristics, including BMO, MFO, TLBO, and GBO. Tested on a modified IEEE 30-bus system with thermal and wind generators, the approach demonstrated that leveraging BMO within the hyper-heuristic framework effectively improved optimal power flow, outperforming standalone metaheuristic methods.

Additionally, Turgut et al. [109] developed a Q-learning-enhanced hyper-heuristic framework integrating BMO with other metaheuristics to estimate the energy consumption of electric buses. Q-learning guided the selection of low-level optimizers including BMO, Aquila Optimizer, Gradient-based Optimizer, Harris Hawks Optimization, and Poor and Rich Optimization-based on performance. Evaluated on benchmark and real-world engineering problems, the framework effectively explored the search space, optimized parameters for a Multiple Linear Regression model, and produced highly accurate fuel consumption predictions.

Finally, Ismail et al. [102,110] developed and implemented a hybrid optimization approach called Hybrid Evolutionary-Barnacles Mating Optimization (HEBMO), which integrates Evolutionary Programming (EP) with the BMO to address both non-convex and convex economic dispatch problems in power systems, focusing on minimizing generation costs while ensuring reliability under various conditions such as line/generator outages and increased power demands. Tested on IEEE 30-bus and 57-bus reliability systems under base-case, stress, and outage scenarios, HEBMO demonstrated superior performance compared to standalone EP and BMO, achieving lower costs, faster computation, and more robust solutions, positioning it as an effective method for practical power system optimization.

Integrating meta-heuristic algorithms with data mining techniques enhances machine learning performance and alleviates challenges associated with parameter tuning. Specifically, coupling BMO with models such as ANN and SVM has been shown to substantially improve outcomes in classification, regression, and forecasting tasks. For ANN, widely used for complex data problems, BMO serves as an effective optimizer for weights, learning rates, network layers, and neuron counts. In the case of SVM, BMO efficiently tunes key kernel parameters to maximize classification accuracy. Additionally, BMO has been hybridized with Decision Trees and Random Forests, optimizing critical hyperparameters to achieve higher accuracy in complex data mining applications. Table 5 summarizes documented hybrid BMO implementations with data mining techniques, followed by a detailed discussion of these integrated strategies.

In their work, Houssein et al. [111] proposed a hybrid approach combining BMO with SVM for gene selection in cancer classification. This method leverages BMO’s optimization capability to identify the most informative genes in microarray datasets, thereby enhancing the accuracy of distinguishing between normal and cancerous tissues and among different cancer types. The approach was tested on both binary and multi-class gene expression datasets, and comparative studies with other bio-inspired algorithms, including Genetic Algorithm, Particle Swarm Optimization, Tunicate Swarm Algorithm, and Artificial Bee Colony, demonstrated that BMO-SVM outperformed these methods, achieving higher predictive accuracy and better selection of relevant genes for classification.

In their work, Mustaffa and Sulaiman [112] introduced a hybrid approach combining BMO with Least Squares Support Vector Machines (LSSVM), named BMO-LSSVM, for predicting COVID-19 confirmed cases. In this model, BMO is used to optimize the hyperparameters of LSSVM, thereby enhancing the model’s predictive performance. The method was applied to daily COVID-19 case data from China, and the experimental results demonstrated that BMO-LSSVM outperformed other hybrid approaches, yielding more accurate and reliable forecasts that can support timely prevention and control measures.

Similarly, Rajesh et al. [113] developed a hybrid approach combining BMO with a Radial Basis Function Neural Network (RBFNN), termed BMO-RBFNN, for efficient parameter estimation of induction motors. In this method, BMO optimizes machine parameters and addresses reactive power dispatch issues, while RBFNN models the motor’s behavior under various operating conditions. The optimized parameters enable accurate estimation of both positive and negative sequence components, improving the assessment of motor performance. Simulation results in MATLAB/Simulink demonstrated that BMO-RBFNN outperforms conventional techniques, such as Genetic Algorithm, in terms of reliability and accuracy in parameter estimation.

In addition, Murugan and Baburaj [114] proposed applying nature-inspired metaheuristic algorithms, including BMO, to enhance machine-learning-based data-mining classification. In this study, BMO was used alongside Black Widow Optimization, Cuckoo Search, and Elephant Herd Optimization to train neural networks on stochastic datasets. The algorithms aimed to improve classification accuracy while reducing runtime and mean squared error. Results demonstrated that BMO and other bio-inspired optimizers effectively enhanced the neural network’s performance, highlighting their potential for solving complex data mining and classification problems.

Moreover, Velumani and Kalimuthu [115] introduced BMO with a Hopfield Neural Network-based Intrusion Detection model (BMOHNN-ID) to enhance the security and reliability of Internet of Things (IoT) environments. The approach focuses on identifying and classifying various intrusion types that threaten IoT networks, which are increasingly used in smart cities, grids, and homes. The proposed method begins by preprocessing IoT data to ensure compatibility with learning, after which the Hopfield Neural Network (HNN) is used to accurately detect and classify intrusions. BMO is employed to fine-tune the HNN parameters, improving detection precision and convergence speed. Additionally, device-specific data, such as routing information, network flow, and topology, are analyzed through REST API modules to build detailed vulnerability profiles. Experimental results demonstrated that the BMOHNN-ID framework achieved superior performance in intrusion classification compared to existing methods, confirming its robustness and efficiency in securing IoT networks.

Furthermore, Mustaffa and Sulaiman [116] developed a hybrid BMO-ANN model in which BMO is used to optimize the ANN’s weights and biases, thereby improving predictive performance. The approach was applied to forecast stock prices using time-series data, with six input variables for predicting the next-day closing price. Evaluation using Mean Squared Error (MSE) and Root Mean Squared Percentage Error (RMSPE) showed that BMO-ANN outperformed other hybrid optimization models, with the improvement statistically significant, demonstrating the effectiveness of BMO in enhancing ANN-based predictive models.

