Journal Description
Algorithms
Algorithms
is a peer-reviewed, open access journal which provides an advanced forum for studies related to algorithms and their applications, and is published monthly online by MDPI.
- Open Access — free for readers, with article processing charges (APC) paid by authors or their institutions.
- High Visibility: indexed within Scopus, ESCI (Web of Science), Ei Compendex, and other databases.
- Journal Rank: JCR - Q2 (Computer Science, Theory and Methods) / CiteScore - Q1 (Computational Mathematics)
- Rapid Publication: manuscripts are peer-reviewed and a first decision is provided to authors approximately 17.6 days after submission; acceptance to publication is undertaken in 3.9 days (median values for papers published in this journal in the first half of 2026).
- Testimonials: See what our editors and authors say about Algorithms.
- Recognition of Reviewers: reviewers who provide timely, thorough peer-review reports receive vouchers entitling them to a discount on the APC of their next publication in any MDPI journal, in appreciation of the work done.
- Journal Cluster of Artificial Intelligence: AI, AI in Medicine, Algorithms, BDCC, MAKE, MTI, Stats, Virtual Worlds, Computers and Journal of Superintelligence.
Impact Factor:
2.6 (2025);
5-Year Impact Factor:
2.3 (2025)
Latest Articles
A Hybrid ARX and Deep Sequence Learning Architecture for Multivariate Industrial Time-Series Forecasting: An Application in Fluid Catalytic Cracking
Algorithms 2026, 19(9), 727; https://doi.org/10.3390/a19090727 - 27 Aug 2026
Abstract
Multi-parametric industrial time-series forecasting is important for predictive monitoring, soft sensing, and decision support in complex process industries. This study proposes a process-informed hybrid ARX-residual deep sequence architecture for short-horizon multi-output forecasting of fluid catalytic cracking unit (FCCU) product yields. The model combines
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Multi-parametric industrial time-series forecasting is important for predictive monitoring, soft sensing, and decision support in complex process industries. This study proposes a process-informed hybrid ARX-residual deep sequence architecture for short-horizon multi-output forecasting of fluid catalytic cracking unit (FCCU) product yields. The model combines a frozen linear ARX branch with causal temporal convolution, a three-layer GRU, causal self-attention, additive attention pooling, residual gating, and a consistency-regularized multi-output objective. Experiments were performed on an open simulated FCCU benchmark containing 20,160 one-minute observations from seven normal and disturbed operating scenarios. The leakage-controlled pipeline uses scenario-wise chronological splitting, train-only median imputation and standardization, exclusion of fault-timing metadata and direct algebraic target components, and 30 min causal windows for five-minute-ahead forecasting. Across ten prespecified random seeds, the proposed model achieved a historical-test RMSE of 0.022809 0.000116, compared with 0.022751 for ARX-like Ridge. Dependence-aware statistical analyses did not establish a consistent statistical advantage for either model across the evaluated runs. Rolling-origin evaluation likewise showed similar point accuracy, while leave-one-scenario-out evaluation revealed severe extrapolation failure for the unseen pressure-drop scenario. The results support the reproducibility of the proposed architecture and the importance of the ARX-based dynamic structure, but they do not establish the statistical superiority of the full deep residual architecture. Independent industrial data or newly prespecified simulation trajectories are required for confirmatory external validation.
