The sparrow population is initialized, with each sparrow’s position randomly determined. The population consists of sparrows, which represent the candidate solutions for the optimization problem. The algorithm sets an initial dimension d, d representing the number of objectives to be optimized in the real-world situation, and the population size n. The sparrow population matrix is expressed as follows: (1)X=[x1,1x1,2⋯x1,dx2,1x2,2⋯x2,d⋯⋯⋯⋯xn,1xn,1⋯xn,d]

At the start of the algorithm, each sparrow is randomly assigned a fitness value. As the iterative process progresses, the algorithm continuously updates the sparrows’ fitness values, thereby guiding them toward better solutions. The expression for the initial fitness value of a sparrow is as follows: (2)fx=[f[x11x12⋯x1d]f[x21x22⋯x2d]⋯f[xn1xn2⋯xnd]]

The fitness calculation formula is as follows: (3)fitness=1n∑i=1n|x^i−xixi|where xi represents the actual value of the i-th data point in the validation dataset, x^i denotes the predicted value of the i-th data point output by the model.

During execution, each sparrow updates its position from its initial state. The first to be adjusted are the producers within the population. Their task is to search for potential food resources continuously. The position update equation for producers is as follows: (4)Xijt+1={xijtexp⁡(−iαrmax)(AL<ST)xijt+QL(AL⩾ST)where xtij represents the j-th dimensional parameter of the i-th sparrow at the t-th iteration; rmax denotes the maximum number of iterations; α is a uniformly distributed random number in the range [0, 1]; ST is the safety threshold, which is a uniformly distributed random number in [0, 1]; AL is the alert value, taken from the range [0.5, 1]; Q represents a standard normal random number; L is a 1 × d unit matrix.

There are two main scenarios during the position update process for scroungers: First, when scroungers can independently find sufficient food without relying on producers, they may replace some producers to balance the roles within the population. This results in position updates for these scroungers. Second, when producers find food, scroungers may occupy their positions, triggering the position-update process.

The position update equation for scroungers is as follows: (5)Xijt+1={Qexp⁡(xworstt−xijtαrmax)(i>n/2)Xpt+1+|Xijt−Xpt+1|A+L(i≤n/2)where A+=AT(AAT)−1, XPt+1 represents the best position occupied by the sparrow; Xworstt represents the worst position occupied by the sparrow; A is a 1 × d matrix where each element is randomly assigned a value of either 1 or −1; If i>n/2, it indicates that the current position of the sparrow is poor, meaning it has failed to find food. Therefore, the search range needs to be expanded. If i≤n/2, the sparrow’s position is relatively good, but it can still achieve more efficient searching and more precise solution localization.

The number of scouters is set as one-fifth of the total population, and their initial positions are randomly generated. Based on the position iteration rules for producers and scroungers in the sparrow population, the corresponding position update equation is derived: (6)Xijt+1={Xbestt+β|Xijt−Xbestt|(fi>fg)Xijt+K(|Xijt−Xworstt|fj−fw+ε)(fi=fg)where Xbestt represents the center position of the population; β is a control parameter that follows a standard normal distribution; K is a random number in the range [−1, 1]; ε is an infinitesimal value to prevent the denominator from being zero; fi represents the current fitness of the sparrow; fg,fw represent the best and worst fitness values of the sparrow, respectively; When fi>fg, it indicates that the current sparrow is on the edge of the population and is highly vulnerable to attacks; When fi=fg it implies that the sparrow senses danger and begins to move toward other sparrows to reduce the risk of predation. The SSA flowchart is shown in Fig. 3, while its Pseudo-code is presented in Algorithm 1. This visually outlines the algorithm’s core steps. It begins by initializing a random population of candidate solutions, each representing a sparrow. The population is then divided into producers and scroungers, and position updates are applied to each group according to distinct strategies. In each iteration:

Producers update their positions based on food-searching behavior, simulating exploration of the solution space.

After all individuals have updated their positions, the fitness function (as defined in Eq. (3)) is evaluated to determine whether the optimality condition is met. The iteration stops when the stopping criterion (e.g., maximum iteration or convergence threshold) is satisfied.

PD represents the control parameters, which are the number of producers. SD is the number of scouters.

The accuracy of machine learning models optimized using SSA is typically evaluated using the following metrics:

Root Mean Square Error (RMSE) [23]: Measures the square root of the average squared differences between predicted and actual values, emphasizing larger errors.

For instance, Xue et al. [26] employed all three metrics to evaluate an ISSA-optimized LSTM model for short-term power load forecasting, achieving significant improvements. Similarly, Liao [27] introduced an improved SSA-LSTM framework that reduced forecasting errors by up to 50%, demonstrating its capability in smart grid prediction tasks. These results highlight SSA’s effectiveness in time-series modeling, which is critical to energy management and demand forecasting in industry.

In industrial environments, especially those involving real-time decision systems or resource-constrained edge devices, convergence speed is as important as accuracy. SSA demonstrates faster convergence through efficient search dynamics. For instance, Zhang and Zhang [28] achieved a 7.09% improvement in accuracy and a 20.15% processing gain using chaotic mapping and dynamic weights. Xiong et al. [29] used adaptive mutation to enhance SSA’s performance in pipeline defect assessment, a key task in industrial infrastructure monitoring. Liu et al. [30] developed PGL-SSA, boosting convergence by 30%–40% in HVAC control systems that require real-time responsiveness and adaptive optimization.

Achieving a dynamic trade-off between exploration and exploitation is essential in handling complex industrial systems characterized by non-convexity, uncertainty, and noise. SSA achieves this balance through its biologically inspired producer-scrounger model. For instance, Ma et al. [31] introduced a lens-imaging-based SSA variant that achieved 96.61% diagnostic accuracy in noisy environments, making it applicable to tasks such as rotating machinery fault diagnosis. Naheliya et al. [5] integrated SSA with ML-ELM to enhance short-term traffic flow prediction, demonstrating reliable, stable performance across multiple datasets via hierarchical exploration–refinement strategies. These studies underscore SSA’s resilience and adaptability in real-time prediction and monitoring systems, where environmental variability and data incompleteness are prevalent. Across diverse machine learning optimization scenarios ranging from intelligent energy forecasting to industrial process control, SSA consistently offers advantages in precision, speed, and adaptive balance. These strengths make it a valuable candidate for further integration into industrial cyber-physical systems, especially where traditional optimizers underperform due to nonlinearities and system noise. A core challenge in metaheuristic design is achieving a dynamic balance between exploration (global search) and exploitation (local refinement). SSA addresses this challenge through its biologically inspired producer–scrounger mechanism and adaptive escape strategies, thereby strengthening its stability and effectiveness in navigating high-dimensional, non-convex search spaces.

To improve SSA’s intrinsic balance between global exploration and local exploitation, various enhancement strategies have been introduced. These include chaotic mapping (e.g., Tent, Logistic), Lévy flights, Cauchy mutations, and reverse learning, which aim to diversify population distributions and strengthen adaptive behavior. For instance, Liu et al. [32] developed an adaptive SSA that adjusts awareness probability and population size based on real-time fitness trends, improving convergence stability across diverse tasks. In a further study, Liu et al. [33] embedded Cauchy reverse learning, sine–cosine modulation, and Lévy flight into SSA for dynamic robot path planning [34]. Their experimental comparison showed that omitting Lévy flights led to slower convergence and suboptimal trajectories, underscoring their critical role in long-distance exploration. Wei et al. [35] and Zhang et al. [36] integrated chaotic maps into SSA to boost search diversity. Their work demonstrated that Tent and Logistic maps were especially effective at avoiding local optima in high-dimensional signal recovery, compared to Cubic or Chebyshev variants. These results, although not full ablation studies, provide partial evidence of the differential contributions of individual components under various industrial settings. Such enhancements are particularly valuable in real-time industrial monitoring and embedded control systems, where responsive yet robust optimization is essential.