Additionally, Behera et al. [117] proposed a hybrid predictive framework that integrates BMO with the Pi-Sigma Neural Network (PSNN) to address the challenges of stock market forecasting. Due to the nonlinear and dynamic behavior of financial data, traditional optimization methods such as gradient descent often struggle to achieve robust convergence and high accuracy. In this study, BMO was employed to fine-tune the parameters of the PSNN, leading to the development of the BMO-PSNN model for predicting the closing prices of five major stock indices. The model’s performance was assessed using the average percentage error (APE), and the comparative results showed that BMO-PSNN achieved significantly lower error rates than the conventional GD-PSNN approach. These findings demonstrate that the hybrid BMO-PSNN model effectively enhances prediction precision, demonstrating BMO’s capability to handle complex, highly nonlinear optimization problems in financial market analysis.

In a related study, Behera et al. [118] introduced a hybrid forecasting framework that integrates BMO with ANN to address the inherent nonlinearity and volatility of financial time series data. In this study, BMO was employed to fine-tune the ANN’s weights and biases, thereby improving the network’s ability to capture complex temporal dependencies in exchange rate prediction. The resulting hybrid model, BMO+ANN, was evaluated on two major currency exchange rates and compared with other evolutionary-based neural models, including DE+ANN and PSO+ANN. Using the Root Mean Square Error (RMSE) as the primary evaluation metric, the experimental findings revealed that BMO+ANN achieved superior forecasting accuracy and robustness. This performance highlights BMO’s capability to enhance the learning efficiency and predictive power of neural architectures for dynamic financial forecasting tasks.

Another example is provided by Li et al. [119], who proposed using BMO for hyperparameter tuning in predictive models estimating supercritical CO2 (SC-CO2) density and niflumic acid solubility. Three machine learning approaches including Polynomial Regression (PR), Extreme Gradient Boosting (XGB), and LASSO, were optimized with BMO to improve accuracy. PR showed the highest predictive capability for both SC-CO2 density (R2 = 0.99207) and niflumic acid solubility (R2 = 0.96949), while XGB and LASSO also delivered competitive performance. The study demonstrates that BMO can effectively enhance model optimization, providing reliable predictions for pharmaceutical applications involving supercritical CO2 as a solvent.

Also, Mustaffa and Sulaiman [120] proposed a hybrid approach combining Feed-Forward Neural Networks (FFNN) with BMO to improve the estimation of the State of Charge (SoC) of electric vehicle batteries. The BMO algorithm was used to optimize the FFNN parameters, enhancing prediction accuracy under varying operational conditions. The model was evaluated on BMW i3 journey data using NMSE, RMSPE, and MAPE. Results demonstrated that the BMO-FFNN achieved superior performance, with NMSE of 0.0954, RMSPE of 5.10%, and MAPE of 3.79%, outperforming other hybrid models using SSA, MFO, and WOA. This approach highlights the potential of BMO-enhanced neural networks for more reliable battery management in electric vehicles.

Likewise, Yu [121] introduced a hybrid model integrating Variational Mode Decomposition (VMD), Extreme Learning Machine (ELM), and BMO for accurate copper price prediction. In this approach, VMD decomposes historical OHLC price data to enhance signal quality, while BMO optimizes the ELM parameters for improved forecasting. The VMD-BMO-ELM model was evaluated using multiple performance metrics, including R2, RMSE, MAPE, RAE, and RSE, and demonstrated superior prediction accuracy compared to baseline methods. These results indicate the model’s effectiveness as a reliable tool for investors, policymakers, and stakeholders in the metals market.

Beyond this, Sulaiman et al. [122] developed a hybrid methodology integrating BMO with the CatBoost algorithm to enhance the accuracy and robustness of State of Charge estimation in electric vehicle batteries. Using an extensive dataset from 72 BMW i3 driving trips, the study implemented comprehensive preprocessing, including outlier removal, imputation of missing values, and feature normalization. BMO was employed to optimize CatBoost parameters, including the learning rate, tree depth, regularization, and bagging temperature, and its performance was compared with PSO-, GA-, and WOA-based CatBoost models. The BMO-CatBoost approach achieved superior results, with an RMSE of 6.1031, an MAE of 4.1303, and an R2 of 0.8211, demonstrating improved predictive accuracy and reliability. These findings highlight BMO’s effectiveness in enhancing battery management systems and its potential for real-world electric vehicle applications.

Following this, Lv and Wang [123] proposed a hybrid modeling framework that combines computational fluid dynamics (CFD) with ML techniques to predict chemical concentration distributions during adsorption processes. The study employed Kernel Ridge Regression (KRR), Decision Tree Regression (DT), and Radial Basis Function Support Vector Machine (RBF-SVM) models, with hyperparameters optimized using the BMO algorithm. BMO-enhanced optimization improved model accuracy, and the RBF-SVM achieved the best performance with an R² of 0.9537, an RMSE of 3.5136, and an MAE of 1.5326. The results highlight the potential of integrating BMO with ML models to accurately capture complex spatial dependencies in solute transport and adsorption processes.

In the same context, Mustaffa et al. [124] proposed a hybrid traffic prediction model that integrates a Feedforward Neural Network (FFNN) with BMO to enhance traffic class prediction. In this approach, BMO optimizes the network’s weights and biases, improving both accuracy and convergence speed. The model was tested on a dataset with four traffic classes—low, normal, high, and heavy—and compared with FFNN models optimized by Particle Swarm Optimization, Whale Optimization Algorithm, and Harmony Search Algorithm. Results showed that the BMO-FFNN achieved the highest accuracy, precision, recall, and F1-score while converging faster than the other metaheuristic-based models, demonstrating its superior capability for reliable and efficient traffic prediction.

Following this, Sulaiman et al. [125] proposed a hybrid approach combining BMO with ANN (BMO-NN) for accurate cooling load prediction in commercial chiller systems. The model leverages seventeen operational parameters, including temperature, flow rates, and electrical data, to capture complex nonlinear relationships. BMO-NN was evaluated against other metaheuristic-based neural networks, including PSO-NN, ACO-NN, SMA-NN, and RSA-NN, as well as the traditional ADAM optimizer, using RMSE, MAE, and R² metrics. The results demonstrated that BMO-NN achieved superior accuracy and stability, with an RMSE of 2.8551, an MAE of 1.8273, and an R2 of 0.7440. SHAP analysis highlighted the algorithm’s ability to effectively prioritize key electrical and thermal features, confirming its effectiveness for proactive energy management in HVAC systems.

