The model represents a proton exchange membrane fuel cell as an electrical circuit whose output is governed by the thermodynamic potential and three principal losses: activation, ohmic and concentration. Activation loss dominates the early part of the polarization curve, reflecting the kinetic barrier associated with electrochemical reactions. Ohmic loss grows with current because electrons moving through electrodes and protons crossing the membrane encounter resistance. Concentration loss becomes more important at high current, when reactants cannot reach electrode surfaces rapidly enough. In the proposed lumped representation, these processes are expressed through a diode-like activation term, an internal resistance and a current-dependent resistance for concentration loss.

Only six parameters need to be estimated: the open-circuit or thermodynamic voltage, the diode ideality factor, the diode reverse-saturation current, internal resistance, a concentration-loss coefficient and an effective maximum-current scale. The model does not evaluate the logarithmic activation term at zero current. Instead, it is fitted over the measured current range, with a minimum fitting current of 0.0200 ampere in the reported single-cell case, while the thermodynamic term represents the open-circuit condition. For a stack, the cell voltage expression is multiplied by the number of cells in series. The researchers minimized the root mean square error between calculated and experimental voltages, with separate parameter bounds established for the small cell and the larger stack.

EARO extends the original artificial rabbits optimizer, a population-based metaheuristic inspired by the foraging and hiding behavior of rabbits. Its population of 100 candidate parameter sets is initialized through four complementary mechanisms: a Sobol-like quasi-random scheme for 30 percent of individuals, opposition-based learning for another 30 percent, chaotic initialization for 20 percent and purely random initialization for the remaining 20 percent. During the search, an adaptive energy factor governs movement between exploration and exploitation. The exploration phase includes elite-guided detour foraging and occasional Levy-flight jumps, while the exploitation phase concentrates on promising solutions through best-guided, hybrid and elite-mean strategies.

The enhanced optimizer also introduces several safeguards against premature convergence. Standard artificial-rabbit updates, differential-evolution mutation and a best-guided Gaussian walk are selected probabilistically, with differential evolution and Gaussian movement each used in 30 percent of updates. Candidates that cross parameter boundaries are reflected and then clipped to remain feasible. Greedy selection accepts a candidate only when it improves the voltage root mean square error, and elite preservation protects the best solution from being lost. If progress stalls, the worst portion of the population is either reinitialized randomly or regenerated around the best candidate. Every 50 iterations, 15 small perturbations are tested near the leading solution as an intensive local-refinement step.

After each global search, the best parameter set is polished with L-BFGS-B, a bounded gradient-based optimizer that uses limited-memory approximations to the inverse Hessian. Because the researchers did not provide an analytical Jacobian, SciPy estimated gradients with a forward finite-difference scheme. The local search used a function tolerance of 10 to the power of minus 15, a gradient tolerance of 10 to the power of minus 12 and a maximum of 10,000 iterations, but its result was accepted only if it improved upon the solution found by EARO. This makes EARO a hybrid method: the metaheuristic searches broadly for a promising region, while the final local search refines the fit. The comparison algorithms were tested in their original, unmodified forms, without the added L-BFGS-B stage.

For the Scribner 850e cell, the experimental dataset contained 23 measured current-voltage points at 353.15 kelvin. The cell had an active area of 5 square centimeters, used a Nafion 117 membrane and was tested with anode and cathode pressures of 1, 1.25 and 1.5 bar under fully humidified conditions. EARO achieved best root mean square errors of 3.010 × 10 to the power of minus 5, 2.977 × 10 to the power of minus 5 and 2.657 × 10 to the power of minus 5 at the three respective pressures. The associated convergence histories stabilized at approximately 160, 230 and 130 iterations, compared with about 280, 240 and 150 iterations for the original artificial rabbits optimizer.

Each optimizer was run 30 times at each operating condition. EARO showed the strongest consistency as well as the smallest best error. At 1 bar, its mean root mean square error was 3.010212 × 10 to the power of minus 5, while the original artificial rabbits optimizer had a mean of 2.35106685 × 10 to the power of minus 4. At 1.25 bar, the corresponding means were 4.6248195 × 10 to the power of minus 5 and 1.39796667 × 10 to the power of minus 4; at 1.5 bar, they were 2.6572892 × 10 to the power of minus 5 and 3.94585023 × 10 to the power of minus 4. The near-constant results across repeated EARO runs produced a standard deviation of only 2.144 × 10 to the power of minus 8 at 1 bar, 5.327593 × 10 to the power of minus 9 at 1.25 bar and 8.05 × 10 to the power of minus 13 at 1.5 bar.

The second case used 28 measured current-voltage points from the NedStack PS6 stack, which contained 65 series-connected cells with an active area of 240 square centimeters per cell. It operated at 343 kelvin and 1 bar with fully humidified reactant streams. EARO’s best root mean square error was 2.69204 × 10 to the power of minus 7, compared with 1.8338747 × 10 to the power of minus 5 for the original artificial rabbits optimizer and larger errors for the other three methods. Across 30 runs, EARO had a mean error of 6.81211 × 10 to the power of minus 7 and a median of 3.21676 × 10 to the power of minus 7. Its reconstructed voltage-current and power-current curves closely followed the experimental data across the stack’s operating range, and its voltage errors were lower than those produced by the four comparators.

Statistical analysis supported the performance differences. A Kruskal-Wallis test rejected equal performance among the five methods in all four datasets, with p-values between 2.61 × 10 to the power of minus 25 and 4.71 × 10 to the power of minus 23. Pairwise two-sided Wilcoxon rank-sum tests with Holm adjustment found EARO had significantly lower errors than every competitor in all 16 comparisons. The smallest effect occurred for the 5-watt cell at 1.25 bar, where EARO still beat the original artificial rabbits optimizer with a Holm-adjusted p-value of 2.278 × 10 to the power of minus 5 and a Vargha-Delaney A12 effect size of 0.8189. In the other 15 comparisons, A12 values ranged from 0.9978 to 1.0, indicating that a randomly selected EARO run had a lower error than a randomly selected competitor run in virtually every case.

The model itself is inexpensive to evaluate because it uses algebraic equations rather than a detailed electrochemical or computational-fluid-dynamics solution. The researchers described a single fitness evaluation as constant-time and the overall search complexity as linear in the number of iterations, population size and six decision variables, with additional overhead from the local-search stage. That may make offline parameter identification and repeated simulation practical in engineering workflows, but the study did not implement the method on embedded processors or demonstrate real-time operation. The authors also proposed that more accurate power predictions could eventually reduce uncertainty in fuel-cell electric vehicles and stationary microgrids, potentially limiting oversizing and improving cost estimates. They cautioned, however, that calculating financial savings would require dedicated system-level modeling. The demonstrated result is therefore narrower but well characterized: a six-parameter steady-state model, fitted with a statistically robust hybrid optimizer, closely reconstructed two laboratory-tested PEM fuel-cell datasets without being validated for transient dynamics or deployed control systems.

Subject of Research: Steady-state PEM fuel-cell circuit modeling and parameter estimation using a hybrid artificial-rabbits optimization algorithm.

Article Title: A novel circuit-level steady-state fuel cell model assisted by enhanced artificial rabbits optimization

Article References: Bayoumi, A., Sakr, W. S., Elbana, M. M., El-Sehiemy, R. A., & Abaza, A. (2026). A novel circuit-level steady-state fuel cell model assisted by enhanced artificial rabbits optimization. Results in Engineering, 32, Article 113499. https://doi.org/10.1016/j.rineng.2026.113499

Image Credits: AI Generated

DOI: 10.1016/j.rineng.2026.113499

Keywords: proton exchange membrane fuel cells, circuit modeling, parameter estimation, metaheuristic optimization, artificial rabbits optimization, polarization curves, voltage prediction, root mean square error, fuel-cell stacks, computational efficiency, novel, circuit-level

The study focuses on the bearing strength of subgrade soils strengthened with geosynthetic materials, which are used in road construction to improve weak soils through functions including separation, reinforcement, filtration and drainage. CBR is a key measure of subgrade bearing capacity and informs pavement design. Conventional soaked CBR testing can be slow and labor-intensive: specimens remain submerged for 96 hours, while Proctor compaction tests to determine optimum moisture content and maximum dry density can extend the work on an individual sample to five or six days. Heterogeneous site conditions may require testing many samples. The compiled dataset therefore offers a potential route to estimating CBR from properties that can be obtained more readily, although the study does not establish that the models can replace laboratory testing in routine practice.