SSA’s modular structure allows it to be synergistically combined with other metaheuristics to leverage complementary algorithmic strengths. For example, Yan et al. [37] proposed a compound framework combining SSA with PSO, GA, and the Firefly Algorithm. This design leveraged SSA’s adaptability, PSO’s swarm dynamics, and GA’s crossover operators to achieve improved solution quality in benchmark problems resembling industrial job-shop scheduling. Xu et al. [38] introduced Firefly-Assisted SSA (FASSA), which incorporated chaotic maps and the golden sine function to enhance convergence. Hou et al. [39] proposed Chaotic Quantum SSA (CQSSA), integrating Gaussian mutation and quantum-inspired behavior for parameter tuning in battery aging models. Notably, they conducted a controlled performance comparison showing that the quantum module significantly reduced solution variance and improved convergence in noisy degradation datasets. These hybrid forms not only enhance SSA’s core algorithm but also provide evidence of how specific components, such as quantum perturbation or swarm inheritance, affect performance under constrained or multi-modal conditions—a critical consideration for industrial deployments.

Hybrid SSA models have been increasingly adopted in various industrial domains where real-time decision-making and robust optimization are critical. In wireless networks and UAV systems, Chen et al. [40] employed an opposition-based SSA to optimize UAV trajectories, significantly enhancing throughput and reducing communication latency. In intelligent IoT scheduling, Khaleel [41] integrated chaotic SSA into job scheduling algorithms, yielding superior energy efficiency under fluctuating workloads. For intelligent transportation, Zheng and Liu [42] proposed ASDSSA to tune LSTM networks for metro traffic prediction, and Zhang and Ding [43] embedded chaotic SSA into stochastic configuration networks (CSSA-SCN), achieving faster convergence and higher accuracy. In power systems, Jiang et al. [44] demonstrated that quantum-enhanced SSA significantly improved ELM performance for NOx emissions modeling. At the same time, Wang et al. [45] incorporated the Slime Mould Algorithm into SSA to solve constrained mechanical design tasks. In multi-objective optimization contexts commonly encountered in industrial control and manufacturing, Multi-Objective SSA (MOSSA) has shown strong practical performance. For instance, Xue et al. [46] proposed a MOSSA variant that combines adaptive mesh evaluation, external archiving, and a scrounger-follow strategy to improve solution diversity and convergence quality. Their method achieved state-of-the-art results on 22 benchmark functions and was successfully applied to parameter optimization in carbon fiber drawing processes.

In energy systems, Lei et al. [47] applied MOSSA to the optimization of guide vane closing laws in pumped storage hydropower plants, accounting for nonlinear operational constraints. The algorithm generated Pareto-optimal settings that improved load rejection performance and reduced system risk under dynamic operating conditions. Similarly, in microgrid management, Lai et al. [48] introduced a fuzzy clustering-enhanced MOSSA to optimize energy cost and renewable energy utilization jointly. Experimental results showed superior Pareto front generation and increased integration of wind and photovoltaic energy compared to traditional algorithms. Although these applications highlight clear performance benefits, few works provide modular performance breakdowns of hybrid components across use cases, limiting deeper generalization. This underscores the need for standardized ablation protocols when applying SSA in complex industrial environments.

To consolidate advances in hybridizing the Sparrow Search Algorithm (SSA), Table 2 summarizes notable hybrid SSA variants, highlighting their key features, computational complexity, application domains, and core advantages. These designs collectively extend SSA’s applicability beyond general-purpose optimizers to intelligent systems that require real-time responsiveness, multi-objective trade-offs, and robustness under non-ideal conditions. This table provides a unified quantitative comparison of these variants, focusing on performance metrics.

The hybridization of SSA with other metaheuristics and domain-specific adaptations has shown considerable potential in overcoming the inherent limitations of traditional SSA. However, several practical insights and open challenges remain in applying these hybrid approaches, particularly in real-world industrial settings. These insights provide valuable guidance on the use of SSA across various applications and on future research directions. SSA’s ability to adapt to different optimization tasks through hybridization is one of its core strengths. For example, integrating Lévy flights into ISSA significantly enhances global exploration in high-dimensional, multimodal landscapes, while chaotic mapping in CSSA improves initialization and helps escape local optima. These enhancements are especially valuable in noisy and highly constrained industrial environments, where the optimization problem often involves complex, high-dimensional search spaces. Furthermore, the adaptive exploration-exploitation balance provided by ASSA makes it particularly suited for dynamic environments, such as real-time control systems and autonomous systems, where the optimization problem evolves.

In multi-objective optimization, MOSSA has proven particularly effective at handling tasks with conflicting objectives, such as energy management in microgrids and resource allocation in industrial scheduling. The use of Pareto dominance and external archiving enables MOSSA to generate diverse, high-quality Pareto fronts, which are essential for industrial systems that must balance multiple competing criteria, such as cost, time, and resource consumption. These capabilities make MOSSA a powerful tool for multi-criteria decision-making in complex environments. In real-time applications, hybrid SSA variants such as ASSA demonstrate their value by dynamically balancing exploration and exploitation based on environmental feedback. This adaptability is crucial for applications where the optimization problem changes in real time, such as in autonomous systems or PID controller tuning. Moreover, surrogate-assisted variants, such as Surrogate-SSA, have shown promise in reducing the computational cost of function evaluations. By using regression models or neural networks to approximate the objective function, these variants can significantly decrease the number of assessments needed, making SSA more practical for real-world applications where function evaluations are expensive.

Another important insight is the promising role of hybrid SSA in deep learning applications. Combining SSA with techniques like Bayesian optimization or reinforcement learning has proven effective for hyperparameter optimization (HPO) and neural architecture search (NAS). These hybrid approaches enable more efficient exploration of the ample, complex hyperparameter space of deep neural networks, thereby improving model performance across tasks such as image classification, speech recognition, and autonomous driving. This capability extends SSA’s applicability beyond traditional optimization tasks and into the rapidly growing field of machine learning. However, several open challenges remain in the application of hybrid SSA. One significant challenge is the scalability of SSA for high-dimensional and large-scale problems. While variants such as QSSA (Quantum-inspired SSA) help mitigate this issue by reducing dimensionality, further research is needed to improve SSA’s performance in very high-dimensional spaces, as encountered in modern big data applications. Additionally, the computational complexity of hybrid SSA variants increases with the addition of hybrid components, underscoring the need to balance exploration and computational efficiency in large-scale optimization problems.