Another contribution was made by Zaheer et al. [126], who proposed a hybrid machine learning framework for detecting botnet attacks in network traffic, leveraging features extracted using BMO. The approach combines k-means clustering, rule-based systems, and decision tree classifiers to enhance detection accuracy and robustness. Experiments on the CTU-13 dataset demonstrated that BMO-based feature selection significantly improved the performance of the hybrid model, achieving accuracies of 99.32% for k-means, 99.11% for the decision tree, and 97.14% for the rule-based system, with high precision across all classifiers. This study highlights the effectiveness of integrating BMO with machine learning algorithms for real-world cybersecurity applications.

Lastly, Alahmari [127] proposed a novel approach, BMOML-TC, that integrates BMO with machine learning techniques for Twitter sentiment analysis to support sustainable urban living. The method employs BERT for feature extraction from tweets and a beta Variational Autoencoder (VAE) for classification, while BMO is used to automatically optimize model parameters. Evaluation on benchmark datasets demonstrated that BMOML-TC effectively classifies tweets, capturing public opinions and sentiments with high accuracy, thereby providing valuable insights for decision-making in urban sustainability initiatives.

Integrating BMO with deep learning models such as CNN, LSTM, GRU, and DBN effectively addresses complex tasks, including image classification, time series analysis, and natural language processing. BMO optimizes key parameters such as weights, learning rates, number of layers, and units, thereby improving model accuracy, convergence speed, and feature selection. For CNNs, commonly used in image processing, challenges arise in selecting the number and size of filters and convolutional layers, as well as the number of learning parameters, where BMO provides effective optimization. LSTM and GRU, well-suited for sequential and time-series data, benefit from BMO-driven tuning of memory units, layers, and learning rates. Table 6 summarizes reported hybrid BMO implementations with deep learning models, followed by a detailed discussion of these integrated approaches.

In their work, Gopalakrishnan et al. [128] introduced integrating BMO with deep learning models to enhance cybersecurity and traffic management in Mobile Edge Computing (MEC) networks. BMO optimizes a Deep Belief Network (DBN) for cyberattack detection, forming a hybrid BMO-DBN model. The system, DLTPDO-CD, also includes BiLSTM-based traffic prediction and adaptive sampling cross-entropy for efficient data offloading. Simulations showed that the BMO-optimized framework improves attack-detection accuracy and network throughput, demonstrating its effectiveness for complex deep-learning tasks in IoT and edge computing.

Similarly, Anantharajan and Gunasekaran [129] developed a hybrid method combining a Deep Autoencoder (DAE) with BMO and a Random Forest (RF) classifier for brain tumor segmentation and classification in MRI images. The approach employs weighted fuzzy kernel-based metrics for feature segmentation, while BMOA tunes the autoencoder’s parameters to enhance classification accuracy. When implemented in MATLAB and evaluated on MRI datasets, the DAE-BMOA-RF framework achieved higher accuracy, sensitivity, and specificity than existing methods, demonstrating the effectiveness of BMO variants in medical image analysis.

A further study by Dutta et al. [130], which proposed a hybrid framework, BMODTL-BMPC, integrating BMO with Deep Transfer Learning for automated malaria parasite detection and classification. The method applies Gaussian filtering to remove noise, followed by Graph Cuts segmentation to identify affected regions. BMO optimizes feature extraction using the NasNetLarge model, while an Extreme Learning Machine (ELM) performs classification. Experiments on benchmark datasets show that BMODTL-BMPC outperforms recent methods in accuracy and reliability, demonstrating the effectiveness of BMO variants in biomedical image analysis.

In another work, Kumar and Ponnusamy [131] introduced BMODL-MICM, a hybrid framework that combines BMO with a deep-learning-based model to improve medical X-ray image classification. The approach applies Wiener filtering for noise removal, uses ShuffleNetv2 for feature extraction, and employs BMO to fine-tune hyperparameters, enhancing convergence and predictive reliability. An Elman Neural Network (ENN) performs the final classification. Experiments on benchmark X-ray datasets showed that BMODL-MICM achieved 99.67% accuracy, outperforming existing deep learning methods and demonstrating the effectiveness of BMO in optimizing medical imaging models.

In a related study, Mustaffa and Sulaiman [132] developed a hybrid BMO-DL approach for accurate estimation of the state of charge (SoC) in Nissan Leaf batteries. BMO is used to optimize the hyperparameters of a deep learning model that predicts SoC from voltage, current, and charge inputs. Experiments showed that BMO-DL achieves lower error rates and higher reliability than conventional methods, demonstrating its effectiveness in improving electric vehicle battery management and operational efficiency.

In the same context, Mustaffa et al. [133] designed a hybrid forecasting model for Earth surface temperature by combining Deep Learning (DL) with BMO to optimize weights and biases. Trained on a global temperature dataset, the model was compared with DL models optimized using PSO, HSA, ACO, and the classical ARIMA method. Evaluation using MAE, RMSE, and R² showed that the BMO-optimized DL model achieved superior predictive accuracy, demonstrating the effectiveness of BMO in improving time-series forecasting for environmental applications.

In another study, Saheed and Chukwuere [134] proposed an explainable ensemble transfer learning framework for detecting zero-day botnet attacks in the Internet of Vehicles (IoV). The model integrates SHAP for interpretability and combines a bidirectional LSTM with autoencoders (BiLAE) for dimensionality reduction. At the same time, BMO optimizes hyperparameters for deep learning models, including ResNet, Inception, Inception-ResNet, and MobileNet. This approach enables efficient detection without the need for large labeled datasets. Experiments showed near-perfect performance, with up to 100% accuracy, precision, recall, and F1-score in internal networks, and 99.88% accuracy in multi-class external networks, outperforming existing methods. The XAI component enhances transparency, supporting real-time, scalable IoV cybersecurity applications.