To build the database, the researchers combined 90 soaked CBR observations from nine previously published studies. The records covered sandy and fine-grained soils classified under the Unified Soil Classification System, with samples representing several combinations of soil properties, geosynthetic materials and reinforcement configurations. Eleven predictors were used: liquid limit, plastic limit, plasticity index, maximum dry unit weight, optimum moisture content, percentage of fines, percentage of sand, geosynthetic tensile strength, number of reinforcement layers, position of the first layer and position of subsequent layers. Soaked CBR was the target variable. Across the dataset, CBR ranged from 1.32% to 88.3%, with a mean of 16.067%. Reinforcement tensile strength ranged from 0.75 to 140, and the number of layers ranged from one to three.

The model comparison used a common 80/20 partition, retaining 72 records for training and holding out 18 for final testing. Input scaling parameters were derived only from the training data and then applied unchanged to the test data, limiting information leakage. The authors evaluated plain and AOA-assisted versions of three learners under the same split: ANN, Ridge regression and XGBoost. AOA is a population-based metaheuristic inspired by the hunting behavior of Aquila eagles. It was used to tune model weights and hyperparameters, with mean squared error serving as the optimization objective for the neural-network training. The AOA configuration used a population of 150 and up to 500 generations, and the ANN had an 11–6–1 architecture: 11 inputs, six hidden neurons and one output neuron.

AOA improved the reported test performance of every base model, although the size of the gain differed. For ANN, R² increased from 0.929 to 0.945, MSE declined from 3.06 to 2.87 and MAE fell from 18.09 to 13.87. Ridge remained the weakest performer despite optimization: AOA-Ridge reached R² = 0.831, MSE = 4.90 and MAE = 42.81, compared with R² = 0.815, MSE = 5.17 and MAE = 47.09 for plain Ridge. The AOA-XGBoost model ranked first under the study’s weighted color-intensity scheme, which assigned weights of 0.5 to R², 0.3 to MSE and 0.2 to MAE. Its advantage was especially visible in MAE, which fell by 57.1% relative to plain XGBoost. For this dataset and modeling setup, AOA-assisted XGBoost was the most accurate of the six evaluated models.

Five-fold cross-validation on the training data was used to test whether the ranking depended on the particular hold-out split. AOA-XGBoost again performed best, with cross-validated R² = 0.8819 ± 0.0765, root mean squared error of 6.4218 ± 3.1846, MAE of 3.5217 ± 1.4826, mean absolute percentage error of 19.6842 ± 4.7315%, and A20 = 0.6427 ± 0.1186. The A20 metric represents the proportion of predictions falling within ±20% of the corresponding measured values. AOA-ANN ranked second, with R² = 0.8347 ± 0.1062, while AOA-Ridge had R² = 0.6487 ± 0.3628. The broadly consistent ordering between the held-out test and cross-validation results supports the reported advantage of the optimized tree-based model, but the cross-validated R² is substantially lower than the 0.980 obtained on the test set, illustrating the sensitivity of performance estimates in a small dataset.

Training behavior for the AOA-ANN was also monitored over 500 generations. Its mean squared error fell from approximately 177 initially to around 95 in the first 20 epochs, then declined in stages to approximately 58 at epoch 40, 50 near epoch 160 and 44 around epoch 190. Improvement slowed after roughly 200 epochs, reaching about 40 by epoch 250 and approximately 38 at the end. The authors interpreted this as convergence toward a near-stable solution, with further optimization offering limited gains. The study also published the final ANN weights and biases and provided a worked calculation for a non-plastic reinforced soil condition, yielding a predicted CBR of 41.35%. That example lies within the observed CBR range and was presented as an implementation demonstration, not as independent validation of the model outside the compiled data.

Two sensitivity methods, the Cosine Amplitude Method (CAM) and Garson’s algorithm, were used to estimate the relative influence of the 11 inputs. Their combined analysis assigned 29.4% of the sensitivity to the number of reinforcement layers and 21.8% to geosynthetic tensile strength. The position of the first reinforcement layer contributed 12.1%, followed by the position of subsequent layers at 9.9% and plastic limit at 7.2%; the other variables together accounted for 19.5%. Thus, the four reinforcement-related variables collectively represented more than 73% of the model’s reported sensitivity. CAM and Garson ranked some secondary variables differently, however, and a separate stability analysis gave dry unit weight the most consistent rank even as the two methods disagreed about the ordering of tensile strength, sand and fines. The percentages are model-based importance measures rather than estimates of causal effects or direct physical contributions to strength.

The most important limitation is the database’s size and composition. Only 90 records were assembled, and differences among source studies could not be eliminated in soil type, material characteristics, specimen preparation or testing conditions. Five-fold validation and the independent hold-out set reduce but do not remove the risk of overfitting, especially for a model with 11 inputs and relatively few observations. The models should therefore be used primarily within the parameter domain represented by the compiled data; predictions outside the reported ranges involve extrapolation. The neural network and XGBoost also retain elements of a black box, and the sensitivity results do not replace direct testing or mechanistic evaluation of soil–reinforcement interaction. The study’s strongest conclusion is therefore bounded but promising: within its experimental dataset and evaluation protocol, AOA-XGBoost was the most accurate and consistently top-ranked model for estimating soaked CBR, and larger independent validation will be needed before its performance can be established beyond the current scope.

Subject of Research: Optimization-assisted machine learning for predicting the California Bearing Ratio of geosynthetic-reinforced subgrade soil

Article Title: New hybrid models integrating the aquila optimizer with machine learning algorithms to predict the strength of geosynthetic-reinforced subgrade soil

Article References: Tiang, J.-J., Ateş, B., Eirgash, M. A., Zhao, Y., Anand, P., Sharma, A., & Lim, W. H. (2026). New hybrid models integrating the aquila optimizer with machine learning algorithms to predict the strength of geosynthetic-reinforced subgrade soil. Frontiers in Built Environment, 12, Article 1947550. https://doi.org/10.3389/fbuil.2026.1947550

Image Credits: AI Generated

DOI: 10.3389/fbuil.2026.1947550

Keywords: geotechnical engineering, machine learning, XGBoost, metaheuristic optimization, California Bearing Ratio, geosynthetics, subgrade soil, sensitivity analysis, pavement design, hybrid models, hybrid, models

Leachate can transport toxic metals and organic contaminants from landfill waste into surrounding soil and groundwater, making the movement and extent of subsurface leakage an environmental concern. The Benowo investigation focused on mapping magnetic anomalies that might mark preferential subsurface pathways or structures relevant to that process. After acquisition, the measurements underwent diurnal correction and removal of the International Geomagnetic Reference Field. Researchers also applied upward continuation, Reduction-to-the-Pole transformation, analytic signal, first vertical gradient and horizontal gradient analyses to improve anomaly localization and delineate source boundaries.

After processing, the Reduction-to-the-Pole magnetic anomalies ranged from −8,000 to +7,200 nT. They were concentrated mainly in the northern and western sectors of the landfill. The study then selected representative anomalies for quantitative interpretation through forward modeling, using a simplified representation of subsurface magnetic bodies. A Flower Pollination Algorithm, a metaheuristic optimization method, was used to adjust the modeled sources and reproduce the observed magnetic responses.

The optimized models identified simplified spherical and cylindrical magnetic source bodies at approximate depths of 11–29 meters. The optimization converged consistently, with residual misfits below 0.1 nT, indicating close numerical agreement between observed and modeled magnetic responses. The resulting distribution of interpreted sources was spatially consistent with the known geological and hydrogeological framework of the study area. That agreement does not establish that every magnetic source represents pollution, but it supports using the anomalies as indicators of where further investigation may be most useful.