Another challenge is SSA’s sensitivity to parameter settings, such as the vigilance factor, population size, and scout ratio. In practice, tuning these parameters for optimal performance can be difficult and time-consuming. While adaptive variants like ASSA improve this issue, further research is needed on self-tuning algorithms or automated parameter adjustment methods that could dynamically adapt these parameters based on real-time feedback from the optimization process. Furthermore, although empirical studies demonstrate the effectiveness of SSA, there is a lack of formal convergence proofs for many hybrid variants of SSA. Understanding the theoretical convergence behavior of these hybrids in noisy, dynamic, or high-dimensional landscapes is critical for their broader adoption, especially in safety-critical applications such as aerospace or autonomous systems. A deeper theoretical understanding of the convergence properties of these algorithms, especially in real-world industrial settings, is essential to ensure their reliability and robustness. SSA’s robustness under uncertainty and noise is another significant challenge. In industrial settings, sensor noise, environmental changes, and faulty data can degrade the performance of SSA. While techniques such as resampling and stochastic ranking have improved SSA’s resilience, further development is needed to systematically handle uncertainty across both the fitness landscape and the solution space, ensuring SSA’s stability in real-time, noisy environments. In multi-objective and multi-constraint optimization, SSA has shown promise but faces challenges due to the computational burden of maintaining Pareto fronts and handling constraint violations. The scalability of these methods in industrial applications is often limited by the complexity involved in managing multiple objectives and constraints. More efficient constraint-handling techniques, such as penalty functions or feasibility rules, as well as advanced multi-objective archiving strategies, are needed to improve SSA’s performance on these tasks.

Looking ahead, integrating SSA with federated learning and edge computing is a promising area for future research. Federated learning, where models are trained on decentralized devices without sharing raw data, presents a new challenge for SSA in distributed optimization. Ensuring that SSA-based methods can scale and converge in federated environments while maintaining data privacy will be an essential direction for future work. Additionally, hybrid SSA with reinforcement learning (RL) offers exciting potential for real-time, adaptive optimization in complex environments. The integration of SSA’s exploration capabilities with RL’s exploitation-driven learning could lead to new optimization paradigms, especially in sequential decision-making tasks. However, integrating SSA and RL remains challenging, and more research is needed to understand how to do so efficiently.

In conclusion, hybrid SSA variants have significantly enhanced the applicability of SSA in solving complex optimization problems in industrial settings. However, challenges related to scalability, parameter sensitivity, convergence theory, and uncertainty handling remain. Future research should focus on developing more adaptive, self-tuning algorithms, improving computational efficiency, and advancing theoretical convergence analysis to make SSA a more powerful tool for industrial optimization tasks. Further exploration of SSA’s integration with federated learning, edge computing, and reinforcement learning will open up new avenues for real-time, adaptive optimization in next-generation industrial systems.

The time complexity of SSA is primarily determined by three key parameters [10]:

Population size (N): A larger population generally improves search diversity and solution accuracy but incurs higher computational costs.

Accordingly, the total time complexity of SSA can be approximated as O(N·T·D). This is comparable to PSO but generally more efficient than GA, thanks to SSA’s more straightforward update rules and the absence of crossover and mutation. This linear scalability makes SSA particularly suitable for large-scale industrial problems such as high-dimensional system modeling, adaptive control tuning, and intelligent scheduling in smart factories.

SSA also exhibits moderate space complexity, requiring only storage of the population and corresponding fitness values. Unlike GA [2], SSA does not require auxiliary data structures (e.g., crossover pools or mutation buffers), making it more memory-efficient. This characteristic is especially advantageous in embedded machine learning applications, such as predictive maintenance in sensor networks, where available RAM and processing power are limited. SSA’s low memory footprint enables practical on-device deployment for real-time control and diagnostics.

To empirically validate SSA’s computational scalability, a series of benchmark tests was conducted in MATLAB using three standard test functions: F5, F7, and F13. These functions represent increasingly complex, multimodal optimization tasks. Their mathematical formulations are provided below: (7)F5(x)=∑i=1n−1[100(xi+1−xi2)2+(xi−1)2] (8)F7(x)=∑i=1ni⋅xi4+random (9)F13(x)=∑i=1n(xi−1)2⋅[1+sin2⁡(3πxi+1)]

For comparative analysis, SSA was evaluated alongside three classic metaheuristic algorithms: PSO [3], GA [2], and SA [65]. All algorithms were configured under uniform conditions: a population size of 400 and a maximum of 1500 iterations. The optimization trajectories are illustrated in Fig. 9.

As shown in Fig. 10, each row corresponds to a specific test function. The left column displays the 3D surface of the objective function (F5, F7, F13), which helps visualize its complexity, modality, and potential local optima. The right column shows the corresponding convergence curves on a logarithmic scale, plotting objective value vs. the number of iterations for four algorithms: GA, PSO, SA, and SSA. The vertical axis represents the objective function value, and the horizontal axis shows the iteration count. This visual layout provides a side-by-side comparison of problem landscape and algorithmic performance. The results in Fig. 9 reveal that SSA consistently outperforms PSO, GA, and SA in both convergence speed and final solution accuracy. Notably: For function F5, SSA found the optimal solution in significantly fewer iterations, demonstrating rapid convergence and high precision. The other algorithms reached the optimum only after ~700 iterations and did not achieve the same level of accuracy. In more complex landscapes, such as functions F7 and F13, SSA exhibited slower early-stage convergence but ultimately escaped local optima, whereas PSO, GA, and SA stagnated. SSA’s superior global search ability enabled it to find better final solutions. This empirical evidence confirms that SSA effectively maintains a balance between exploration and exploitation, a key trait for navigating non-convex loss surfaces in machine learning and industrial control applications.

The Sparrow Search Algorithm (SSA) is distinguished by role-conditioned, risk-aware dynamics—producers, scroungers, and risk perceivers—whose update rules are explicitly gated by an alarm variable R2 and a safety threshold ST. Producers expand in safe states (R2<ST) and retreat when threatened (R2≥ST); scroungers either drift around the current best or disperse from poor basins; a minority of risk perceivers probe/escape danger. These tri-role operators provide a built-in exploration–exploitation scheduler and allow identities to change over iterations, which contrasts with single-kernel update schemes [66].

Contrast with the SCSO family. Sand Cat Swarm Optimization (SCSO) and its recent hybrids are typically single-kernel or staged designs that rely on sensitivity-range control, spiral/random walks, and opposition-based learning to balance search—rather than SSA-style tri-role switching. A 2024 variant augments SCSO with dynamic spiral search for exploitation and lens opposition-based learning for diversification, and even hybridizes with SSA in late stages to escape local optima; performance is reported on CEC2005/CEC2022 with Wilcoxon tests [64]. Contrast with GSA multi-strategy upgrades. Recent work embeds SSA follower behavior as a module within an improved Gravitational Search Algorithm (GSA), alongside a globally optimal Lévy random walk and lens-imaging opposition-based learning. Here, diversification/intensification is orchestrated by adaptive switching functions and role-free kernels (not tri-role gating), then validated on 24 benchmarks and engineering cases, emphasizing gains in accuracy, convergence speed, and stability [67].