Likewise, Shanmugaraja et al. [135] introduced a deep learning framework combined with BMO for early prediction of liver disease. The model integrates a deep convolutional neural network (DCNN), semantic image segmentation (SIS), and a guided attention mechanism to extract high-density features from CT images. BMO optimizes feature selection, enhancing the model’s ability to detect asymmetric patterns and subtle tissue abnormalities. The DCNN-BMO model classifies liver CT scans into five disease categories, achieving 98.04% accuracy, demonstrating its effectiveness in supporting early diagnosis and monitoring of liver disease.

Another investigation was carried out by Shankar et al. [136], which developed a hybrid COVID-19 diagnosis framework, BMO-CRNN, combining a Cascaded Recurrent Neural Network (CRNN) with BMO. BMO optimizes CRNN hyperparameters, including learning rate, batch size, activation function, and epoch count, improving classification performance on chest X-ray images. Preprocessing enhances image quality, while CRNN extracts deep features for detection. Experiments showed that BMO-CRNN achieves 97.01% sensitivity, 98.15% specificity, 97.31% accuracy, and 97.73% F-measure, outperforming existing methods and demonstrating the effectiveness of BMO in medical diagnostics.

In the same context, Sardar et al. [137] designed an ensemble framework combining Convolutional Neural Networks (CNNs) with BMO to improve drought prediction. The model uses vegetation indices such as NDVI, SAVI, ARVI, and EVI from satellite data to classify drought severity as low, moderate, or severe. Integrating BMO into the CNN enhances predictive performance, demonstrating the effectiveness of hybrid metaheuristic–deep learning approaches for complex environmental forecasting.

In another work, Venugopal et al. [138] developed a communication signal modulation recognition framework, CSM-FFDNN, that combines fractal feature extraction with deep neural networks. The model employs the Sevcik Fractal Dimension (SFD) to capture signal characteristics, while BMO optimizes DNN hyperparameters to enhance classification performance. Experiments show that CSM-FFDNN achieves higher recognition accuracy and outperforms existing state-of-the-art methods across multiple evaluation metrics in modulation signal classification.

A further study by Pughazendi et al. [140], which proposed a Graph Sample and Aggregate Attention Network optimized with BMO (GSAAN-BMO-SA-OPR) for sentiment-based online product recommendation. BMO is used to optimize the network for classifying customer feedback such as excellent, good, very good, bad, and very bad. Experiments on the Amazon product dataset showed improved performance across MSE, MAE, MAPE, accuracy, precision, recall, and F-score, demonstrating the effectiveness of BMO in enhancing recommendation systems and big data analytics.

Similarly, Gade et al. [141] introduced an improved Lite Swin Transformer (OLiST) model for brain MRI analysis, combining CNN-extracted local features with the transformer’s global feature-extraction capability. BMO was used to optimize hyperparameters and enhance performance. Evaluated on open-source brain tumor MRI datasets from Kaggle, the OLiST-BMO model achieved superior classification accuracy and efficiency compared to other transfer learning methods, demonstrating the potential of BMO-assisted hybrid deep learning models in medical image analysis.

In another study, Venkata et al. [142] designed a BMO-BiLSTM framework for intrusion detection in complex networks. The model uses preprocessing steps like missing data handling, categorical encoding, and SMOTE/ADASYN for class balancing. BMO performs feature selection, reducing dimensionality and improving efficiency, while Bi-LSTM captures bidirectional temporal dependencies for accurate classification. Experiments on NSL-KDD and BoT-IoT datasets showed binary accuracies of 98.12% and 99.46%, with strong multi-class performance, outperforming conventional and deep learning methods in precision, recall, F1 Score, and AUC-ROC.

Beyond this, Sulaiman and Mustaffa [143] proposed a CNN-LSTM-BMO framework to forecast chiller power consumption in commercial buildings. BMO fine-tunes model parameters to handle non-linear and temporal complexities. Compared with GA, PSO, ACO, and DE, the model achieved the lowest RMSE of 0.5523, the highest R2 of 0.9435, and 27% faster convergence. SHAP analysis identified temperature-related features as key predictors, demonstrating that BMO-enhanced deep learning can improve energy forecasting and HVAC optimization.

Following this, Yang and Yang [144] introduced a dynamic BMO-enhanced LSTM (DBM-LSTM) framework to improve intrusion detection in distributed optical fiber sensors. BMO adaptively tunes the LSTM model, enhancing the separation of true disturbances from background noise after preprocessing and wavelet-based feature extraction. Tested on various real-world disturbance types, DBM-LSTM achieved high classification accuracy, demonstrating the effectiveness of BMO in enhancing signal interpretation for IoT-based infrastructure monitoring.

In a related study, Kumar and Reddy [145] developed a BMO-based hybrid framework for hotspot detection in PV systems. The approach combines a Log Inverse Bilateral Edge Detector (LIBED) with a Gated Bernoulli Logmax Recurrent Unit (GBLRU) to analyze thermal images. Images are enhanced using CLAHE and α-Modified Histogram Blending, followed by LIBED-based contour detection and feature extraction. BMO selects the most relevant features for GBLRU classification, while a Haversine Self-Organizing Map (HSOM) isolates defective hotspots. Experiments showed the model achieved over 97% accuracy and 94% efficiency, outperforming existing PV fault detection methods.

Lastly, Hamza et al. [146] designed SEM-TPS, an energy management and traffic flow prediction framework for autonomous vehicles. The model integrates a Type-II Fuzzy Logic System (T2FLS) with BMO to optimize the membership functions and uses a bidirectional GRNN (Bi-GRNN) to accurately predict traffic flow. Experiments showed that SEM-TPS improves energy efficiency and prediction accuracy, outperforming existing state-of-the-art methods for autonomous vehicle systems.

BMO has been effectively hybridized with domain-specific optimization techniques to address complex engineering and scientific problems. By integrating BMO with algorithms or models tailored to specific domains, such as power system optimization, renewable energy management, industrial process control, or time-series forecasting, hybrid approaches combine the strengths of both methods. BMO provides global exploration and adaptive parameter tuning, while the domain-specific component offers problem-specific guidance, constraint handling, or objective modeling. This synergy improves solution quality, convergence speed, and robustness across diverse applications. Table 7 summarizes reported hybrid BMO implementations with domain-specific optimization methods, followed by a detailed discussion of these integrated strategies.