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(This article belongs to the Section Evolutionary Algorithms and Machine Learning)
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Open AccessArticle
A Hybrid BWM-VIKOR and Super-Efficiency SBM Framework for Benchmarking Green Export Performance: Empirical Evidence from the Vietnamese Textile Industry Under ESG Complexity
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Nhut Thi Minh Vo and Van Thanh Tien Nguyen
Algorithms 2026, 19(9), 726; https://doi.org/10.3390/a19090726 - 27 Aug 2026
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The Vietnamese textile and garment industry faces a critical sustainability paradox under the impending Carbon Border Adjustment Mechanism (CBAM). Firms are pressured to maintain high-volume export growth while aggressively minimizing carbon and resource intensity. To empirically resolve this tension, this study develops a
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The Vietnamese textile and garment industry faces a critical sustainability paradox under the impending Carbon Border Adjustment Mechanism (CBAM). Firms are pressured to maintain high-volume export growth while aggressively minimizing carbon and resource intensity. To empirically resolve this tension, this study develops a novel three-phase benchmarking framework that integrates the Best–Worst Method (BWM), VIKOR, and Super-Efficiency Slacks-Based Measure (Super-SBM) under Variable Returns to Scale. Applied to 12 listed enterprises using 2024 fiscal data, the methodology first identifies Energy Intensity as the paramount strategic priority via the BWM. Next, VIKOR mathematically compresses six heterogeneous environmental, social, and governance (ESG) criteria into a single composite index, thereby eliminating standard Data Envelopment Analysis dimensionality constraints. The Phase 3 Super-SBM results reveal profound sector heterogeneity. The macro-scale giant VGT defines the absolute efficiency frontier with an unprecedented score of 18.6729 and zero operational slack. However, the λ reference matrix identifies mid-cap operators such as Tien Son Thanh Hoa and Binh Duong Garment as highly replicable, agile benchmarks for the broader industry. Crucially, the non-radial projection analysis uncovers hidden structural vulnerabilities. The data show that while certain firms possess massive operational buffers, others operate on the absolute edge of the efficiency frontier, leaving them dangerously exposed to impending carbon-taxation shocks. Furthermore, the model identifies critical instances of ESG decoupling in which green investments fail to yield proportional increases in export revenues. These findings suggest that addressing the sustainability paradox requires targeted structural interventions informed by diagnostic benchmarking. Policymakers and corporate executives must integrate open innovation frameworks and systematic problem-solving methodologies to structurally decouple economic output from fossil-fuel energy dependence and outdated labor-arbitrage models.
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Open AccessArticle
Labeled Null Semantics for Incomplete Decision Tables: Certain, Possible, and Conditional Decision Reasoning
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Duc Nghia Vu and Janos Demetrovics
Algorithms 2026, 19(9), 725; https://doi.org/10.3390/a19090725 - 27 Aug 2026
Abstract
Decision tables are widely used for representing and executing decision logic in business rules systems, regulatory compliance, and automated workflows. However, real-world decision tables often contain incomplete condition values. Existing rough set approaches typically treat missing values uniformly and cannot distinguish between occurrences
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Decision tables are widely used for representing and executing decision logic in business rules systems, regulatory compliance, and automated workflows. However, real-world decision tables often contain incomplete condition values. Existing rough set approaches typically treat missing values uniformly and cannot distinguish between occurrences of the same unknown value and occurrences of different unknown values. This paper introduces Labeled Null Decision Tables (LN-DTs), a framework that extends decision table semantics with labeled nulls from incomplete database theory. Missing values are represented by labeled nulls, where identical labels denote the same unknown value and distinct labels may denote different values. We define a possible-world semantics in which each possible world corresponds to a complete valuation of nulls. Based on this semantics, we define certain, possible, and conditional decisions. We develop symbolic algorithms that avoid explicit enumeration of possible worlds, analyze their computational complexity, and establish precise relationships with rough set approximations. We show that LN-DT possible decisions are always contained in the rough upper approximation, that the rough lower approximation is sound for LN-DT certain decisions under completeness and well-formedness, and that labeled null identities and constraints can yield strict precision gains by eliminating tolerant rules that cannot match in any admissible possible world. To provide evidence beyond small illustrative examples, we also include a medium-scale synthetic benchmark suite containing 105 instances with up to 500 rules and 32 labeled nulls. The benchmarks vary the number of rules, the number of labeled nulls, and the constraint type, and report runtime, precision, and verification metrics. Across all benchmark instances, the symbolic evaluator produces known results with no solver timeouts, the LN-DT possible decision set is contained in the rough upper approximation in 100% of cases, and the hybrid evaluator agrees with exact symbolic evaluation in 100% of cases. The average rough upper decision set size is 1.905, while the average LN-DT possible decision set size is 1.019, corresponding to an average upper-bound reduction of approximately 46.5%. These results provide medium-scale evidence that LN-DT is practically feasible and that labeled-null constraints can yield measurable precision gains over tolerance-based rough set approximation.