Within-SSA improvements. New SSA variants preserve the tri-role backbone while refining operators: an Improved Search Strategy (ISS) for producers (inspired by the Black-winged Kite algorithm) enlarges early-iteration roam and tightens late-stage steps; a Group Follow Strategy (GFS) for scroungers (COOT-inspired) limits premature crowding around elites; and a Random OBL (ROBLS) pulse after each iteration re-injects diversity. Comparative studies vs. PSO/GWO/MFO/WOA/SSA on 24 functions and the CEC2017 benchmark, with Wilcoxon tests, provide evidence of consistent gains [66]. Positioning axes used in this review. Operator granularity. SSA’s role-conditioned updates vs. staged/single-kernel schemes in SCSO and multi-strategy GSA. Risk handling. SSA uses explicit alarm/safety thresholds (R2,ST); SCSO/GSA rely on annealing, sensitivity ranges, or adaptive switches without tri-role gates. Hybridization hooks. SSA acts both as a core framework (ISS/GFS/ROBLS) and as a plug-in for other swarms (e.g., SCSO→LSSCSO; GSA→SSA follower), typically paired with Lévy/spiral walks and (lens) opposition learning—evaluation protocol. Recent studies emphasize CEC suites (2005/2017/2022), nonparametric tests (Wilcoxon), and engineering validations; our comparisons follow the same reporting. SSA’s identity-switching, risk-gated tri-role mechanism defines a distinct methodological niche among recent meta-heuristics. Contemporary SCSO and GSA lines either import SSA components or compete via staged kernels plus OBL/Lévy/spiral—a different path to balance exploration and exploitation. Our subsequent experiments and summaries interpret results through these axes.

In industrial applications, many optimization tasks face issues related to uncertainty, noise, and explainability. The Sparrow Search Algorithm (SSA) has made progress in addressing these problems, but there is still room for further improvement. Through its adaptive vigilance mechanism, SSA can respond to some extent to uncertainty and noise, but it still faces challenges in complex, dynamic environments. Firstly, uncertainty is widespread in industrial environments, driven by factors such as sensor errors, missing data, and environmental changes. Existing SSA methods, with their adaptive vigilance mechanism, can dynamically adjust search strategies to adapt to environmental changes. However, this uncertainty is not limited to ecological dynamics; it also involves random fluctuations in objective functions and random changes in model parameters. For example, Ma et al. [68] successfully addressed uncertainty in imbalanced medical data by introducing SSA into a feature selection optimization method. Additionally, An et al. [69] combined SSA with Deep Extreme Learning Machines (DELM) to propose a wind power forecasting model that effectively handled uncertainty and fluctuations in wind power prediction. Although SSA has demonstrated strong robustness in these applications, its ability to handle uncertainty in more complex environments still needs to be strengthened. To address this, future research could combine SSA with Bayesian optimization to model uncertainty and thereby optimize the search strategy. Using techniques such as Gaussian Process Regression, SSA could better assess the confidence levels of current solutions and dynamically adjust the balance between exploration and exploitation, thereby further improving the algorithm’s adaptability in uncertain environments.

Secondly, noise is a common issue in industrial applications, mainly due to sensor data interference, environmental noise, or equipment failure. SSA improves its robustness to noise through its multi-role mechanism. The Producer explores new areas to avoid local optima, while Scouters perceive environmental changes to optimize the search path. For example, Fan et al. [70] proposed an SSA-based medical image contrast enhancement method that effectively handled noise in images. Li et al. [71] also proposed a noise-reduction method combining SSA and Variational Mode Decomposition for filtering signal noise in valve-leak detection. However, in high-noise environments, SSA may still experience slow convergence or become trapped in unstable solution spaces. In the future, SSA could integrate robust optimization and stochastic ranking techniques to enhance its noise-handling capabilities, especially in real-world industrial applications such as fault diagnosis and predictive maintenance.

In industrial systems, explainability is also a critical issue. Especially in safety-critical applications, the explainability of optimization results not only helps understand the algorithm’s decision-making logic but also enhances the system’s transparency and reliability. Kong et al. [72] proposed a rockburst intensity prediction method combining SSA and the CatBoost model, and used Shapley Additive Explanations (SHAP) to analyze the explainability of the model’s output. Furthermore, Zhang et al. [73] applied SSA to optimize hyperparameters, improving the physical interpretability of the model, demonstrating SSA’s potential to enhance model explainability. To further improve the explainability of SSA, future research could combine SHAP or LIME methods to help users understand the decision-making logic behind optimization results. Recent SSA variants primarily extend search dynamics via chaotic maps, Lévy/Cauchy perturbations, and reverse/opposition learning, or hybridize SSA with other metaheuristics to rebalance exploration–exploitation. For example, FASSA (SSA + Firefly) with chaotic/golden-sine components targets faster escape from local minima, and CQSSA augments SSA with quantum-inspired perturbation and Gaussian mutation—reported to reduce solution variance and stabilize convergence on noisy battery-degradation data. MOSSA adds a multi-objective layer with external archiving and Pareto dominance, emphasizing solution diversity, and has been applied from carbon-fiber drawing to microgrid operation. HSSA-style hybrids (e.g., SSA + GA/SA) intensify local search while retaining SSA’s global roaming, whereas adaptive or opposition-based forms dynamically tune producer–scrounger roles or initial populations to preserve diversity. Across papers, complexity is typically stated around O(N·D) or, when iteration count is explicit, O(N·T·D), with multi-objective archiving introducing additional overhead (often described qualitatively). Most variants add only a small number of extra hyperparameters (e.g., chaos intensity, quantum factor, archive thresholds) beyond vanilla SSA. Benchmarks span standard synthetic suites and industrial datasets (e.g., battery SOH/SOC/RUL, NOx modeling, microgrids, UAV/robotics path planning, scheduling), with MOSSA and CQSSA repeatedly appearing in energy and manufacturing contexts. Public code/data are variably reported; many studies use open datasets but do not release source code, which we flag as an area for community improvement. (Design patterns and examples: chaotic/Lévy/Cauchy/reverse learning; FASSA & CQSSA details; MOSSA mechanisms and applications; HSSA/ASSA/CSSA/OSSA roles; complexity/scalability notes). Although SSA has made progress in handling uncertainty, noise, and explainability, there are still challenges to address in industrial applications. Future research should focus on enhancing SSA’s capabilities in these areas. In particular, SSA’s search efficiency and explainability need improvement in high-dimensional, dynamic, and uncertain environments.

Wan et al. [74] proposed a network combining Residual Networks (ResNet) and Bidirectional Gated Recurrent Units (BiGRU) to predict potential damage types and provide early warnings by analyzing changes in muscle and skeletal poses in video images. To improve the model’s efficiency, the Sparrow Search Algorithm (SSA) was used for optimization. Experiments across four datasets showed that the optimized model had the lowest error among other methods and demonstrated strong adaptability. This study demonstrated the effectiveness of SSA in deep learning models, particularly in image anomaly detection and predictive analysis tasks, offering a new solution. In the state-of-health (SOH) prediction of batteries, Zhou et al. [75] proposed an SSA-optimized convolutional bidirectional long short-term memory (CNN-Bi-LSTM) model. By analyzing battery aging data and constructing feature indicators highly correlated with battery degradation, the model used a CNN-Bi-LSTM to extract features, and SSA was used to optimize the model’s hyperparameters. Experimental results showed that the model performed better than other methods, with RMSE values lower than 0.6%. This further validates SSA’s ability to enhance predictive accuracy in battery health prediction.