Magnetic surveying alone cannot confirm the presence, composition or movement of landfill leachate, and the interpreted bodies are simplified models rather than direct images of buried waste or contamination plumes. The researchers therefore treated the anomaly zones as targets for subsequent hydrochemical sampling, borehole work or complementary geophysical surveys. By integrating high-resolution magnetic measurements with transformation-based processing and metaheuristic forward modeling, the study demonstrates a scalable, non-invasive approach to identifying subsurface features that could guide environmental risk assessment and groundwater protection at municipal landfills.

Subject of Research: High-resolution magnetic surveying and metaheuristic modeling of possible leachate pathways at the Benowo municipal landfill in Surabaya, Indonesia.

Article Title: Integrating high-resolution magnetic surveys and metaheuristic optimization for quantitative characterization of subsurface magnetic sources in a municipal landfill

Article References: Minarto, E., & Lesar, Z. R. A. (2026). Integrating high-resolution magnetic surveys and metaheuristic optimization for quantitative characterization of subsurface magnetic sources in a municipal landfill. Scientific Reports. https://doi.org/10.1038/s41598-026-76581-y

Image Credits: AI Generated

DOI: 10.1038/s41598-026-76581-y

Keywords: landfill leachate, magnetic surveying, Benowo landfill, metaheuristic optimization, groundwater protection, magnetic anomalies, forward modeling, environmental geophysics, Integrating, high-resolution, magnetic, surveys

The core insight behind the work is that more computation does not always mean better diagnosis. Existing deep learning and optimization-assisted mammographic classification frameworks often suffer from high-dimensional feature redundancy, increased computational complexity, and limited interpretability. When a model relies on thousands of learned features, many of them turn out to be irrelevant noise that inflates memory requirements, slows training, and increases the risk of overfitting. Subramaniam’s framework, designated SFS-FS-BC, instead begins with just 30 handcrafted radiomic descriptors extracted from lesion regions and lets an optimization algorithm decide which of them actually matter for distinguishing benign from malignant tissue.

The choice of optimization engine is what gives the study its distinctive flavor. Stochastic fractal search is a population-based metaheuristic inspired by the growth and diffusion patterns of natural fractals, the branching structures seen in everything from river deltas to lung tissue. In the algorithm, each candidate solution, called a particle, represents a possible subset of features encoded as continuous values between zero and one. During the diffusion phase, particles perform Gaussian random walks through the search space using two complementary strategies: one directed toward the best solution found so far, which accelerates exploitation of promising regions, and one centered on each particle’s current position, which preserves the diversity needed for global exploration.

After diffusion, a ranking-based update mechanism refines the population. Particles are sorted by fitness, measured as the classification accuracy achieved by their feature subset under cross-validation, and weaker solutions are improved through stochastic interactions with stronger ones. Once the optimization converges, the continuous particle vectors are converted into binary feature masks using a fixed threshold of 0.5: values at or above the threshold select a feature, values below discard it. The result is a compact, optimized feature subset that feeds directly into the k-nearest neighbor classifier, which labels a test sample by majority vote among its five closest neighbors measured with Euclidean distance.

The experimental design reflects careful attention to a problem that plagues many machine learning studies in medicine: data leakage. The framework employed a patient-wise stratified 5-fold cross-validation protocol in which all images from the same patient were kept within a single fold, preventing the model from learning one patient’s imaging signature and then being tested on it again. Normalization parameters were computed exclusively from training subsets, and the feature selection optimization itself was run independently within each training fold. All reported metrics represent means and standard deviations across 30 independent experimental runs, and pairwise Wilcoxon signed-rank tests confirmed that the improvements over baseline methods were statistically significant at p < 0.01.

The numbers tell a compelling story. On CBIS-DDSM, a curated subset of the Digital Database for Screening Mammography containing 891 benign and 675 malignant lesions, the framework achieved 97.3 percent accuracy, 97.1 percent precision, 97.5 percent recall, an F1-score of 97.3 percent, and an area under the ROC curve of 0.991. On INbreast, a high-quality full-field digital mammography dataset with 220 benign and 190 malignant cases, performance climbed to 98.7 percent accuracy and 0.995 AUC. Perhaps most telling is the comparison with the baseline: a k-nearest neighbor classifier using all 30 features without selection managed only 87.6 percent accuracy on CBIS-DDSM, meaning the fractal optimization alone accounted for nearly a ten-point gain.

Feature reduction proved equally important. The stochastic fractal search compressed the original 30-dimensional feature space to an average of 12.67 optimized features, and an analysis of selection frequencies across 30 runs revealed which descriptors the algorithm consistently favored. Texture-based measures such as contrast, entropy, homogeneity, and correlation appeared again and again, confirming that tissue heterogeneity patterns are among the strongest signals of malignancy. Morphological descriptors like circularity and eccentricity were also repeatedly selected, underscoring the clinical observation that malignant lesions tend to have irregular, poorly defined shapes compared with benign masses.

Convergence behavior further distinguished the approach from its competitors. The optimization typically stabilized within roughly 35 to 40 iterations, despite a maximum limit of 100, thanks to a convergence-based early stopping mechanism that halts the search when the best fitness fails to improve beyond a tolerance of 10 to the minus 6 for ten consecutive iterations. In head-to-head comparisons, particle swarm optimization required nearly 65 iterations and genetic algorithms about 80 to approach comparable fitness values. An ablation study confirmed that every component contributes: removing fractal diffusion, ranking-based updates, or Z-score normalization each degraded performance, while the full pipeline reached 98.47 percent accuracy on the combined datasets.

The study is candid about its limits. The framework depends on expert-provided lesion annotations and segmentation masks rather than performing fully automated lesion localization, and it was evaluated only on public datasets without an independent external test set, so the results cannot yet be read as proof of clinical generalizability. Runtime comparisons with deep learning methods were conducted on CPU hardware and should be interpreted cautiously, since many competing architectures were originally implemented on GPU-accelerated systems. The work also addresses only binary benign-malignant classification, not the full clinical workflow of detection, segmentation, and risk assessment.

Even with those caveats, the implications are significant. Because the selected features correspond to interpretable morphological, intensity, and texture characteristics that radiologists already assess, the framework offers a transparency that black-box deep learning models often lack. Its low computational footprint makes it a plausible candidate for resource-constrained clinical environments where GPU infrastructure is unavailable, potentially supporting screening workflows and second-opinion analysis. The author points toward multi-institutional validation, automated segmentation integration, and hybrid radiomics-deep learning architectures as the next steps. For now, the study stands as an elegant demonstration that sometimes the smartest way forward in medical AI is not a bigger model, but a better-chosen handful of features, found with a little help from the mathematics of fractals.

Subject of Research: Fractal optimization-driven feature selection and k-nearest neighbor classification of benign and malignant breast lesions in mammographic images

Article Title: Breast cancer classification in mammographic images using fractal diffusion feature selection and k nearest neighbor

Article References: Subramaniam, K. (2026). Breast cancer classification in mammographic images using fractal diffusion feature selection and k nearest neighbor. Discover Artificial Intelligence, 6(1), Article 1236. https://doi.org/10.1007/s44163-026-02284-y

Image Credits: AI Generated

DOI: 10.1007/s44163-026-02284-y

Keywords: breast cancer, mammography, stochastic fractal search, feature selection, k-nearest neighbor, computer-aided diagnosis, radiomics, machine learning, CBIS-DDSM, INbreast, metaheuristic optimization, medical imaging

The motivation is a widening crisis. Epidemiological research cited in the study indicates that roughly 30 to 35 percent of college students worldwide report symptoms of depression, anxiety, or psychological distress during their college years, and longitudinal data suggest a 40 percent rise in reported mental health issues among students over the past decade. Students with untreated conditions show a 20 to 25 percent lower grade point average and are twice as likely to leave their degree programs than their peers. Traditional assessment tools, however, struggle to keep pace with this burden.

Self-report instruments such as the Patient Health Questionnaire-9 for depression and the Perceived Stress Scale introduce recall bias and social desirability effects, impose a high burden on respondents, and offer only cross-sectional snapshots rather than longitudinal views of wellbeing. Clinical interviews, while diagnostically useful, cannot be scaled to screen large populations and are often unavailable because of stigma, cost, and insufficient campus counseling services. The episodic character of traditional assessment also cannot reflect the dynamic contextual variation of mental state that typifies the college experience, leaving clinicians and educators with an incomplete picture precisely during high-stress periods such as examinations or project deadlines.