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Open AccessArticle
A Chirality Calculation Algorithm for Supersecondary Protein Structural Motifs
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Aleksey Olegovich Lutsenko, Alla Eduardovna Sidorova, Natalia Timurovna Levashova and Pavel Andreevich Levashov
Algorithms 2026, 19(9), 724; https://doi.org/10.3390/a19090724 - 27 Aug 2026
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Coiled coils, collagen superhelices, and -sheets belong to the supersecondary level of protein structure. Each of these classes of structural motifs is characterized by a particular chirality. However, methodology for mathematical determination of chirality of specific structures found in real proteins is
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Coiled coils, collagen superhelices, and -sheets belong to the supersecondary level of protein structure. Each of these classes of structural motifs is characterized by a particular chirality. However, methodology for mathematical determination of chirality of specific structures found in real proteins is currently underdeveloped. The aim of this work is to present a universal algorithm for calculating the chirality sign and value for supersecondary structure elements. In this algorithm, the basic calculation principles are the same for all three classes of structures, allowing different motifs to be compared directly. The results for a number of structures from each of the three classes are presented in tables and graphical plots. The calculated chirality signs generally agree with the predicted ones. The results also show that the chirality value is related to the number of amino acid residues in the structure and their distribution among the secondary structure elements. The relationship between amino acid composition and the chirality value is discussed using several examples. The more evident factors that determine the chirality sign and value for a particular structure are a promising subject for future research.
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Open AccessArticle
MiLTL: A Cross-Modal Contradiction Cascade for On-Device Voice Phishing Detection
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Bongjin Jung and Joongho Chang
Algorithms 2026, 19(9), 723; https://doi.org/10.3390/a19090723 (registering DOI) - 27 Aug 2026
Abstract
Voice phishing (vishing) causes financial and psychological harm, yet deployed detectors that scan transcripts for scam vocabulary are more fragile than their benchmark scores suggest: their near-perfect accuracy on standard Korean corpora is memorization, collapsing under scammer paraphrase or language-model rewriting. We construct
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Voice phishing (vishing) causes financial and psychological harm, yet deployed detectors that scan transcripts for scam vocabulary are more fragile than their benchmark scores suggest: their near-perfect accuracy on standard Korean corpora is memorization, collapsing under scammer paraphrase or language-model rewriting. We construct KorMMP, a benchmark keeping real regulator-sourced scam audio and real benign speech but decorrelating transcript from label, and MiLTL, an on-device detector built on affective and neutrosophic channels, including a cross-modal contradiction signal (XM) formulated to weigh lexical warmth against vocal coldness. In the reported evaluation, XM’s measured contribution is confidence banding and escalation routing rather than ranking accuracy. A scoring rule with zero gradient-learned parameters at inference screens every segment, referring ambiguous calls to a small on-device language model; raw audio stays on the device. We measure both stages on a commodity CPU container and smartphone; these budgets cover the detector only and exclude speech recognition, which we expect to dominate a live end-to-end budget. With no training on the hard benchmark, MiLTL achieves an AUROC of 0.965 (recording-level cluster bootstrap 95% CI 0.943–0.984), while every evaluated comparator stays below 0.69: text-only, audio-only, fusion, 7B multimodal. MiLTL scores lower on the saturated corpus, as expected for a detector designed not to rely primarily on lexical shortcuts. KorMMP is a controlled stress test of lexical decorrelation, not a measure of in-the-wild detection; its harmful and benign audio come from different corpora, so the source and label are structurally confounded, and the residual source effects cannot be fully excluded. XM is author-defined, constructed rather than naturally occurring in the synthetic stratum and not yet validated against human perception; this is the principal open limitation of the work. Within that scope, the work provides a reproducible basis for on-device vishing defense and a benchmark for detector robustness under vocabulary shift.