For predicting the temperature of coal spontaneous combustion, Wang et al. [76] proposed an SSA-optimized convolutional neural network (CNN) model. The model analyzed the relationship between key gas indicators and coal temperature during the coal oxidation process and optimized the CNN hyperparameters using SSA. Compared to other models, the SSA-CNN showed the smallest relative error (0.155) and the lowest RMSE (8.4500). This study demonstrated SSA’s effectiveness in predicting the temperature of coal spontaneous combustion, indicating that SSA-optimized CNN models can accurately predict complex physical processes. In the field of secondary supply temperature prediction, An et al. [77] proposed a hybrid model combining SSA-optimized convolutional neural networks (CNN) and support vector machines (SVM). The model improved predictive accuracy through reasonable data preprocessing and variable selection, while accounting for lag effects. Experimental results showed that the SSA-CNN-SVM model significantly reduced prediction errors across multiple heat exchange stations, achieving a maximum MAPE reduction of 1.5% and outperforming other prediction models.

For building energy consumption prediction, Lei et al. [78] used a hybrid method combining entropy weight K-means (EWKM) with random forests (RF) for feature selection, followed by SSA optimization of the Bi-LSTM model. Experimental results showed that the RF-SSA-BiLSTM model reduced prediction errors by 24.55% in both high- and low-energy-consumption months, demonstrating greater robustness than other models, including RF-BiLSTM, RF-PSO-BiLSTM, and RF-CNN-BiLSTM.

Cai et al. [79] proposed a dam deformation prediction model based on Long Short-Term Memory (LSTM) networks and CEEMDAN optimization. By combining adaptive noise signal decomposition with LSTM feature selection, Cai successfully improved the prediction accuracy of dam deformation, reducing errors by over 53.62% compared to traditional methods. This study demonstrated that SSA-optimized LSTM models perform well on long time-series data and non-linear features. These studies illustrate that SSA’s application in deep learning extends beyond hyperparameter optimization to include model-structure optimization. SSA has proven effective for tasks such as battery prediction, coal spontaneous combustion temperature, and building energy consumption, demonstrating its strong potential to improve deep learning model performance.

The main advantages of the Sparrow Search Algorithm (SSA) in deep learning lie in its global optimization ability and strong adaptability. SSA, as a swarm intelligence algorithm, can effectively avoid local optima and find global optima in complex high-dimensional spaces. In many deep learning tasks, SSA can optimize hyperparameters, neural network structures, and feature selection, significantly enhancing model performance and robustness. Firstly, SSA’s global optimization ability is one of its key advantages. Hyperparameter optimization in deep learning often determines the model’s performance. Traditional algorithms like gradient descent are prone to getting stuck in local minima, whereas SSA can explore the entire search space, helping avoid this issue. For example, in [76], a combined SSA with a CNN-BiLSTM to optimize battery health prediction. The experimental results showed that the SSA-optimized model significantly improved accuracy compared to traditional models, validating SSA’s global search ability in complex tasks. Similarly, Wang et al. [76] studied on predicting the temperature of coal spontaneous combustion showed that SSA improved model accuracy, thereby minimizing prediction errors.

Additionally, SSA’s adaptability is another notable advantage. SSA can automatically adjust its search strategy in complex task environments to optimize model parameters, further improving model performance. In building energy consumption prediction, Lei et al. [78] combined SSA with Bi-LSTM, and the results showed that SSA significantly reduced prediction errors, demonstrating its adaptability in complex datasets. By automatically adjusting optimization parameters, SSA can improve model performance across a variety of applications. However, despite its significant advantages, SSA faces several challenges. First, SSA can be computationally expensive, particularly in high-dimensional tasks. As deep learning models often have large parameter spaces, the computational cost of SSA can be pretty high, as noted in Jiani Zhou’s battery health prediction study, where SSA’s optimization was effective but computationally intensive. Therefore, improving SSA’s computational efficiency and reducing its computational time on large datasets is a key area for future research.

Secondly, SSA’s convergence speed can be slow, especially when optimizing complex deep learning models. This may lead to longer optimization times. Cai et al. [79] noted that SSA’s convergence speed was slow when applied to long time-series data for dam deformation prediction, which limits its effectiveness in real-time applications. Therefore, enhancing SSA’s convergence speed and adaptability will be crucial for its further application in deep learning. Furthermore, SSA faces challenges in processing high-dimensional data, particularly with the “curse of dimensionality.” As deep learning tasks become more complex and data dimensions grow, this may slow down SSA’s search efficiency and affect its optimization performance. Although Wang et al. [76] showed that SSA improved model performance in predicting coal spontaneous combustion temperatures, the algorithm’s performance could still be limited when dealing with large-scale data.

In conclusion, SSA’s advantages in deep learning stem from its global optimization and strong adaptability, which effectively address local optima and improve model performance across multiple applications. However, as the scale and complexity of tasks increase, the computational cost, convergence speed, and ability to handle high-dimensional data remain key challenges. To enhance SSA’s efficiency and application, future research may need to integrate it with other efficient algorithmic strategies, such as parallel computing or reinforcement learning, to improve its effectiveness in deep learning.

Optimizing hyperparameters in deep learning architectures is crucial for improving model performance but often requires costly trial-and-error. SSA, owing to its adaptive search capacity, has been widely employed to automate this process. Researchers proposed an SSA-based deep learning framework (NDID-SSADL) to optimize parameters for near-duplicate image detection, achieving a peak accuracy of 94.50% [73]. To improve convergence speed and precision, researchers developed the HSSA [6], which synergizes SSA’s global exploration with PSO’s local exploitation. When applied to deep neural networks, HSSA led to a 10%–17% increase in prediction accuracy across a variety of classification tasks. Wan et al. [74] extended this line of work by evaluating SSA variants across diverse applications: HSSA reduced neural network error rates, while AIC-SSAIDL significantly improved image captioning scores (CIDEr: 137.45), enhanced medical image segmentation quality (PSNR + 4–6 dB), and facilitated lightweight model design (60% smaller, 2 × faster). These results collectively demonstrate SSA’s generalization capability across complex, heterogeneous visual tasks.

In visual understanding, accurate segmentation is often constrained by the need to determine optimal threshold values from complex distributions. SSA has been employed to optimize entropy-based thresholding methods, thereby improving segmentation quality and computational efficiency. One may find an integrated SSA with the two-dimensional maximum entropy method to enhance image thresholding performance, demonstrating superior noise tolerance and higher segmentation accuracy than traditional methods [75]. To address multi-thresholding needs, Wang et al. [76] proposed a CSSA that integrates Rényi entropy for multi-entropy thresholding. In construction material imaging, CSSA improved segmentation accuracy while maintaining low computational cost, demonstrating the method’s adaptability to industrial scenarios.

Geometric vision tasks such as camera calibration and pose estimation involve solving complex nonlinear optimization problems, often under noisy or sparse input conditions. SSA has been introduced in these areas to enhance convergence accuracy and stability. An et al. [77] designed a refined SSA variant incorporating elite opposition-based learning, significantly reducing reprojection errors in camera calibration tasks. This method outperformed conventional calibration techniques in terms of both precision and computational efficiency. In the context of 3D pose estimation, Lei et al. [78] proposed an SSA variant with dynamically restricted search areas to tackle the Perspective-n-Point (PnP) problem. This approach accelerated convergence in high-dimensional search spaces while maintaining accuracy, confirming SSA’s effectiveness in geometric optimization problems.