Digital phenotyping through smartphones offers an alternative. Phones are rich sensor platforms that can record behavioral and environmental predictors of mental health without any user interaction. The study builds on the StudentLife dataset, which contains ten weeks of multimodal measurements from 48 Dartmouth undergraduates, including physical activity through accelerometry, sleep cycles inferred from phone monitoring, social engagement through conversation detection, geographical pathways, and self-reported feelings. The sensing infrastructure ran in the background on Android devices, recording roughly 672,000 hours of passive data alongside 1,920 completed self-report surveys.

The computational challenge lies in combining heterogeneous data streams with disparate sampling rates, patterns of missingness, and predictive relevance. Simple concatenation or late averaging of modalities fails to capture the complex nonlinear interactions between behavioral domains that define human psychology. The researchers therefore designed a cross-modal attention network with modality-specific encoders—temporal convolutional networks with dilated convolutions for continuous sensor streams, dense feedforward networks with embedding layers for sparse survey data—followed by multi-head scaled dot-product attention that learns dependencies between modalities bidirectionally, and a hierarchical fusion strategy combining weighted concatenation with a transformer layer.

Crucially, the architecture was not hand-designed. The team introduced the Addax Optimization Algorithm, a metaheuristic inspired by two behaviors of the addax antelope native to the Sahara: foraging, in which the animals track rainfall to locate areas with abundant vegetation, and excavation, in which they dig depressions in the sand to rest and shield themselves from sandstorms. In the algorithm, each addax represents a candidate neural architecture, the foraging phase drives exploration of the search space, and the digging phase refines solutions locally. The novel version adds a chaotic circular mapping mechanism to prevent premature convergence and a Lévy flight mechanism that introduces large jumps to escape local optima.

The search space encompassed about 47 parameters—28 discrete choices such as encoder type, attention head count, and fusion strategy, plus 19 continuous hyperparameters including learning rate and dropout rate. The optimization objective combined regression loss, classification loss, model complexity regularization, and an attention sparsity term that encourages interpretable cross-modal interactions, with at least 70 percent of attention weights required to be near zero. The Addax algorithm reached an optimal fitness of 0.894 in 42 iterations, outperforming particle swarm optimization, genetic algorithms, ant colony optimization, and Bayesian optimization, with statistically significant differences confirmed by repeated-measures ANOVA. Full optimization took 8.7 hours, a 12.1 percent improvement over Bayesian optimization.

The optimized network initially achieved 87.4 percent accuracy for depression detection on the StudentLife test set, with sensitivity of 85.6 percent and an area under the ROC curve of 0.923. Stress classification reached 83.7 percent accuracy, and the predicted mental health index correlated strongly with GPA. Modality weight analysis revealed that survey data dominated depression prediction, followed by sleep patterns and activity data, while activity data was the strongest predictor of stress. Attention weights shifted systematically with the academic calendar: location and activity were strongest during exam weeks, while sleep dominated depression prediction during regular coursework. Ablation studies confirmed that removing the attention mechanism reduced depression accuracy by 13.6 percentage points.

But the test set contained only seven students, a limitation the authors confronted directly. When the model was evaluated on the College Experience Study dataset—a longitudinal study of over 200 students collected over five years, including passively collected sensor, survey, and brain-imaging data—zero-shot transfer achieved 72.3 percent depression classification accuracy, and fine-tuning on 140 local participants raised this to 83.9 percent. The authors conclude that the initial 87.4 percent result can be interpreted as overoptimistic. Even with fine-tuning, a false positive rate of roughly 16 percent implies that for every 100 students flagged, about 15 or 16 are healthy—too high for autonomous screening or policy-level deployment.

The authors propose a phased, human-in-the-loop implementation instead. The model could serve as an early notification tool for counseling staff during predictable peak stressors such as examinations, project deadlines, and term transitions, with human judgment ultimately used for decision-making. Confidence thresholds above 0.95 would reduce flags by roughly 60 percent while preserving about 70 percent of true positives. Before any real-world deployment, the researchers recommend prospective validation across 3 to 5 institutions with at least 500 total participants, continuous institutional calibration, regular bias audits, and privacy-preserving methods such as on-device processing or federated learning. Only once false negatives for severe depression fall below 3 percent could the technology approach actual decision-making, and even then it would supplement rather than replace existing clinically focused systems.

Subject of Research: Deep learning-based multimodal mental health assessment in college students using passive smartphone sensing

Article Title: Metaheuristic-optimized cross-modal attention networks for multimodal mental health assessment in college students

Article References: Liu, W., & Qian, C. (2026). Metaheuristic-optimized cross-modal attention networks for multimodal mental health assessment in college students. Frontiers in Systems Neuroscience, 20, Article 1847214. https://doi.org/10.3389/fnsys.2026.1847214

Image Credits: AI Generated

DOI: 10.3389/fnsys.2026.1847214

Keywords: digital phenotyping, cross-modal attention network, Addax Optimization Algorithm, neural architecture search, passive smartphone sensing, college student mental health, depression detection, StudentLife dataset, College Experience Study, metaheuristic optimization, multimodal deep learning, stress prediction

The research, led by Yan Zhang of the National Key Laboratory of Radar Signal Processing at Xidian University together with Guangxun Du, Feng Luo, and Yueqian Liang of the Information Sciences Academy of CETC in Beijing, addresses a gap that has persisted across the mission-planning literature. While individual studies have tackled task allocation, path planning, or synchronization in isolation, the authors note that no prior work has simultaneously handled the full combination of constraints their framework targets: capability-based task requirements, variable-sized vehicle subsets, strict multi-vehicle simultaneity, cross-domain compatibility between different types of unmanned platforms, and complex precedence and synchronization dependencies among tasks.

At the heart of the problem is a coupling that has long frustrated mission planners. Deciding which vehicles should perform which tasks and deciding what flight paths those vehicles should follow are not independent questions. The timing of a synchronized strike, for example, depends on how long each vehicle takes to reach the target, which depends on its path, which in turn depends on where it was sent in the first place. Solving these layers sequentially with naive methods risks producing plans that look feasible on paper but fall apart once real trajectories are substituted for rough estimates.

The framework the researchers propose is a two-layer swarm intelligence architecture that hierarchically decomposes the problem. The upper layer handles task allocation using a continuous encoding scheme, a mathematical representation that allows metaheuristic search algorithms to explore the space of possible assignments smoothly rather than jumping between discrete configurations. Offline preprocessing steps guarantee that constraint satisfaction is built into the encoding itself, so that infeasible assignments are filtered out before they ever reach the trajectory stage.

The lower layer is devoted to path synchronization, and it is here that the framework introduces what the authors identify as a key innovation: a bias-free coupling between the two layers. The allocation layer computes travel costs using a max-time formulation, meaning it evaluates each candidate assignment according to the slowest vehicle in the group rather than the average. A rigorous endurance check then embeds the exact temporal slack that the synchronization layer will later need. The result is a guarantee that no plan deemed feasible during allocation becomes infeasible after the actual trajectories are adjusted to meet synchronization requirements.

To absorb that temporal slack, the synchronization layer deploys four adaptive strategies: circular loitering, in which a vehicle orbits a holding point until its appointed arrival time; constant-altitude transition, which adjusts timing while maintaining a fixed altitude; constant-heading transition, which preserves a vehicle’s direction of travel while modulating its path; and free transition, which allows full three-dimensional maneuvering when no directional or altitudinal constraints apply. A four-layer selection mechanism chooses among these strategies based on the operational domain, the available maneuvering space, heading requirements, and the magnitude of the delay that must be absorbed.

The elegance of this design lies in its conservatism. Because the allocation layer deliberately overestimates travel time using the max-time cost, it reserves more endurance budget than any real trajectory will actually consume. When the synchronization layer later refines the paths, it draws on that reserved slack, tightening the timing without ever exceeding the resources the allocation layer already accounted for. This eliminates a failure mode common in loosely coupled approaches, where trajectory refinement invalidates the assumptions under which tasks were assigned.