Full article
(This article belongs to the Special Issue Lightweight and AI-Driven Cybersecurity Algorithms for IoT Networks)
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Open AccessArticle
Ensemble and Boosting of Neural Networks and Extreme Gradient Boosting Models for the Modelling of Atmospheric Corrosion of Steel and Zinc
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Zheming Zhang and Jie Zhang
Algorithms 2026, 19(9), 722; https://doi.org/10.3390/a19090722 - 27 Aug 2026
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This paper proposes several ensemble and boosting approaches for combining neural networks and extreme gradient boosting (XGB) models for the modelling of atmospheric corrosion of steel and zinc. The invested modelling approaches include bootstrap aggregation of neural networks, bootstrap aggregation of XGB models,
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This paper proposes several ensemble and boosting approaches for combining neural networks and extreme gradient boosting (XGB) models for the modelling of atmospheric corrosion of steel and zinc. The invested modelling approaches include bootstrap aggregation of neural networks, bootstrap aggregation of XGB models, bootstrap aggregation of neural networks and XGB models, and further model boosting of the state-of-the-art models using neural networks or XGB. It is shown that bootstrap aggregation of XGB models gives the best prediction performance for the steel corrosion data, while the bootstrap aggregation of XGB models with neural network correction of model errors gives the best prediction performance for the zinc corrosion data in terms of performance on the unseen testing data. Sensitivity analysis is carried out for the top performing models. The sensitivity analysis results show that XGB models tend to give non-smooth sensitivity functions due to the stepwise prediction functions from decision tree-based model. Thus, care needs to be taken when interpreting model sensitivity especially when the data set is small. The bootstrap-aggregated neural networks give smooth sensitivity functions and excellent performance on the unseen data under small data sets.
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Open AccessArticle
Parallel Numerical Simulation of 3D Anisotropic Elastic Wave Equations with Sparse Matrix Based on Compact Staggered Finite Difference
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Lin Jiang, Huan Wen, Ming Wang, Changjian Zhang and Yong Wang
Algorithms 2026, 19(9), 721; https://doi.org/10.3390/a19090721 - 27 Aug 2026
Abstract
Numerical simulation of elastic waves in anisotropic media is a fundamental technique for seismic exploration and the characterization of subsurface geological structures. Compared with the conventional finite-difference method, the compact finite-difference method offers higher numerical accuracy and more effective suppression of numerical dispersion,
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Numerical simulation of elastic waves in anisotropic media is a fundamental technique for seismic exploration and the characterization of subsurface geological structures. Compared with the conventional finite-difference method, the compact finite-difference method offers higher numerical accuracy and more effective suppression of numerical dispersion, making it well suited for high-precision elastic-wavefield simulations. However, its reliance on derivative-matrix operations imposes significant computational limitations. As the size of the computational domain increases, the derivative matrices grow rapidly in dimension, leading to substantial memory consumption and computational costs, which hinder the efficient simulation of large-scale three-dimensional (3D) anisotropic elastic-wave propagation. To address this limitation, we develop a high-precision discretization scheme for the 3D anisotropic elastic-wave equations based on compact finite-difference theory, while retaining its favorable characteristics of low numerical dispersion and high computational accuracy. To overcome the high memory requirements and low computational efficiency associated with dense derivative matrices, the derivative matrices are sparsified and implemented using sparse matrix storage and operations to eliminate redundant computations. Furthermore, the algorithm is optimized within a parallel computing framework to enable efficient and high-precision numerical simulation of large-scale 3D anisotropic elastic-wave equations. Numerical experiments on representative anisotropic models demonstrate that the proposed sparsified compact finite-difference algorithm preserves the low numerical dispersion and high wavefield accuracy of the conventional compact finite-difference method while substantially reducing memory consumption and computational costs for large-scale models, with significant parallel acceleration. The proposed method accurately and efficiently captures elastic-wave propagation in complex anisotropic media. This study overcomes the limitations of the compact finite-difference method in large-scale numerical simulations and provides an effective computational approach for high-precision, large-scale seismic-wave forward modeling under complex geological conditions.