Beyond traditional computer vision tasks, SSA has also been applied to artistic and domain-specific scenarios that require both precision and domain adaptability. Cai et al. [79] developed a Multi-strategy Improved SSA (MISSA) for detecting similarity in sci-fi paintings. By integrating hierarchical pyramid structures and adaptive search strategies, MISSA achieved a 15% boost in detection accuracy and a 30% reduction in processing time compared to baseline methods. Similarly, Sundaram et al. [80] introduced CPSSA-CLAHE, which applies chaotic Pareto SSA to optimize parameters in contrast-limited adaptive histogram equalization (CLAHE) for iris image enhancement. The generated synthetic samples were class-consistent, improving CNN training accuracy to 95.5% and reducing the Equal Error Rate (EER) to 0.6809. Overall, SSA and its improved variants demonstrate strong capability in vision-based machine learning tasks, especially in optimizing high-dimensional search spaces under constraints on time, accuracy, and generalization—key concerns in industrial imaging systems, such as defect detection, biometric analysis, and vision-based control.

To enhance clarity and provide a structured overview of key studies in this subsection, Table 3 summarizes the application tasks, datasets or experimental setups, SSA variants used, and the corresponding key outcomes.

SSA has demonstrated strong performance in optimizing hyperparameters and improving convergence in image processing tasks. However, it struggles in high-dimensional search spaces with highly complex nonlinear relationships. One major limitation is the algorithm’s reliance on a static search space, which can be inefficient when models need to adapt to rapidly changing environments (e.g., real-time video processing or autonomous driving). Future improvements may involve combining SSA with dynamic learning models, such as online or reinforcement learning, to create adaptive systems that evolve in real time. Additionally, integrating SSA with generative models such as GANs (Generative Adversarial Networks) could open new avenues for automated data augmentation, thereby improving model robustness.

One of the most notable applications of SSA in robotics is autonomous path planning, where real-time routing and adaptive navigation are crucial. For instance, Liu et al. [88] combined SSA with a bio-inspired neural network (BINN) to optimize path planning for uncrewed aerial vehicles (UAVs) in mountainous terrain. The approach utilized SSA for global path generation and BINN for dynamic obstacle avoidance. The hybrid model demonstrated a 20% reduction in path length and a 35% improvement in path stability, while also offering real-time replanning capabilities. Similarly, Ding et al. [89] proposed an improved SSA algorithm integrated with dual logistic mapping and lens inverse learning for autonomous vehicle navigation. This method achieved an 18.7% increase in fitness scores, smoother turning trajectories, and a 2.4-fold improvement in replanning speed, highlighting its efficiency in overcoming initialization imbalance and early stagnation in local optima. In a more complex scenario, Xu et al. [90] introduced a variant of SSA (ISSA) for robotic path planning, incorporating chaotic circle mapping and Lévy flight strategies. This version demonstrated substantial improvements, reducing path lengths by 15%–20% and achieving a 30% faster convergence rate compared to traditional SSA, while preserving strong adaptability under dynamic conditions. Additionally, Zhou et al. [91] addressed path planning for uncrewed combat aerial vehicles (UCAVs) in cluttered environments. By integrating Dynamic Fitness Regulation Learning (DFRL), Random Differential Learning (RDL), and Elite Example Equilibrium Learning (EEEL), their multi-strategy enhanced SSA (MESSA) outperformed 11 competing algorithms, achieving the lowest average cost and demonstrating strong reliability and adaptability under complex constraints.

In the domain of human-robot interaction and rehabilitation, SSA has proven valuable in improving precision and responsiveness, particularly in upper-limb rehabilitation systems. For example, Chen et al. [92] introduced MSISSA, an enhanced SSA model incorporating opposition-based learning and nonlinear step control, to better recognize motion intentions from sEMG signals. This model showed a 2.835% improvement in classification accuracy and reduced recognition time, demonstrating its potential to enhance real-time control in rehabilitation contexts.

Beyond path planning and rehabilitation, SSA has also contributed to the broader field of robotic control. Yan et al. [93] developed an ISSA variant that improved global-local balance mechanisms for general robotic control tasks. This model performed 23% faster convergence and achieved 15% higher accuracy than traditional SSA on benchmark problems. The effectiveness of ISSA was further validated through its application to robotic PID controller tuning and path planning, proving its adaptability to complex engineering problems while avoiding local optima. Collectively, these applications underscore SSA’s effectiveness as an adaptive, efficient optimization framework in robotics, supporting real-time path planning, dynamic control, and biosignal-based human-machine interaction. Its hybridized variants further enable deployment in safety-critical, non-stationary, and high-dimensional environments, aligning with the evolving demands of modern industrial automation and autonomous systems. Table 4 summarizes recent SSA applications in robotics and motion planning, highlighting the scenarios, datasets, algorithmic variants, and performance outcomes.

SSA’s main limitation in robotics is the computational cost associated with high-dimensional, multi-agent systems. Pathfinding tasks in highly dynamic environments, such as those involving moving obstacles or changing terrain, are particularly challenging for SSA as they may require extensive recalculations. In multi-robot coordination, SSA faces difficulties in ensuring global optimality while maintaining real-time performance. Hybrid approaches integrating SSA with other algorithms, such as deep reinforcement learning (DRL) or evolutionary strategies, could help address these challenges by improving adaptability and convergence rates. Moreover, combining SSA with sensor fusion techniques could enhance robots’ situational awareness, enabling more intelligent decision-making in autonomous systems.

SSA’s application to microgrid optimization has attracted attention, especially for integrating renewable sources, storage, and interactions with the external grid. Kattepogu et al. [94] proposed an Enhanced SSA (ESSA) to optimize power flow in smart grids integrated with renewable energy sources. By combining elite reverse learning and firefly mutation strategies, ESSA reduced operational costs by up to $114.41/h and minimized emissions by 75,560 lb/MWh, all while enhancing voltage stability. These results underscore the effectiveness of SSA in sustainable grid operations under economic and environmental constraints. Fathy et al. [95] also explored SSA in microgrid operation optimization, demonstrating that it could reduce operational costs by 1.44% and carbon emissions by 54.76% in single-objective scenarios, and achieve 42.78% cost savings and 0.118% emission reductions in multi-objective scenarios. These outcomes reflect SSA’s potential to enhance both economic and environmental performance in microgrid applications. Nguyen et al. [96] extended this work by incorporating elite reverse learning into a multi-objective SSA for optimal microgrid scheduling. This method successfully minimized lifecycle operational costs and enhanced distributed generation outputs, even under dynamic conditions. Qiao et al. [97] used a Random Walk SSA (RSSA) for the economic optimization of Combined Cooling, Heating, and Power (CCHP) microgrids fueled by biomass. By introducing chaotic mapping and stochastic walk mechanisms, RSSA improved convergence speed and reduced operational costs by 2.2%–3.1%, demonstrating its suitability for biomass-based energy systems in rural areas.