In their work, Ahmed et al. [147] applied BMO to image contrast enhancement by formulating it as an optimization problem using grey-level mapping. Evaluated on benchmark datasets such as Kodak, MIT-Adobe FiveK, H-DIBCO, and standard images, the method achieved superior contrast enhancement compared to state-of-the-art techniques. BMO was also effective as a preprocessing step for image binarization, demonstrating its versatility in image processing applications.

Similarly, Zamli and Kader [148] introduced the Barnacle Sequence Strategy (BSS), a BMO-based method for sequence-based t-way software testing. The approach optimizes input ordering to enhance interaction coverage among software components. Experiments showed that BSS achieves competitive test suite sizes for small interaction strengths and limited event sequences, matching or outperforming existing strategies.

Following this, Tariq et al. [149] proposed a BMO-based Maximum Power Point Tracking (MPPT) strategy for centralized thermoelectric generator systems under nonuniform temperature conditions. The optimized model achieved 99.93% tracking efficiency, extracted 5.6% more energy than competing methods, and reduced voltage fluctuations, thereby improving stable grid connectivity. BMO reached the global optimum within 18 iterations, converging 53.7% faster than PSO, confirming its reliability and efficiency in challenging operating conditions.

In another work, Sulaiman et al. [150] developed an SF-BMO approach that integrates the Superiority of Feasible Solution (SF) technique with the Barnacles Mating Optimizer to solve the optimal power flow problem with cost minimization. By effectively handling constraints without penalty functions, SF-BMO avoids trial-and-error tuning. Tests on the IEEE 30-bus system showed that SF-BMO achieves lower generation costs and outperforms other SF-based metaheuristic methods in optimal power flow optimization.

In a related application, Priya et al. [151] designed a hybrid BMO-ANFC approach to enhance the lifetime of power electronics in brushless DC drives. BMO optimizes the adaptive neuro-fuzzy controller by considering motor speed and semiconductor temperature to improve reliability and prevent early faults. Experimental results show that BMO-ANFC outperforms conventional controllers, offering enhanced performance, extended device lifetime, and more effective management of high-power switching operations.

In another study, Ai et al. [152] applied BMO to nonlinear geophysical inverse problems, representing its first use in geophysical parameter estimation. BMO effectively handles ill-posed and non-unique problems without requiring an accurate initial model. Validated on synthetic and real magnetic anomaly datasets, with SMA preprocessing to remove regional anomalies, BMO demonstrated superior convergence, robustness, and stability compared to standard PSO, highlighting its potential for geophysical inversion and parameter estimation.

Beyond this, Peddakapu et al. [153] developed a BMO-optimized control strategy for multi-microgrid systems to reduce frequency and tie-line power fluctuations caused by renewable intermittency and load variations. The approach employs a cascade CFOID–FOPIDN controller for secondary automatic generation control, with BMO tuning its parameters to enhance stability. Simulations incorporating diverse energy sources and uncertainties showed that the proposed controller significantly minimizes deviations and improves dynamic performance, demonstrating its effectiveness in microgrid stabilization.

A further study by Rajamani et al. [154] used BMO to optimize abrasive water jet cutting of fiber-intermetallic laminates. By tuning process parameters such as traverse speed, waterjet pressure, and nozzle height, the method improved cut quality metrics, including kerf taper, surface roughness, and kerf deviation. The results demonstrate the effectiveness of BMO for enhancing machining precision and surface quality in difficult-to-machine composite materials.

Also, Jamal and Shamsuddin [155] employed BMO to optimize overcurrent relay coordination in power systems. BMO tunes the time dial setting and plug setting to minimize total relay tripping time while maintaining the required coordination time interval. Tested on the IEEE 8-bus system with IEC-based IDMT characteristics, BMO outperformed GA and PSO, demonstrating its effectiveness in improving power system protection reliability.

Another example is provided by Deepa et al. [156], which introduced a BMO-based Multi-Resolution PID (MRPID) controller to improve speed regulation of hybrid stepper motors under variable operating conditions. BMO fine-tunes MRPID parameters to achieve high precision and fast response. The system uses a low-voltage, low-current converter to drive the VSI powering the hybrid stepper motor efficiently. MATLAB simulations comparing BMO-MRPID with ANFIS and MFO demonstrated superior dynamic performance, including a rise time of 0.0007 s, settling time of 0.1 s, and minimal steady-state error, highlighting its robustness and accuracy for industrial and robotic motion control.

Following this, Zakaria et al. [157] proposed a single-stage UAV fault detection framework that integrates BMO with the discrete cosine transform (DCT) to reduce the complexity of traditional multi-stage FDI systems. Their approach designs a BMO-driven fitness function that evaluates specific harmonic peaks namely the 3rd, 5th, and 7th to identify abnormal behavior in UAV operation. Validated through Software-in-the-Loop simulations, the method demonstrated strong real-time potential, achieving an optimal 5-second analysis window and low prediction errors. The study shows that combining BMO with frequency-domain features can provide an efficient and accurate anomaly-detection mechanism, offering a streamlined alternative to enhance UAV reliability and operational safety.

In another work, Aziz et al. [158] proposed a hybrid SES-BMO model that combines Single Exponential Smoothing with BMO to optimize both the smoothing parameter and initial value for improved time series forecasting. The approach achieved an average 8-day forecast accuracy of 90.2%, ranging from 83.7% to 98.8%. The study also highlighted the advantage of Repeated Time-Series Cross-Validation over traditional data-splitting methods for rapid decision-making, demonstrating BMO’s effectiveness in enhancing parameter selection for practical forecasting applications.