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(This article belongs to the Special Issue Modelization and Numerical Methods in Science and Engineering)
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LTFP: Lead-Time-Aware Failure Prediction Based on Service GNNs for AIOps
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Haodong Zou, Yichen Zhao, Xin Chen, Ling Wang, Jinghang Yu and Luokai Jiang
Algorithms 2026, 19(9), 720; https://doi.org/10.3390/a19090720 - 26 Aug 2026
Abstract
Failures in cloud-native systems can disrupt service availability and system reliability, while their early symptoms are often weak and dispersed across metrics, logs, traces, and interdependent services. Existing methods commonly flatten heterogeneous telemetry or model monitoring variables without preserving service identities. We propose
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Failures in cloud-native systems can disrupt service availability and system reliability, while their early symptoms are often weak and dispersed across metrics, logs, traces, and interdependent services. Existing methods commonly flatten heterogeneous telemetry or model monitoring variables without preserving service identities. We propose LTFP, a lead-time-aware failure-prediction framework whose graph nodes represent services. LTFP uses modality-specific temporal encoders and gated fusion to form service states, as well as an edge-weight-aware Graph Attention Network to propagate these states over a sparse hybrid graph constructed from known dependencies and training-fitted correlations. Joint graph-level and node-level heads predict whether a failure will occur within a configured future window and rank likely responsible services. We evaluate LTFP on seven subsets from three representative cloud-native systems. Comparisons with representative source-code baselines are reported at the pipeline level, with each method retaining its original learning objective and input configuration. At the 600 s prediction-window setting, LTFP obtains a macro-average window-level precision, recall, and F1 of 92.0%, 90.4%, and 90.5%, respectively. Together with the localization and ablation results, these findings support the effectiveness of service-centered multimodal modeling under the evaluated protocol.
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(This article belongs to the Special Issue Scalable Algorithms for Large-Scale Graph Neural Networks)
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An Explainable Educational Data Mining Framework for Misconception Detection and Differentiated Instruction
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Mostafa Aboulnour Salem
Algorithms 2026, 19(9), 719; https://doi.org/10.3390/a19090719 - 26 Aug 2026
Abstract
Artificial Intelligence (AI) and Generative Artificial Intelligence (GenAI) increasingly support personalised learning, intelligent assessment, and data-informed educational decision-making. However, persistent misconceptions among gifted students may remain undetected because high achievement can conceal conceptually coherent misunderstandings. This study develops and empirically evaluates a teacher-governed,
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Artificial Intelligence (AI) and Generative Artificial Intelligence (GenAI) increasingly support personalised learning, intelligent assessment, and data-informed educational decision-making. However, persistent misconceptions among gifted students may remain undetected because high achievement can conceal conceptually coherent misunderstandings. This study develops and empirically evaluates a teacher-governed, closed-loop framework integrating Educational Data Mining (EDM), Learning Analytics (LA), ensemble machine learning, Explainable Artificial Intelligence (XAI), GenAI, and differentiated instruction. Educational data from 255 gifted secondary-school learners were transformed into learner profiles and analysed using Random Forest, XGBoost, Boost, Support Vector Machine, Artificial Neural Network, and Logistic Regression, which were then combined via validation-derived weighted probabilistic ensembling. The validation-weight ensemble achieved 96.88% accuracy, 92.00% precision, 100% recall, an F1-score of 95.83%, ROC-AUC of 0.9979, and PR-AUC of 0.9963, outperforming the individual classifiers in overall classification performance. SHAP provided learner-specific explanations, with average response time emerging most frequently as the leading explanatory feature. These explanations informed GenAI-supported personalised interventions, which teachers validated before differentiated delivery. Post-intervention evidence was subsequently incorporated into learner reassessment and profile updating. The principal contribution lies in the operational integration of learner profiling, weight prediction, explainability, evidence-conditioned instructional generation, professional validation, and reassessment within a continuous educational cycle. The findings provide initial empirical evidence for the framework’s computational feasibility and interpretability while supporting further external and longitudinal validation across educational contexts and learner populations.