SSA has also been applied in renewable energy forecasting and maximum power point tracking (MPPT) for photovoltaic systems. Zhang et al. [98] combined SSA with the Firefly Algorithm to optimize a BiLSTM model for wind power forecasting. The hybrid model achieved an accuracy of 98.5%, with a minimal mean squared error (MSE) of 0.005, improving both prediction precision and computational efficiency. Similarly, Chen et al. [99] employed SSA to optimize LSTM parameters for photovoltaic (PV) power prediction. By incorporating chaotic mapping and mutation strategies, the hybrid SSA-LSTM model achieved 20%–60% improvements in forecast accuracy, outperformed traditional approaches, and maintained stable performance across diverse weather conditions. Yuan et al. [100] proposed an SSA-based DMPPT algorithm for photovoltaic microgrids. This algorithm outperformed traditional techniques like Perturb & Observe (P&O) and PSO, delivering faster tracking speeds and superior steady-state performance, especially under partial shading conditions.

SSA and its hybrid extensions offer scalable and efficient solutions to optimization problems in renewable energy systems. By addressing cost–emission trade-offs, enhancing prediction accuracy, and accelerating MPPT convergence, SSA contributes to the reliable and sustainable operation of next-generation smart grids and distributed energy infrastructures. To assist readers in comparing SSA implementations across different renewable energy and grid optimization contexts, Table 5 lists the specific application problems, experimental setups, SSA improvements, and observed benefits.

One of the main challenges in using SSA for renewable energy and grid optimization is the need to account for the uncertainty and variability of renewable energy sources, which are challenging to model accurately in real time. Additionally, optimizing these systems at scale while accounting for both economic and environmental factors remain complex. Future research could focus on hybrid SSA algorithms that incorporate forecasting models to predict energy generation patterns, as well as dynamic models that adapt to real-time changes in grid operation.

The use of SSA-enhanced deep learning and kernel-based methods has significantly improved long-term battery health forecasting, leading to higher accuracy and better model generalization. Liu et al. [101] proposed an Improved SSA with Long Short-Term Memory (ISSA-LSTM) model for lithium-ion battery RUL estimation. By optimizing LSTM parameters using SSA, the model achieved a 30%–40% increase in accuracy compared to traditional methods. This improvement is critical for predicting degradation trajectories across datasets, thereby enhancing the safety and efficiency of battery management systems (BMS). Yang et al. [102] advanced this work by combining Convolutional Neural Networks (CNNs) and Bi-directional LSTM (BiLSTM) networks, optimized with SSA, to more accurately predict capacity degradation. The CNN component ensures stable feature representation, while the BiLSTM effectively captures long-term aging patterns. Leave-One-Out Cross-Validation (LOOCV) tests validated the model’s reliability for large-scale battery fleet monitoring.

Further, Li et al. [103] introduced an Enhanced Global Sparrow Search Algorithm (EGSSA)-optimized Multi-Scale Kernel Extreme Learning Machine (MSKELM) model for SOH estimation. By leveraging efficient feature preprocessing and nonlinear kernel learning, this model achieved a remarkable Root Mean Squared Error (RMSE) of 0.29%, exceeding conventional methods by over 50% in predictive precision. Zhang et al. [104] applied SSA to optimize an Elman Neural Network (ENN) for temperature-sensitive SOH prediction. The model incorporated differential thermal voltammetry (DTV) features, achieving Mean Absolute Error (MAE) < 0.9% and RMSE < 1.4% on the Oxford battery aging dataset. This approach effectively addresses the limitations in training speed and the local optima encountered in traditional SOH estimators, thereby enhancing model accuracy under variable conditions.

In the context of SOC estimation, SSA-based enhancements in neural networks and hybrid estimators have demonstrated substantial improvements, particularly under dynamic and real-world conditions. Feng et al. [105] designed an Adaptive Crossover Mutation SSA (ACMSSA)-optimized Backpropagation (BP) network for SOC estimation in mining vehicle batteries. The incorporation of adaptive crossover-mutation strategies with dynamic population updating reduced errors to less than 1.6%, improving estimation accuracy by 30%–40% under challenging field conditions. Similarly, Zhang and Xiang [106] proposed a dual optimization model combining PSO and SSA for SOC estimation under varying temperatures. This model, which integrates Adaptive Fuzzy Reasoning Least Squares (FFRLS) and the Extended Kalman Filter (EKF), reduced SOC error to less than 0.015, achieving a 50% improvement in accuracy over standard methods.

Li et al. [107] introduced an ISSA-BP model utilizing enhanced update rules for SOC estimation, achieving error rates below 1%. This model demonstrated fast convergence and strong generalization, making it suitable for electric vehicle and energy storage applications. Hai et al. [108] developed a cloud-based SOC estimation framework (IFCMC-SSA-BP) optimized for EVs. The model achieved an error of less than 0.01% under optimal temperature conditions and maintained accuracy within a 5% margin in dynamic environments, ensuring reliable real-time performance across diverse operational scenarios.

Beyond conventional prediction models, several studies have explored the use of multi-strategy SSA variants to enhance model flexibility, improve convergence efficiency, and strengthen resilience in complex battery modeling and parameter identification tasks. Hou et al. [39] proposed CQSSA, a hybrid algorithm combining tent chaotic mapping, quantum-inspired behavior, and Gaussian mutation to identify battery model parameters. In tests conducted under pulse discharge and Urban Dynamometer Driving Schedule (UDDS) scenarios, CQSSA outperformed other algorithms, such as PSO, Genetic Algorithm (GA), and Grey Wolf Optimization (GWO), in both accuracy and convergence speed.

Similarly, Xue et al. [109] introduced a Multi-Strategy SSA (MGSSA), which incorporates a ring topology, leader-based search, and cooperative learning. MGSSA outperformed 17 benchmark algorithms on standard functions and was successfully applied to RUL prediction, effectively addressing common SSA limitations such as early stagnation and imbalanced search behavior.

SSA-based optimization strategies are increasingly becoming key enablers in battery health prediction, real-time SOC/SOH estimation, and electrochemical model parameter identification. Their ability to adapt to nonlinearities, handle large datasets, and converge rapidly under constrained environments makes them highly suitable for embedded BMS applications and large-scale energy storage deployment. Table 6 summarizes representative SSA-based studies for battery health estimation, SOC/RUL prediction, and electrochemical modeling, providing a comparative overview of datasets, methods, and key findings.

A limitation of SSA in this domain is its reliance on accurate historical data to train the prediction models, which may not always be available or sufficiently detailed. Additionally, SSA can struggle to handle the complex, multi-modal nature of battery degradation, where different types of degradation (e.g., capacity fade, power fade) interact in non-linear ways. Future developments could include integrating SSA with deep learning models, particularly recurrent neural networks (RNNs) or long short-term memory (LSTM) networks, to capture long-term degradation trends better. Moreover, incorporating real-time monitoring data from IoT devices could enable SSA to dynamically adjust its predictions and optimization strategies, further enhancing the performance and longevity of energy storage systems.

SSA has been widely used to optimize key parameters in fault classification models, such as Support Vector Machines (SVMs), Extreme Learning Machines (ELMs), and Broad Learning Systems (BLSs), thereby improving diagnostic accuracy and generalization. Wu et al. [110] used SSA to optimize an SVM classifier for bearing fault diagnosis on the CWRU dataset, achieving improved performance compared to grid search and PSO-based optimization. Lv et al. [111] combined refined composite multiscale dispersion entropy (RCMDE) with an SSA-optimized SVM model, achieving 100% classification accuracy under both normal and noisy conditions, underscoring its resilience and reliability in real-world industrial signal environments. Dong [112] proposed an SSA-optimized CNN for bearing fault diagnosis, achieving 99.4% accuracy and improved adaptability under big data.