Validation was extensive. The researchers ran simulations across scenarios involving up to 50 vehicles and 16 tasks, evaluated under four different objective functions. They compared eight metaheuristic algorithms within their framework and benchmarked the overall approach against an exact mixed integer linear programming solver. The comparative studies confirmed that the framework achieves a superior balance between solution quality and computational efficiency, finding near-optimal plans in a fraction of the time required by exact methods while scaling to problem sizes that would overwhelm classical solvers.

The significance of this work extends beyond the specific benchmarks. Heterogeneous swarms are increasingly central to both civilian and defense applications, from coordinated environmental monitoring that pairs aerial and maritime platforms to search-and-rescue operations that must combine the endurance of fixed-wing aircraft with the hovering precision of rotorcraft. Each of these scenarios embeds the same structural difficulty: tasks that require specific capabilities, groups of vehicles that must act together, and sequences in which the completion of one task gates the start of another. A framework that handles all of these features simultaneously, while guaranteeing that feasibility survives the transition from assignment to trajectory, provides a reusable foundation for mission planners across domains.

The authors acknowledge the broader context of swarm research, citing surveys that document the rapid growth of UAV swarm studies and the persistent challenge of integrating task assignment with path planning under realistic operational constraints. Their contribution is to show that the coupling problem, long treated as a reason to simplify assumptions, can instead be engineered around: by designing the two layers to share a common, conservative accounting of time and endurance, the framework turns a source of fragility into a source of rigor. As unmanned systems grow more capable and missions grow more complex, approaches that preserve feasibility by construction rather than by after-the-fact repair may prove to be the template that autonomous swarm coordination has been waiting for.

Subject of Research: Integrated task allocation and path synchronization for heterogeneous unmanned vehicle swarms using a two-layer swarm intelligence optimization framework

Article Title: Task-Path Coordination for Heterogeneous Swarms with Complex Dependency and Synchronization Requirements: A Swarm Intelligence Framework

Article References: Zhang, Y., Du, G., Luo, F., & Liang, Y. (2026). Task-Path Coordination for Heterogeneous Swarms with Complex Dependency and Synchronization Requirements: A Swarm Intelligence Framework. International Journal of Aeronautical and Space Sciences. https://doi.org/10.1007/s42405-026-01304-6

Image Credits: AI Generated

DOI: 10.1007/s42405-026-01304-6

Keywords: heterogeneous swarms, task allocation, path synchronization, swarm intelligence, UAV mission planning, metaheuristic optimization, mixed integer linear programming, multi-vehicle coordination, unmanned aerial vehicles, constraint satisfaction, computational efficiency, aerospace engineering

The review, led by Muhammad Sabo Yahaya of Universiti Teknologi PETRONAS in Malaysia and Federal Polytechnic Daura in Nigeria, together with colleagues from Malaysia and Nigeria, focuses on the One-Parameter-at-a-Time (OPAT) paradigm for Combinatorial Interaction Testing (CIT). The approach traces its origins to the In-Parameter-Order (IPO) algorithm introduced in 2002 and its generalized successor, IPOG, which extended the technique to arbitrary interaction strengths. Rather than generating complete test cases one at a time, OPAT builds a test suite incrementally by introducing one parameter per stage. Two complementary mechanisms drive this construction: horizontal growth, which extends existing test cases by assigning values to a newly introduced parameter in a way that maximizes coverage of previously unseen interactions, and vertical growth, which adds new test cases only when necessary to cover any interactions that horizontal expansion could not reach. This incremental structure allows OPAT to reuse existing configurations while maintaining strong scalability as systems grow more complex.

Despite the paradigm’s importance, no previous review had ever synthesized the OPAT literature in isolation. Prior surveys examined combinatorial testing from broader perspectives, treating metaheuristics as black-box optimizers or focusing narrowly on pairwise testing. The new study, published on 15 October 2026, addresses this gap through a systematic search of 1,300 publications across four major digital libraries, ultimately identifying 40 primary studies published between 2000 and 2026. The screening process was rigorous: two independent reviewers achieved a Cohen’s Kappa agreement of 0.83 during title and abstract screening and 0.89 during full-text eligibility assessment, with a third senior reviewer arbitrating any persistent disagreements. Quality assessment showed that 82.5 percent of the included studies scored at least 3.0 out of 4.0 on a four-criterion checklist evaluating algorithmic clarity, experimental rigor, quantitative reporting, and baseline comparison.

The review’s central contribution is a unified taxonomy that classifies OPAT research into five categories: deterministic refinements, scaling and distribution strategies, advanced feature-enhanced strategies, metaheuristic and hybrid strategies, and specialized OPAT adaptations. Deterministic refinements improve the original IPO and IPOG algorithms through better heuristics, dynamic programming, and structural modifications. IPOG-D, for instance, introduces a recursive doubling mechanism that dramatically improves scalability: in one reported experiment, it required only 3 percent of standard IPOG’s execution time for 5-way testing of 20 four-valued parameters, though it generated 51 percent more test cases. MIPOG applies enhanced greedy optimization during both growth phases, consistently producing smaller suites than IPOG, Jenny, and ITCH, particularly at interaction strengths of 4 or higher, but at increased computational cost. VIPO simplifies horizontal growth decisions to accelerate generation while maintaining competitive suite sizes across 11 benchmark configurations.

Scaling and distribution strategies address a different bottleneck: the memory and time constraints that emerge when combinatorial problems reach industrial scale. G_MIPOG partitions both memory and computation across a grid of computers, demonstrating logarithmic speedups as coverage strength increased in tests involving 6-way interactions of 7 to 10 five-valued parameters. MC-MIPOG exploits shared-memory multicore architectures, achieving near-linear speedup as parameter counts increased from 5 to 16 at interaction strength 4 on a 2.4 GHz Core 2 Quad processor. TS_OP distributes the workload using MapReduce and Tuple Space across a network of five workstations, significantly reducing per-machine memory utilization, though at the cost of non-deterministic outputs due to network overhead.

Feature-enhanced strategies tackle the practical realities that pure algorithms often ignore. Real systems impose constraints: certain parameter combinations are invalid, infeasible, or meaningless. The ACTS tool, developed by researchers at the National Institute of Standards and Technology, embeds IPOG variants within a comprehensive framework supporting constraint specification, mixed-strength testing, and multiple user interfaces, and has been adopted by over 1,200 organizations. IPOG-C minimizes redundant constraint checks by selectively evaluating only relevant constraints, while IPO-SAT transforms constraint handling into a satisfiability problem amenable to SAT solvers. Seeding mechanisms, implemented in strategies such as SCIPOG and SCIPOG-VS, allow domain knowledge to be injected directly into the generation process, ensuring that critical or high-risk configurations are always included in the final suite.

Metaheuristic and hybrid strategies represent the most recent evolutionary branch, embedding OPAT’s structured construction within stochastic optimization frameworks. The Harmony Search Algorithm dominates this category, appearing in 77.8 percent of the analyzed stochastic OPAT studies, including OPAT-HS, HCATS, OPATHS, PWiseHA, PHOSC, SCHOP, eIPOG, and eHS. The enhanced Harmony Search variant eHS reported a 90.91 percent success rate in reducing test suite sizes across 33 configurations compared to IPOG, but achieved zero percent success in execution time superiority, illustrating the inherent tension between search quality and computational overhead. GAMIPOG combines a genetic algorithm with deterministic OPAT components, achieving scalability up to interaction strength 15. The hybrid HOS strategy applies a genetic algorithm for horizontal growth and Simulated Annealing for vertical growth, achieving optimal sizes for 61 of 71 benchmark configurations.

Specialized adaptations extend OPAT beyond conventional parameter interaction problems. DEO applies the paradigm to sequence covering arrays for event-driven systems, where the order of events matters as much as their combination. PMC automates test data generation directly from source code for C and C++ unit testing. N-IPO leverages Fibonacci-based value selection to reduce suite sizes for large input domains, while ReqOrder and ParaOrder support input-output relations and variable interaction strengths. These adaptations demonstrate the framework’s flexibility but also its fragmentation: each targets a niche, and none has achieved the broad industrial penetration of tools like ACTS.