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(This article belongs to the Special Issue Artificial Intelligence Algorithms and Generative AI in Education (2nd Edition))
Open AccessArticle
A Hierarchical FFT–ANFIS Algorithm for Detection, Localization, and Severity Assessment of Inter-Turn Short-Circuit Faults in Doubly Fed Induction Generators
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Mimouna Abid, Souad Laribi, M’Hamed Larbi, Habib Benbouhenni, Riyadh Bouddou and Nicu Bizon
Algorithms 2026, 19(9), 718; https://doi.org/10.3390/a19090718 - 26 Aug 2026
Abstract
Early and reliable diagnosis of inter-turn short-circuit (ITSC) faults is critical to maintaining the reliability, availability, and safe operation of doubly fed induction generators (DFIGs) used in wind energy conversion systems (WECSs). Incipient winding faults are particularly challenging to identify because their electrical
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Early and reliable diagnosis of inter-turn short-circuit (ITSC) faults is critical to maintaining the reliability, availability, and safe operation of doubly fed induction generators (DFIGs) used in wind energy conversion systems (WECSs). Incipient winding faults are particularly challenging to identify because their electrical signatures can be masked by the inherent spectral complexity of DFIG operation and variations in wind and operating conditions. This study proposes a hybrid Fast Fourier Transform-Adaptive Neuro-Fuzzy Inference System (FFT–ANFIS) diagnostic framework for the detection, localization, and severity assessment of ITSC faults in both stator and rotor windings. The proposed approach employs the FFT method to extract fault-sensitive harmonic components from stator-current signals, which are subsequently used as diagnostic features by an Adaptive Neuro-Fuzzy Inference System (ANFIS). By integrating spectral feature extraction with nonlinear neuro-fuzzy classification, the proposed framework provides an efficient and interpretable mechanism for distinguishing healthy and faulty operating conditions and assessing fault severity. The methodology is evaluated using MATLAB/Simulink simulations under healthy and multiple ITSC fault conditions with different fault locations and severity levels. The results demonstrate 100% classification accuracy for stator faults, rotor faults, and multiple short-circuit (MSC) fault conditions, together with near-zero prediction error in fault-severity estimation. These results confirm the high discriminative capability of the selected FFT-based spectral features and the effectiveness of ANFIS in establishing the nonlinear relationship between fault signatures and fault conditions. In addition, the proposed framework maintains low computational complexity and is therefore suitable for real-time condition-monitoring applications. Compared with existing diagnostic approaches, the proposed method provides a unified framework for multi-fault diagnosis while combining high diagnostic accuracy, computational efficiency, and interpretable decision-making. The proposed FFT–ANFIS framework consequently offers a practical approach for early fault detection and condition-based maintenance of DFIG-based wind turbines, with the potential to reduce unplanned downtime, maintenance requirements, and energy-production losses.
Full article
(This article belongs to the Special Issue AI-Driven Control and Optimization in Power Electronics)
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Enhancing Inner Linearizations Assisted by Gradient-Based Expansion Point Optimization
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Víctor Reyes, Ignacio Araya, Nicolas Hidalgo and Felipe Lazo
Algorithms 2026, 19(9), 717; https://doi.org/10.3390/a19090717 - 26 Aug 2026
Abstract
Nonlinear Continuous global Optimization Problems (NCOPs) are well-known problems that arise in many applications, from engineering to robotics. The Branch & Bound method is a widely used approach for solving NCOPs to global optimality, often interleaving techniques like bisection and filtering. A key
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Nonlinear Continuous global Optimization Problems (NCOPs) are well-known problems that arise in many applications, from engineering to robotics. The Branch & Bound method is a widely used approach for solving NCOPs to global optimality, often interleaving techniques like bisection and filtering. A key aspect of this approach is identifying feasible solutions early in the search process, which enables effective pruning of the search tree and avoids unnecessary computational effort. Inner linear relaxation techniques, such as the AbsTaylor strategy, have proven effective for identifying feasible regions; however, they heavily rely on a heuristically chosen expansion point (often the box midpoint), which directly impacts solution quality and relaxation success. In this work, we propose a novel gradient-based strategy to dynamically optimize the selection of this expansion point. By employing Gradient Descent to minimize a Mean Squared Error (MSE) objective formulated exclusively over the active constraints, we systematically guide the expansion point safely away from boundaries and into a strictly feasible interior region. To manage computational overhead, we evaluate restricted iteration budgets alongside algorithmic variants, specifically introducing a point inheritance strategy for warm-starting and comparing Batch versus Incremental gradient updates. Experimental results on a well-known benchmark set demonstrate that this gradient-based approach minimizes the probability of relaxation failure, significantly enhancing pruning effectiveness and overall solver efficiency compared to the original strategy.