Likewise, Renaldo Maximus and Balaji [159] designed a hybrid FL-BMO approach for energy-efficient clustering and routing in wireless sensor networks. Fuzzy logic manages uncertainties in sensor data, while BMO optimizes cluster head selection based on residual energy, intracluster distance, sink proximity, and cluster balance. A nature-inspired hybrid cross-layer routing strategy (NiHCLR-SFO) further optimizes path selection. Simulations showed that FL-BMO outperforms existing protocols, improving network lifetime, packet delivery, and throughput while reducing energy consumption, delay, and packet loss, demonstrating its effectiveness for reliable wireless sensor network performance.

Finally, Thou et al. [160] developed a modified BMO for optimal chiller loading in HVAC systems, addressing maintenance and breakdown challenges. The method allows manual control of chiller on/off statuses and introduces continuous optimization cycles with filtering and sorting of the best load distributions. Results showed comparable performance to the original BMO at high cooling loads and up to 11% energy savings at lower loads, enhancing both reliability and practical applicability for efficient building energy management.

BMO can be effectively combined with multiple strategies simultaneously, forming multi-strategy hybrid frameworks. These approaches integrate metaheuristics, machine learning, deep learning, and domain-specific optimization techniques, along with algorithmic enhancements, to exploit the complementary strengths of each component. In such hybrids, BMO typically provides global exploration and adaptive parameter tuning, while other strategies contribute predictive modeling, problem-specific guidance, or local exploitation. The combination of these methods has been shown to improve convergence speed, solution quality, robustness, and adaptability to complex real-world problems. Table 8 summarizes representative multi-strategy hybridization of BMO, which are discussed in detail in the following to highlight their design principles and effectiveness.

In their work, Jia and Sun [161] developed IBMO-SVM, a hybrid model that combines an improved BMO (IBMO) with SVM to enhance feature selection and kernel parameter tuning. IBMO incorporates Gaussian mutation, logistic modeling, and refraction learning to improve convergence, stability, and the exploration–exploitation balance. Validated on 23 benchmark functions and 20 real-world datasets, including high-dimensional cases, IBMO-SVM outperformed standard BMO-SVM and six state-of-the-art methods, demonstrating superior accuracy and robustness, especially for high-dimensional data.

Similarly, Mondal et al. [162] proposed BM-BOA, a hybrid meta-heuristic that combines BMO and the Butterfly Optimization Algorithm (BOA) for automated diagnosis of pulmonary emphysema. BM-BOA optimizes lung segmentation using a multi-objective function based on image variance and entropy and fine-tunes activation functions in NN and CNN classifiers. Features are extracted via Weber local binary patterns, and the model classifies lungs into normal, mild, moderate, and severe emphysema. Experiments on benchmark and real-time datasets showed that BM-BOA improves segmentation and classification accuracy, offering an efficient and reliable emphysema detection system.

In another work, Mahesh et al. [163] introduced a hybrid JB-BMO algorithm combining Jaya and Barnacles Mating Optimization for content-based medical image retrieval and classification. The method uses an optimized Local Weber and Gradient Pattern descriptor for feature extraction, enhanced with JB-BMO to improve retrieval accuracy. For classification, an improved CNN is employed, with JB-BMO tuning the activation functions and the number of training epochs. Experiments on public medical image datasets showed that this hybrid approach outperforms existing methods, demonstrating the effectiveness of BMO variants in optimizing both feature extraction and deep learning classification.

Also, Liang et al. [164] developed a hybrid BMO-SVM approach for soft fault diagnosis in analog circuits. The improved BMO incorporates Dynamic Search Scope, Self-Reproduction, and Lévy Flight to enhance parameter optimization, while fuzzy mutual information with minimum redundancy and maximum relevance reduces feature dimensionality. Experiments on UCI datasets and circuit tests showed high classification accuracy of 92.9% for distributed fault parameters and 99.07% for fixed parameters, outperforming other optimization-based classifiers and demonstrating their effectiveness in fault detection.

Subsequently, Alrayes et al. [165] proposed BND-BMOML, a hybrid BMO–machine-learning model for botnet detection in IoT networks. BMO is used for feature selection, an ENN performs detection, and chicken swarm optimization optimizes hyperparameters. By standardizing data and selecting relevant features, the model efficiently distinguishes normal from malicious IoT activities. Experiments on benchmark datasets showed that BND-BMOML outperforms existing methods, demonstrating BMO’s effectiveness in enhancing IoT security.

In a related study, Liu et al. [166] introduced an IBMO-SVM framework for accurate state-of-charge estimation in lithium-ion batteries. The improved BMO integrates a cubic chaotic mapping, a hyperbolic sinusoidal control factor, and a Gauss–Cosey variation to enhance the exploration–exploitation balance and convergence. IBMO optimizes SVM parameters for precise state-of-charge prediction. Comparative tests showed superior convergence and performance, with the IBMO-SVM model achieving low error rates and high correlation, demonstrating its reliability for battery management systems.

In another work, Albraikan et al. [167] developed MBMODL-WD, a hybrid framework combining a Modified Barnacles Mating Optimizer with Deep Learning for automated weed detection in agriculture. The system applies Gabor filtering for noise reduction, DenseNet-121 for feature extraction, and a self-population-based BMO for hyperparameter optimization, with an ENN for classification. Simulations demonstrated that MBMODL-WD achieves 98.99% accuracy, outperforming other deep learning methods and proving its robustness and efficiency for innovative agriculture applications.

Another example is provided by Malibari et al. [168], who formulated MDL-BADDC, a hybrid framework that combines BMO variants with deep learning to achieve accurate atherosclerosis diagnosis and classification. The approach uses Quasi-Oppositional BMO (QOBMO) for optimal feature selection, a deep stacked autoencoder for classification, and the Krill Herd Algorithm to fine-tune model parameters. Experiments on three biomedical benchmark datasets showed that MDL-BADDC outperforms conventional methods, achieving higher accuracy and reliability in medical diagnosis.

Following this, Gupta et al. [169] proposed HR-BMSO, a hybrid Rat–Barnacle Mating Swarm Optimization approach for software bug prediction. The method integrates HR-BMSO with a CNN for feature extraction and an Attention-based LSTM for classifying software modules as faulty or non-faulty, thereby addressing class imbalance. Experiments showed that the model achieves high accuracy and F1 Score, outperforming conventional methods, demonstrating the effectiveness of BMO-based variants in enhancing predictive performance for software engineering tasks.