Perhaps the review’s most sobering finding concerns reproducibility. The authors demonstrate that direct cross-study benchmarking of execution times is mathematically invalid due to highly heterogeneous self-reported hardware environments and the closed-source nature of most academic tools. Numerical results from different studies cannot be combined into a universal performance ranking without controlling for differences in hardware, implementation environments, benchmark configurations, and parameter settings. The limited availability of executable implementations and source code constitutes what the authors describe as a substantive research gap, not merely a methodological limitation of their own review. Without accessible implementations, independent reproduction and controlled head-to-head evaluation remain impossible.

Looking forward, the review identifies several promising directions: unified optimization frameworks that simultaneously balance scalability, optimality, and feature integration; exploration of underutilized metaheuristics such as Particle Swarm Optimization, Tabu Search, and hyper-heuristics; intelligent and adaptive test generation leveraging historical testing data and fault patterns; deterministic parallel algorithms; and large-scale industrial validation on real-world systems rather than synthetic benchmarks. The authors argue that transitioning OPAT research into industrial-grade, open-source software engineering pipelines requires not only more effective optimization mechanisms but also standardized, transparent, and reproducible empirical evaluation practices. For a field that has quietly underpinned software quality assurance for over two decades, the message is clear: the algorithms have matured, but the science of measuring them has not kept pace.

Subject of Research: One-Parameter-at-a-Time strategies for combinatorial interaction testing in software test suite generation

Article Title: Constructing t-way test suites: a systematic survey and qualitative synthesis of the One-Parameter-at-a-Time approach

Article References: Yahaya, M. S., Hashim, A. S., Mamman, H., Abdullahi, S., Umer, U., Adamu Aliyu, D., & Godowoli, I. M. (2026). Constructing t-way test suites: a systematic survey and qualitative synthesis of the One-Parameter-at-a-Time approach. Frontiers in Computer Science, 8, Article 1946723. https://doi.org/10.3389/fcomp.2026.1946723

Image Credits: AI Generated

DOI: 10.3389/fcomp.2026.1946723

Keywords: combinatorial interaction testing, One-Parameter-at-a-Time, software testing, t-way test suite generation, IPOG algorithm, metaheuristic optimization, Harmony Search Algorithm, constraint handling, systematic literature review, reproducibility, parallel computing, software quality assurance

The heart of the problem lies in how batteries are modeled. Traditional equivalent circuit models represent a cell as a network of resistors and capacitors, which is computationally cheap and therefore attractive for embedded battery management systems, but integer-order components carry hidden assumptions. Real batteries do not behave like ideal capacitors; their charge transfer and diffusion processes are distributed across time scales and across the physical volume of the electrodes, producing frequency-dependent impedance that lumped elements simply cannot replicate. The result is systematic voltage error, poor performance under varying temperatures, and the need for constant recalibration as the cell ages. Fractional-order models solve this by allowing non-integer exponents in the calculus that describes the system, capturing memory effects and non-exponential relaxation naturally. A key element is the constant phase element, whose exponent alpha slides continuously between the behavior of a resistor and a capacitor, and whose value of one half corresponds to the classic Warburg diffusion element seen in electrochemical impedance spectroscopy.

But fractional-order models come with a price: identifying their parameters is brutally difficult. The team adopted an R(RQ)(RQ)W structure, an advanced extension of classical second-order and PNGV models, in which an ohmic resistance is followed by two parallel resistor-constant-phase-element branches and a Warburg element. Each component maps onto a distinct region of the Nyquist plot, the standard graphical representation of impedance data. The ohmic resistance appears as the high-frequency intercept on the real axis, the two RQ branches form overlapping depressed semicircles in the mid-to-high frequency range corresponding to charge transfer and slower interfacial reactions, and the Warburg element produces the characteristic 45-degree low-frequency tail of solid-phase diffusion. Eight parameters must be extracted simultaneously, and they are strongly coupled, meaning an error in one drags the others off course. Metaheuristic optimizers, which explore search spaces without gradients, are the usual tool, but they frequently converge to local optima that look good numerically yet produce physically meaningless parameters.

To choose the best optimizer fairly, the researchers staged a systematic tournament of ten metaheuristic algorithms: three established methods, particle swarm optimization, grey wolf optimization, and artificial bee colony, against seven recent bio-inspired contenders including the sea lion, golden jackal, fox, honey badger, seahorse, sand cat, and marine predator algorithms. Each ran with an identical budget of 10,000 swarm members and 100 iterations across 20 independent trials. Scoring by root mean square error, mean absolute percentage error, and runtime, the Marine Predators Algorithm, which mimics the Lévy flight and Brownian motion strategies of foraging marine animals, emerged as the most robust performer. A Friedman statistical ranking placed it first with an average rank of 2.00, narrowly ahead of the Honey Badger Algorithm, and its mean runtime of 114 seconds comfortably beat both the honey badger’s 150 seconds and the artificial bee colony’s punishing 2,518 seconds. Yet even the winner showed troubling discrepancies for the second semicircle’s resistance and capacitance and the Warburg coefficient, confirming that raw optimization power alone was insufficient.

The first fix is elegantly physical. Instead of letting the optimizer start from arbitrary bounds, the team derived initial parameter estimates directly from the geometry of the Nyquist plot. A parallel resistor-capacitor circuit traces a perfect semicircle of radius R over two; replacing the capacitor with a constant phase element rotates that semicircle by an angle theta that depends analytically on the fractional exponent alpha, following the relation theta equals 90 degrees times one minus alpha. By extending the measured arcs to full circles, reading off their real-axis intercepts, and measuring the rotation angles of their apexes, the researchers could calculate the ohmic resistance, both branch resistances, both constant phase element exponents and capacitance offsets, and even the Warburg value from the lowest-frequency data point. Six of the eight parameters were thus estimated before optimization even began, shrinking the search space from bounds spanning twenty-fold in each direction to a tight window around physically consistent values.

The second fix attacks dimensionality. Rather than asking the optimizer to juggle all eight parameters at once, the two-stage refinement alternates between metaheuristic optimization of six parameters and analytical recovery of the remaining two. Once the first stage converges on R0, R1, Q1, alpha1, alpha2, and W1, the residual impedance, obtained by subtracting those known contributions from the measured spectrum, is fitted by global least squares to extract R2 and Q2 over the second branch’s frequency band. A Trust Region Reflective algorithm then polishes the estimates, and the cycle repeats for ten iterations with bounds that tighten by a factor of two at each stage. The swarm size drops from 10,000 in the brute-force baseline to just 2,000 in the first stage and 100 thereafter, cutting the iteration count by roughly 80 percent while improving precision.

The validation was unusually thorough. On 50 synthetic impedance profiles generated by Latin Hypercube Sampling, where the true parameter values were known exactly, the full framework achieved an overall mean absolute percentage error of just 7.27 percent, compared with a catastrophic 24,462 percent for standard marine predator optimization and an even worse result for two-stage refinement without informed initialization. The mean root mean square error fell to 1.74 times ten to the minus five, a 92.4 percent reduction relative to the baseline, with a median near ten to the minus six. Scatter plots of estimated versus true parameters clustered tightly along the ideal 45-degree line for all eight quantities, while competing methods showed dispersion spanning orders of magnitude. Crucially, the team demonstrated a subtle pitfall: methods 1 and 2 sometimes achieved low numerical error while their simulated Nyquist plots visibly failed to match the target data, proof that a low objective function value does not guarantee a physically accurate model.

Robustness testing added further confidence. Under 1 percent Gaussian noise the overall parameter error rose only from 7.27 to 12.92 percent, and under 2 percent noise to 18.41 percent, with no instability or divergence. Removing the five lowest-frequency data points, simulating instruments that cannot capture the Warburg region, barely changed the error at 7.38 percent, because the initialization relies on mid-to-high-frequency arc geometry. A transfer test on the simpler R(RQ)W structure showed the initialization concept generalizes across model topologies when the correct structure is known, though the authors are careful to note that automatic model-structure selection from raw data remains an open challenge. Against three state-of-the-art published methods, chaotic adaptive fractional particle swarm optimization, hybrid genetic-particle swarm optimization, and complex-order beetle swarm optimization, the new framework delivered curve-fitting errors one to two orders of magnitude lower, with the rivals showing parameter errors often exceeding several hundred percent for the second branch and Warburg elements.