Advanced SSA variants have also been integrated with deep neural networks to improve fault recognition performance under noisy or uncertain factory environments. Ma et al. [31] proposed a Lévy flight and mirror-opposition-based SSA (LSSA) to optimize hyperparameters of a VMD-GRU model. When applied to noisy bearing signals, the LSSA-VMD-GRU framework significantly outperformed traditional models, offering enhanced noise resilience and faster convergence. Kong et al. [113] developed an improved SSA (ISSA) incorporating chaotic mapping and differential mutation strategies, and applied it to optimize ELM for hydropower generator vibration fault classification. The resulting model achieved 95.8% accuracy, validating its applicability in extensive rotating equipment monitoring.

In industrial real-time fault-monitoring systems, SSA has demonstrated effectiveness in optimizing lightweight diagnostic models for deployment on edge devices. For instance, Kiruthika and Bindu [114] proposed a secure communication architecture for innovative grid systems focusing on data transmission between Phasor Measurement Units (PMUs) and Phasor Data Concentrators (PDCs), which are vulnerable to cyberattacks. To address this, an SSA-based Convolutional Neural Network (CNN) model was developed for intelligent fault classification and cyber-attack detection. The system combined AES encryption for data privacy with an SSA-CNN-based classifier to detect data manipulation attempts and classify operational states, including faults, power swings, and zone locations, on the NE-39 Bus system. Results showed high classification accuracy, enhanced robustness against cyber threats, and reduced computational latency compared to traditional online methods, highlighting SSA’s suitability for secure, real-time industrial monitoring. Additionally, Liu et al. [115] introduced an SSA-optimized Extreme Learning Machine (SSA–ELM) framework for wind turbine bearing fault diagnosis. Their method achieved high classification accuracy, showcasing SSA’s efficiency in improving diagnostic performance under variable conditions. These studies underscore SSA’s potential in maintaining high performance in edge-deployed, low-latency predictive maintenance applications, aligning with the requirements of Industry 4.0 intelligent monitoring systems. Table 7 offers a structured summary of SSA applications in fault diagnosis and monitoring systems, with details on signal types, classification tasks, algorithmic variants, and resulting accuracy metrics.

The main limitation of using SSA in industrial diagnostics is its scalability for large, multi-sensor systems. Real-time monitoring requires SSA to balance high accuracy with computational efficiency, a challenge in large-scale deployments. Future research could investigate more computationally efficient SSA variants or hybrid methods that combine SSA with deep learning to enhance predictive capabilities further, making them more suitable for deployment in large, sensor-rich industrial environments.

To address the challenges posed by frequent changeovers and production diversification, Li et al. [116] proposed SSA-based strategies for solving enhanced Flexible Job-Shop Scheduling Problems (FJSPs). One study established a makespan-minimization FJSP model that integrates both machine setup time and transport delays. It introduced an improved SSA that incorporates a dimensional location update strategy, a critical-path-based neighborhood search, and an earliest-completion-time-based population initializer. Experimental comparisons against PSO and GWO demonstrated the model’s superior solution feasibility and stability in large-scale scheduling scenarios, significantly improving overall manufacturing efficiency. In energy-sensitive contexts, Luan et al. [117] introduced the Energy-saving Flexible Job-Shop Scheduling Problem (EFJSP), aiming to minimize power consumption and processing costs simultaneously. An Improved SSA (ISSA) was proposed, featuring a hybrid initialization method, a quantum rotation gate (QRG), and a sine–cosine strategy to enhance convergence. Additionally, an adaptive adjustment mechanism and variable neighborhood search (VNS) were employed to strengthen diversity and avoid local optima. Extensive benchmark testing confirmed the ISSA’s superior performance over conventional metaheuristics, yielding up to 17.2% energy savings and more balanced production loads.

Beyond scheduling, SSA has also shown promise in optimizing workshop layouts to reduce material-handling time and improve logistics efficiency. Bi et al. [118] applied SSA to minimize total transport distances while maximizing non-logistics adjacency in a real-world workshop layout. The resulting design, validated through Flexsim simulation, achieved a reduction in transport distance of up to 325 m and a 24.84% improvement in adjacency relationships compared with both genetic algorithms and the original configuration. These results demonstrate SSA’s utility in spatial optimization tasks that directly impact production throughput. Collectively, these studies underscore SSA’s adaptability and effectiveness in handling both temporal and spatial optimization challenges within industrial systems. Through intelligent design of search strategies and hybridization with problem-specific heuristics, SSA enables high-quality solutions for job scheduling, energy optimization, and layout configuration, making it a valuable tool for advancing smart manufacturing. To provide a structured comparison of SSA applications for scheduling and layout optimization tasks, Table 8 summarizes models, datasets, SSA variants, and primary outcomes across multiple manufacturing scenarios.

While SSA is effective in solving smaller to medium-sized scheduling problems, its scalability for larger, multi-objective problems with complex constraints is limited. Hybrid SSA techniques that combine machine learning for predictive scheduling or deep reinforcement learning could further enhance SSA’s ability to deal with highly dynamic manufacturing environments. Additionally, integrating SSA with Industry 4.0 technologies such as IoT and digital twins may lead to more brilliant, more adaptive systems that can better handle real-time constraints.

Qiu et al. [119] proposed an Improved Cluster-based Sparrow Search Algorithm (ICSSA-CHS) to optimize cluster head selection in Wireless Sensor Networks (WSNs) integrated with edge computing. The method incorporates chaotic maps and adaptive reverse learning to improve convergence and energy balance. Experimental evaluations of benchmark WSN scenarios showed that ICSSA-CHS prolonged network lifetime and improved overall communication efficiency, making it suitable for edge-based industrial monitoring systems.

Wang et al. [120] developed a hybrid SSA to optimize PID controller parameters in the servo control systems of industrial robots. By embedding a Gaussian mutation operator and chaotic mapping into the standard SSA framework, the method achieved improved response speed and stability. Experimental validation of robotic joint simulations demonstrated enhanced trajectory tracking and reduced steady-state error, illustrating SSA’s applicability to precise control tasks at the edge.

Zhao et al. [121] introduced an Enhanced SSA (ESSA) for optimal operation of hybrid hydrogen–electric microgrids under edge control architecture. The proposed method combines elite reverse learning and firefly-inspired mutation mechanisms to optimize economic cost, power balance, and emission objectives under demand response constraints. Simulations showed that ESSA significantly outperformed standard methods in both computational efficiency and solution quality, validating its potential in edge-based energy management systems.

These studies showcase SSA’s growing role in optimizing edge-intelligent industrial control systems—from embedded sensor coordination to real-time robot control and distributed energy systems. Thanks to its fast convergence, low memory footprint, and high adaptability, SSA serves as an effective tool for intelligent decision-making at the industrial edge, aligning with the demands of Industry 4.0 and 5.0. Table 9 consolidates key SSA-based studies on real-time edge control optimization, including tasks such as PID tuning, energy dispatch, and wireless coordination, along with their respective setups and performance highlights.

One challenge for SSA in edge systems is its computational cost, which can be a limiting factor in environments with constrained memory and processing power. Future improvements could involve developing more lightweight SSA variants optimized for edge devices with limited resources. Additionally, combining SSA with techniques such as federated learning or reinforcement learning could improve its adaptability and scalability in distributed industrial control systems.