In another study, Ahmed et al. [170] introduced an improved BMO (IBMO) for epidemic time-series forecasting, enhancing the exploration phase of the original BMO by incorporating Lévy flight into the sperm cast mechanism. The IBMO was then hybridized with LSSVM to form the IBMO-LSSVM model, which was applied to forecast COVID-19 trends in Malaysia. Benchmarking against standard test functions and other well-known algorithms demonstrated that the proposed approach achieves superior accuracy in most cases and maintains competitive performance in others, highlighting its effectiveness for both optimization and predictive modeling tasks.

Similarly, Anish and Joe Prathap [171] developed a multi-disease prediction framework combining deep feature extraction with a hybrid metaheuristic optimizer. Features from the Restricted Boltzmann Machine layers of a Deep Belief Network are optimized using the Deviation-based Hybrid Grasshopper–BMO (D-HGBMO) method. The optimized features are fed into an ensemble of Deep Neural Networks, Extreme Learning Machines, and LSTMs to predict multiple diseases simultaneously. D-HGBMO-based feature tuning and ensemble weighting significantly improved prediction accuracy, demonstrating the effectiveness of BMO variants in complex healthcare applications.

In a related application, Sahu and Minz [172] designed a hybrid Barnacle Mating–Bird Swarm Optimization (HBM-BSO) integrated with a deep learning ensemble (Res-LSTMDN) for multi-disease classification of plant leaves. The approach combines adaptive image segmentation with ResNet150, LSTM, and DNN, while HBM-BSO optimizes the parameters of LSTM and DNN to enhance classification accuracy. Experimental results demonstrated that the proposed method significantly outperforms existing models in precision and other performance metrics, highlighting the effectiveness of BMO-based hybrid optimization for agricultural disease detection applications.

Also, Nalayini and Prakash [173] formulated a hierarchical data aggregation strategy for Fog-enabled IoT networks using a Chaotic BMO(HDAG-CBMO). The approach enhances network lifetime and energy efficiency by optimizing node selection based on factors such as residual energy, neighbor distance, and centroid degree. A chaotic-based initialization improves the starting positions of the barnacle population, while a learning-based data offloading method reduces response time for IoT requests. Simulation results demonstrate that HDAG-CBMO effectively balances energy consumption and extends the operational lifetime of Fog-assisted IoT systems.

Likewise, Alamgeer et al. [174] proposed an optimal Fuzzy Wavelet Neural Network-based Road Damage Detection (OFWNN-RDD) method for flood management that integrates a modified BMO (MBMO) for hyperparameter tuning. The approach uses Gabor filtering for noise reduction and DenseNet121 for feature extraction from remote sensing images. MBMO enhances the standard BMO by incorporating self-population-based initialization to improve convergence and solution quality. Finally, the FWNN classifier identifies road damage, and simulation results demonstrate that OFWNN-RDD achieves superior accuracy, reaching 98.56%, outperforming existing methods in flood-related road damage detection.

In a related study, Vijayalakshmi et al. [175] introduced an Elitist BMO with a Hybrid Deep Learning model (EBMOHDL-WC) to enhance smart waste management in IoT-enabled environments. The method integrates EBMO to optimize hyperparameters of the MobileNetv2 feature extraction model and employs a hybrid deep learning classifier for accurate waste classification. Experimental evaluation on a Kaggle garbage dataset demonstrated that the proposed approach outperforms conventional methods, highlighting its potential for improving efficiency and accuracy in smart city waste management applications.

Subsequently, Ahmed et al. [176] developed IBMOLSSVM, a hybrid BMO model enhanced with a Gauss distribution and integrated with LSSVM to predict COVID-19 cases and vaccination trends. The approach uses BMO’s exploration–exploitation balance, improved via Gauss distribution, to optimize LSSVM hyperparameters. Tested on real-world data from Malaysia, the model demonstrated superior accuracy and stability compared to conventional BMO, neural networks, and other hybrid forecasting methods, proving its effectiveness for real-time epidemiological predictions.

An additional contribution came from Chaudhari et al. [177], who formulated a hybrid deep-learning and bio-inspired-optimization framework for agricultural drought assessment using satellite imagery and vegetation indices (NDVI, ARVI, SAVI, EVI). The model combines CNN with the Sparrow Search Algorithm (SSA) and BMO, treating vegetation indices as the optimization population to enhance feature extraction. On data from the Kolar region, CNN–BMO achieved 94% accuracy with faster convergence than a standalone CNN, demonstrating that BMO improves efficiency and predictive performance for remote sensing–based agricultural monitoring.

Another example is provided by Bhukya and Sadanandam [178], who proposed OC-RSRGM, an Optimal Clustering with Rough Set-Based Rule Generation Model for big data classification in a MapReduce environment. The approach combines Optimal Fuzzy c-Means clustering with an enhanced BMO to avoid local optima, followed by Rough Set-based rule generation for classification. Implemented on Hadoop MapReduce, OC-RSRGM effectively handles continuous and uncertain data, providing accurate insights. Experiments showed a computation time of 5.43 s, demonstrating the efficiency of integrating BMO with fuzzy clustering and Rough Set theory.

In a related study, Visnu Darsini and Babu [179] developed an intelligent framework for predicting crop Minimum Support Price (MSP) using the Intensity-based Barnacle Mating Honey Badger Algorithm (I-BMHBA). The approach integrates deep learning and optimization: crop data are processed through an autoencoder and CNN to extract features, which are then refined via I-BMHBA-based feature selection. The selected features are used to train an optimized RBF–GRU network for MSP prediction and profit analysis. Results showed that I-BMHBA improves prediction accuracy and profit recommendations compared to benchmark models, demonstrating its potential for smart agricultural decision-making.

In another work, Halawani et al. [180] introduced NIMADL-HDA, a hybrid framework combining metaheuristic optimization and deep learning for cardiovascular disease detection and classification. Healthcare data are standardized using Z-score normalization, and BMO is applied for feature selection to reduce dimensionality while retaining key medical attributes. A CLSTM network performs classification, and the Prairie Dog Optimization (PDO) algorithm fine-tunes hyperparameters. Validation on benchmark datasets showed that NIMADL-HDA outperforms conventional methods in accuracy, precision, and robustness, demonstrating the effectiveness of BMO-based optimization in healthcare analytics.