Finally, the method proved itself on real hardware. The team measured electrochemical impedance spectra from commercial LG INR21700M50LT nickel-manganese-cobalt cells in three states: pristine, initially degraded at 90 percent state of health, and significantly aged at 80 percent state of health and 50 percent state of charge. Across 20 independent runs per condition, the full framework reduced mean root mean square error by 38.0, 32.5, and 76.6 percent respectively compared with the standard optimizer, and achieved parameter coefficients of variation as low as 0.016 percent, meaning repeated identifications landed in the same parameter basin with remarkable consistency. That repeatability is what makes the parameters trustworthy inputs for state of charge and state of health estimation, the foundation of reliable battery diagnosis, degradation tracking, and second-life applications. The authors acknowledge their framework assumes the two impedance arcs remain geometrically distinct, and extending it to overlapping arcs and adaptive topology selection is future work. But the central lesson stands: injecting electrochemical knowledge into the starting point of an optimization can accomplish what brute-force computation cannot, at a fraction of the cost.

Subject of Research: Physics-informed parameter identification for fractional-order lithium-ion battery models using electrochemical impedance spectroscopy

Article Title: Physics-informed parameter identification of fractional-order battery models using Nyquist-based initialization and two-stage metaheuristic refinement

Article References: Wang, S.-C., & Liu, Y.-H. (2026). Physics-informed parameter identification of fractional-order battery models using Nyquist-based initialization and two-stage metaheuristic refinement. Results in Engineering, 32, Article 113425. https://doi.org/10.1016/j.rineng.2026.113425

Image Credits: AI Generated

DOI: 10.1016/j.rineng.2026.113425

Keywords: lithium-ion batteries, fractional-order models, electrochemical impedance spectroscopy, parameter identification, metaheuristic optimization, Marine Predators Algorithm, Nyquist plot, battery management systems, constant phase element, state of charge, state of health, equivalent circuit model

Fault prediction is not a new idea in software engineering. For decades, researchers have tried to build models that learn from historical data which modules or services are prone to defects, allowing teams to focus testing and review effort where it matters most. What makes the SOA setting especially hard, the authors argue, is the nature of the data itself. Service-oriented systems generate high-dimensional datasets with dozens or hundreds of features describing message structures, quality-of-service metrics, usage patterns, and interface descriptions. These features are often redundant, meaning many of them carry overlapping information, and the classes are imbalanced, meaning faulty services are far rarer than healthy ones. Any model that naively learns from such data tends to be overwhelmed by the majority class of well-behaved services and misses the rare failures that actually cause outages.

Temporal dependencies add a further layer of difficulty. In an SOA environment, the state of a service at any given moment depends on its history: response times fluctuate, workloads spike, and interactions with other services leave traces that unfold over time. Traditional fault predictors, which often rely on simple classifiers and static features, throw this temporal structure away. The framework proposed by Singh and Kumar is designed to capture it explicitly by combining two deep learning architectures that have each proven powerful in other domains but have not, according to the authors, been paired in this way for SOA fault prediction before.

The first component is a Transformer encoder, the architecture made famous by large language models. Its key mechanism is self-attention, which allows the model to weigh the relationships between every pair of elements in a sequence, no matter how far apart they are. Applied to service data, self-attention lets the model capture global dependencies: a latency anomaly early in a service interaction chain can influence how the model interprets events much later in that chain. The second component is a bidirectional long short-term memory network, or BiLSTM. LSTM networks are a form of recurrent neural network equipped with gating mechanisms that let them retain information over long sequences without the vanishing-gradient problems that plague simpler recurrent models. The bidirectional variant processes each sequence both forwards and backwards, so the representation of any moment incorporates both what came before and what came after. Stacked together, the Transformer encoder handles global context while the BiLSTM extracts bidirectional temporal patterns, producing a rich fused representation of each service’s behavior.

Powerful architectures, however, can be undermined by messy inputs, and this is where the second innovation of the paper comes in. The researchers developed a dual-strategy feature selection method that fuses two nature-inspired metaheuristic optimization algorithms: the coati optimization algorithm, known as COA, and the sand cat swarm optimization algorithm, or SCSO. Metaheuristics of this kind search vast combinatorial spaces, such as the space of all possible feature subsets, by mimicking behaviors observed in nature. COA draws inspiration from the foraging and predatory strategies of coatis and is particularly strong at exploration, meaning it spreads its search widely across the solution space and avoids getting trapped early in local optima. SCSO, modeled on the hunting behavior of sand cats that locate prey by sound, excels at exploitation, meaning it intensifies the search around promising regions to refine solutions with precision. By hybridizing the two, the method balances wide-ranging exploration with focused exploitation, a combination the authors describe as being applied for the first time in software fault prediction.

The feature selection stage matters for three concrete reasons. First, it reduces redundancy by discarding features that duplicate information already captured by others, which shrinks the input space and reduces the risk of overfitting. Second, it addresses the class imbalance problem by selecting the most informative service features, sharpening the differences between faulty and non-faulty instances so the classifier is not swamped by the majority class. Third, it improves efficiency, since a compact feature set means the deep network has fewer inputs to process. In effect, the COA-SCSO hybrid acts as a smart filter upstream of the Transformer-BiLSTM engine, ensuring the deep model sees only the signals that genuinely distinguish troubled services from healthy ones.

The results reported in the study are striking. On the evaluated benchmark dataset, drawn from the research of Liang Chen on web service clustering, the proposed framework achieved 99.0 percent accuracy, 98.2 percent precision, 98.5 percent recall, 98.3 percent F1-score, 99.2 percent ROC-AUC, and a Matthews correlation coefficient of 97.1 percent. The Matthews correlation coefficient is often considered one of the most demanding metrics for imbalanced classification because it takes all four cells of the confusion matrix into account, so a value of 97.1 percent suggests the model performs consistently well even where simpler accuracy figures can flatter a weak predictor. Compared with state-of-the-art methods evaluated in the study, the improvements reached up to 4.5 percent in accuracy, 5.1 percent in precision, 3.7 percent in recall, 4.4 percent in F1-score, 2 percent in ROC-AUC, and 8.2 percent in MCC, a particularly large gain on the most rigorous of those measures.

The authors did not stop at headline numbers. They subjected their results to statistical validation, including paired significance testing and multi-algorithm comparison procedures of the kind standard in machine learning research, to confirm that the observed improvements were not artifacts of a single lucky run. According to the paper, the performance advantages held consistently across the evaluated cross-validation folds, lending quantitative weight to the claim that the framework is genuinely more effective and robust than its competitors under the benchmark setting. The pipeline also reflects a broader trend in the field: earlier work by the same lead author explored hybrid optimization with deep Q-networks for SOA fault prediction, and the wider literature includes sparrow-search-optimized dual recurrent networks and beluga-whale-inspired feature selection, showing how intensely researchers are mining nature-inspired optimization to sharpen deep learning pipelines for software reliability.

The practical implications could be significant for anyone who runs large-scale service ecosystems. Predicting faults before they surface means maintenance teams can prioritize code review, testing, and monitoring on the riskiest services, converting firefighting into prevention. Because the framework combines automatic feature selection with deep temporal modeling, it requires less manual feature engineering than classical approaches, moving the field closer to deployable, low-touch reliability tooling for cloud platforms, microservice fleets, and enterprise integration hubs. The fact that the architecture is modular, with the optimizer and the neural network as separable components, also suggests it could be adapted to related prediction tasks, from defect forecasting in conventional software to quality-of-service estimation in distributed systems.

Yet the authors are careful about the limits of their claims. The reported figures come from a specific benchmark setting, and the paper states explicitly that further validation is required to assess robustness under heterogeneous and dynamically evolving service environments, the very conditions real production SOA systems face as services are updated, replaced, and scaled. Deep models are also more computationally demanding to train than the simple classifiers used in much of the earlier literature, and metaheuristic feature selection introduces its own hyperparameters. Still, the study marks a notable step: it demonstrates that pairing global self-attention with bidirectional temporal memory, filtered through a dual-strategy nature-inspired optimizer, can push SOA fault prediction to near-perfect measured performance on standard benchmarks. As service-oriented architectures continue to underpin the digital economy, tools that can see failures coming, and do so reliably, are likely to move quickly from research papers into the operational toolkit of engineering teams worldwide.

Subject of Research: A hybrid Transformer-BiLSTM deep learning framework with COA-SCSO feature selection for predicting faults in service-oriented architecture software systems

Article Title: Enhancing fault prediction in SOA-based systems via hybrid transformer–BiLSTM with COA–SCSO feature selection method

Article References: Singh, R., & Kumar, K. (2026). Enhancing fault prediction in SOA-based systems via hybrid transformer–BiLSTM with COA–SCSO feature selection method. Knowledge and Information Systems, 68(1), Article 284. https://doi.org/10.1007/s10115-026-02899-8

Image Credits: AI Generated

DOI: 10.1007/s10115-026-02899-8

Keywords: software fault prediction, service-oriented architecture, Transformer, BiLSTM, deep learning, feature selection, metaheuristic optimization, coati optimization algorithm, sand cat swarm optimization, web services, class imbalance, self-attention

The bandgap is the single most important electronic property for any material intended to absorb or emit light. It defines the energy difference between the valence band, where electrons are bound to atoms, and the conduction band, where electrons are free to move and carry current. For a solar cell, the bandgap determines which portion of the solar spectrum can be harvested and sets a hard ceiling on theoretical efficiency. For light-emitting diodes and photodetectors, it dictates the color of light emitted or the wavelength detected. In perovskite materials, this energy gap can be tuned across a wide range simply by changing the chemical ingredients, which is precisely what makes them so attractive to researchers and so difficult to model.

Organic perovskites follow a crystal structure conventionally described by the formula ABX3, where the A site is occupied by an organic cation such as methylammonium or formamidinium, the B site by a metal, and the X site by a halide. The cation site is the source of much of the difficulty. Unlike a simple inorganic atom, an organic cation brings molecular shape, orientation, dipole moments and dynamic disorder into the crystal lattice. These molecules can tilt, rotate and hydrogen-bond with the surrounding framework, subtly distorting the geometry of the octahedra that actually carry the electronic states. The result is a tangled, nonlinear relationship between composition and bandgap that resists simple interpolation and defeats many conventional machine learning models, which the authors identify as suffering from high dimensionality, feature redundancy and poor generalization in nonlinear feature spaces.

To build their dataset, the researchers assembled 1208 material samples described by 30 feature descriptors, drawing on 201 literature and open-source data points related to hybrid organic-inorganic perovskites. This kind of curated dataset is the raw fuel of materials informatics, and its quality largely determines the ceiling on any model trained on it. The team acknowledges that experimental bandgap measurements scattered across decades of publications come with uncertainty: different measurement techniques, sample preparation conditions and reporting conventions introduce noise that can mislead a learning algorithm. Rather than ignoring that uncertainty, the pipeline confronts it head-on in the first stage of processing.

That first stage is a Simplified Adaptive Fuzzy Min-Max Neural Network, abbreviated SAFMMNN, which handles the preprocessing. Fuzzy min-max networks work by enclosing data points in hyperboxes, geometric regions in feature space whose boundaries can overlap and carry degrees of membership rather than crisp labels. This allows the model to represent ambiguous and noisy measurements gracefully, softening the influence of outliers and improving normalization before the data reaches the main predictor. In effect, the fuzzy layer acts as a filter and a translator, converting messy real-world compositional data into a cleaner, more structured representation that downstream layers can learn from more reliably.

Feature selection, the second pillar of the pipeline, is handled by a novel hybrid metaheuristic the authors call hyb-DLO-SFWOA, combining the Draco Lizard Optimizer with the Superb Fairy-wren Optimization Algorithm. Metaheuristics of this kind are search strategies inspired by animal behavior, designed to explore vast combinatorial spaces without exhaustively enumerating every possibility. The Draco Lizard Optimizer, introduced as a general-purpose global optimization method, and the Superb Fairy-wren Optimization Algorithm, designed specifically for feature selection problems, are fused here to pick the subset of descriptors that maximizes relevance to the bandgap while minimizing redundancy among the features themselves. Redundant descriptors do not merely waste computation; they can distort model training, inflate overfitting risk and obscure which physical factors genuinely drive the electronic structure. By pruning the feature space, the hybrid optimizer ensures the neural network sees the most informative, least redundant view of each material.

At the heart of the system sits CADHRANN itself, a deep learning model whose name encodes its three defining ideas. The discrete Hopfield component draws on a class of recurrent neural networks known for associative memory, capable of storing and retrieving patterns, which suits the discrete, combinatorial nature of chemical composition data. The context axial mechanism is designed to capture complex spatial dependencies, allowing the network to attend to relationships among features along structured axes rather than treating every descriptor as an isolated number. The reverse attention component then directs the model to focus on the features and interactions that most strongly contradict or refine an initial prediction, a strategy that can sharpen decision boundaries in crowded regions of feature space where many compositions produce similar intermediate representations. Together, these mechanisms aim to model the subtle structural and electronic couplings that simpler regressors average away.

The final ingredient is optimization of the network itself. Training deep architectures is a nonconvex problem littered with local minima, and gradient-based methods alone can stall in poor solutions or converge unstably. The authors deploy the Duck Swarm Algorithm, another nature-inspired metaheuristic drawn from the collective foraging behavior of ducks, to tune the CADHRANN parameters. By having the swarm algorithm search the parameter landscape in parallel with the learning process, the framework improves both convergence stability and final predictive performance, according to the study. The result is a three-layer pipeline: fuzzy preprocessing to tame uncertainty, metaheuristic feature selection to compress the descriptor space, and swarm-optimized deep learning to map the refined features onto bandgap values.

The reported performance numbers are striking. An MAE of 0.008 and an RMSE of 0.010, in the units of bandgap energy, imply predictions that deviate from measured values by amounts far smaller than the typical scatter between different experimental measurements of the same material. A MAPE of 0.34 percent means the average relative error is roughly one third of one percent. In practical terms, a screening campaign that once required expensive density functional theory calculations, each costing hours of supercomputer time per material, could potentially be replaced by near-instantaneous model inference across thousands of candidate compositions. Because the framework is described as computationally efficient, the authors position it as a practical tool rather than a laboratory curiosity, suitable for integration into high-throughput virtual screening workflows that propose new perovskite formulations for synthesis and testing.

As with any claim of near-perfect accuracy in machine learning, independent validation on external datasets will be the decisive test, since models trained and evaluated on curated data can sometimes overstate their true generalization. Nevertheless, the study lands in a field with real momentum. Machine learning approaches to perovskite bandgap prediction have proliferated in recent years, spanning ensemble methods, broad learning systems, knowledge distillation under data scarcity and explainable models for ABX3 compounds, all aimed at the same goal: finding stable, efficient, ideally lead-free light absorbers faster than trial-and-error chemistry allows. If the CADHRANN framework’s combination of fuzzy preprocessing, biologically inspired feature selection and swarm-optimized deep attention proves robust, it could become a template for predicting other composition-sensitive properties, from carrier mobility to defect tolerance, and help compress the discovery timeline for the perovskite solar cells and optoelectronic devices that researchers have been chasing for more than a decade.

Subject of Research: Machine learning prediction of bandgap energy at the cation site in organic perovskite materials

Article Title: Prediction of bandgap at the cation site in organic perovskite materials using context axial discrete Hopfield reverse attention neural network

Article References: Hung, N. T. C., & Lee, M. (2026). Prediction of bandgap at the cation site in organic perovskite materials using context axial discrete Hopfield reverse attention neural network. Journal of Materials Science. https://doi.org/10.1007/s10853-026-13304-8

Image Credits: AI Generated

DOI: 10.1007/s10853-026-13304-8

Keywords: perovskites, bandgap prediction, machine learning, deep learning, Hopfield neural network, feature selection, metaheuristic optimization, solar cells, optoelectronics, computational materials science, hybrid organic-inorganic perovskites, materials informatics