Also, Magoo and Singh [181] designed an intelligent chatbot framework using Hybrid Water Wave–Barnacle Mating Optimization (HWW-BMO) to improve query understanding and response accuracy. User queries are preprocessed into weighted feature vectors, which are optimized by HWW-BMO and fed into a hybrid H-ExtLSTM model for intent detection and response prediction. Optimizing both ELM and LSTM parameters via HWW-BMO enhances performance. Experiments across multiple datasets showed that the framework outperforms existing methods, demonstrating the effectiveness of combining BMO with Water Wave Optimization for natural language processing tasks.

A further study by Adnan et al. [182], who designed predictive models for the apparent viscosity of waxy crude oils using metaheuristic-optimized machine learning, including BMO. The study analyzed 622 experimental values under polymer-free and polymer-doped conditions. Models included BMO-optimized RBF networks, TLBO, MPA, tree-based methods, and Gaussian Process Regression (GPR). GPR achieved the highest accuracy, while BMO-RBF models also provided reliable predictions. Outlier detection via the Leverage method confirmed data validity, highlighting the potential of BMO and related metaheuristics for modeling complex petroleum properties.

In a related application, Indira et al. [183] introduced a hybrid ABMO-ANN model for short-term load forecasting in microgrids. The Adaptive BMO (ABMO) optimizes feature selection and ANN parameters, overcoming limitations of conventional static methods. The proposed ABMO-ANN method demonstrated superior performance compared to regression tree (RT), support vector machine (SVM), standalone ANN, and PSO-based ANN models, achieving substantial reductions in mean absolute percentage error (MAPE) and improvements in root mean square error (RMSE), correlation coefficient, symmetric MAPE, and agreement index.

Also, Al-Dhaifallah et al. [184] proposed an efficient MPPT method for PV systems by integrating a Converged BMO (CBMO) with an Adaptive Neuro-Fuzzy Inference System (ANFIS). CBMO was applied offline to obtain optimal voltage values under varying irradiance and temperature conditions, which were then used by ANFIS to predict the optimal operating voltage in real time. The CBMO–ANFIS model was implemented in MATLAB/Simulink and evaluated under diverse climatic scenarios. The results demonstrated fast convergence, high stability, and a tracking efficiency of 99.3%, outperforming conventional MPPT techniques.

In another work, Ahmed et al. [185] introduced the Selective Opposition-Based Constrained Barnacle Mating Optimizer (SO-C-BMO), which enhances the original BMO by incorporating environmental constraints and selective opposition to improve exploration, convergence speed, and solution quality. Its effectiveness was validated through real-world case studies, showing faster convergence and superior statistical results. Furthermore, SO-C-BMO was coupled with a Least Squares Support Vector Machine (LSSVM) to form SO-C-BMO-LSSVM, which accurately tuned LSSVM hyperparameters for time-series forecasting. Thanks to its selective opposition mechanism, the approach effectively handles multimodal and non-convex problems, outperforming several well-known metaheuristics in both accuracy and convergence behavior.

Subsequently, Alrayes et al. [186] developed BCOBMO-DL, a hybrid model that combines blockchain and deep learning to enhance IoT security. Data are preprocessed using linear scaling normalization, and COBMO performs optimal feature selection. Detection is handled by a self-attention BiGRU model incorporating fractal theory, with hyperparameters tuned via the Reptile Search Algorithm (RSA). Evaluation on the NSLKDD dataset showed that BCOBMO-DL outperforms existing methods, providing higher accuracy and robustness in detecting sophisticated cyberattacks while ensuring data privacy.

Following this, Saraswathi and Murali Bhaskaran [187] proposed HBBSO-RDBN, a hybrid deep learning model for oral cancer detection that combines a Recurrent Deep Belief Network (RDBN) with metaheuristic optimization. Preprocessing uses median filtering and CLAHE to reduce noise, while RDBN integrates a DBN and an RNN architecture to improve classification. Hyperparameters, including the learning rate, number of epochs, and number of hidden neurons, are optimized using Hybrid Beetle–Barnacle Swarm Optimization (HBBSO), which merges BMO with Beetle Swarm Optimization. Experiments show HBBSO-RDBN outperforms PSO-RDBN, GWO-RDBN, BSO-RDBN, and BMO-RDBN, achieving higher accuracy and robustness in oral cancer detection.

Similarly, Kathole et al. [188] designed an educational chatbot using deep learning optimized with ADT-BMO, a hybrid Barnacles Mating Optimizer. ADT-BMO enhances feature selection, fusion, and tuning of hidden neurons, activation functions, and epochs for the AA-DTCN-SC network, refining features from BERT, TransformerNet, and Text CNN. The model achieves accurate intent recognition and context-aware responses, outperforming DTCN, RNN, and Bi-LSTM in accuracy, efficiency, and scalability for intelligent educational support.

In another work, Shikalgar et al. [189] developed a deep residual fuzzy encoder framework enhanced with BMO for crop yield prediction. Crop data are preprocessed via random drop imputation, normalization, and outlier detection, with feature selection using ReliefF, where BMO optimizes the number of neighbors. Kho-Kho Optimization (KKO) fine-tunes fuzzy encoder hyperparameters. The hybrid model achieved 95.6% accuracy, a 10% false discovery rate, and an F1 Score of 89.85%, demonstrating practical and reliable agricultural yield forecasting.

Finally, Nair and Azath [190] introduced an educational chatbot using deep learning optimized with ADT-BMO to improve intent recognition and response relevance. Student queries are converted into vector representations via BERT, TransformerNet, and Text CNN, and ADT-BMO performs weighted feature selection and fusion. The fused features feed into an AA-DTCN-SC network, whose parameters are also optimized by ADT-BMO. The system achieves 85.4% accuracy and 92.6% precision, outperforming traditional chatbot methods.