Full article
(This article belongs to the Section Algorithms for Multidisciplinary Applications)
Open AccessArticle
Feature Attribution Dynamics Under Imbalanced Learning Algorithms: An Explainable Machine Learning Framework for Burnout Risk Prediction
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Tanishq Patel, Gagan Sharma, Pradeepta Kumar Sarangi, Merry Saxena, Ashwin Dobariya, Valeriu Manuel Ionescu and Nicu Bizon
Algorithms 2026, 19(9), 716; https://doi.org/10.3390/a19090716 - 26 Aug 2026
Abstract
Imbalance in classes is one of the critical issues in machine learning practice, especially in the context of healthcare and organizational applications, where the class of interest, representing subjects at high risk of some adverse event, holds significant clinical and organizational value. In
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Imbalance in classes is one of the critical issues in machine learning practice, especially in the context of healthcare and organizational applications, where the class of interest, representing subjects at high risk of some adverse event, holds significant clinical and organizational value. In this paper, a comparative machine learning framework is presented to assess the influence of Synthetic Minority Over-sampling Technique (SMOTE) and stratified validation strategies on burnout risk prediction under extreme class imbalance scenarios. There was an apparent class imbalance ratio of 7.16:1 between the two classes of Not at Risk and At Risk (Moderate or High). There were sixteen possible experimental setups that were used, where each algorithm was evaluated using two approaches for addressing the class imbalance problem, with and without using SMOTE, along with hold-out and 5-Fold Stratified Cross-Validation. Based on the results, SMOTE provided a significant improvement in the performance of minority class detection in all the models evaluated without having any negative impact on the global model accuracy. Additionally, the application of SMOTE along with Stratified Cross-Validation was found to be the most effective in terms of achieving balance in classification performance. Overall, the use of XGBoost along with SMOTE and 5-Fold Stratified Cross-Validation provided the best results in this respect, with the highest minority class F1-Score and ROC-AUC performance. In particular, the SHAP-based analysis showed that SMOTE contributed to redistributing the attributions among a wide set of clinically relevant features such as stress level, hours of work overtime, and anxiety. Overall, the use of SMOTE and Stratified Cross-Validation was proven to significantly improve the performance of burnout risk classification in imbalanced data samples.
Full article
(This article belongs to the Special Issue Machine Learning for Advanced Healthcare: Bridging Innovation and Clinical Implementation)
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Intelligent Method for COVID-19 Diagnosis: Construction and Comparative Analysis of ResKAN18
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Dan Li, Zan Yang, Yanan Li and Wei Nai
Algorithms 2026, 19(9), 715; https://doi.org/10.3390/a19090715 - 26 Aug 2026
Abstract
In response to the challenge of balancing accuracy and generalization in medical image classification using convolutional neural networks (CNNs), this paper proposes ResKAN18, a hybrid structure that embeds the learnable spline function of the Kolmogorov–Arnold network (KAN) into the ResNet18 classification head for
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In response to the challenge of balancing accuracy and generalization in medical image classification using convolutional neural networks (CNNs), this paper proposes ResKAN18, a hybrid structure that embeds the learnable spline function of the Kolmogorov–Arnold network (KAN) into the ResNet18 classification head for intelligent diagnosis of COVID-19 in chest X-ray images. ResKAN18 includes three variants: ResKAN18—Large (four layers of KAN, hidden-layer dimensions [256, 128, 64]), ResKAN18—Standard (four layers of KAN, hidden-layer dimensions [128, 64, 32]), and ResKAN18—Simple (three layers of KAN, hidden-layer dimensions [64, 32]), which can achieve a flexible balance between accuracy and efficiency with different depths of KAN. A systematic comparison has been conducted between four classic CNN baselines including ResNet18, VGG16, DenseNet121, ShuffleNetV2, and three ResKAN18 variants on a benchmark dataset containing 3880 chest X-rays (COVID-19, normal, viral pneumonia). The results have shown that ResKAN18—Large can achieve an accuracy of 98.80% on the independent test set, which is 1.21% higher than ResNet18 and 0.69% higher than DenseNet121—its parameter count is 13.97M, inference delay is 8.25 ms/image, and training–validation accuracy difference is only 1.50%. The accuracy and performance stability of the dataset under random partitioning conditions are superior to the other two variants and all classic CNN baselines. All ResKAN18 variants have achieved zero missed diagnoses for COVID-19, while ResNet18 has shown missed diagnoses (0.9944). Taking into account the trade-off between accuracy, generalization, and inference efficiency, ResKAN1—Large is recommended as the default configuration, while for edge deployment scenarios with severely limited resources, ResKAN18—Simple can provide a cost-effective alternative with an extremely low latency of 2.50 ms/image and only 3.1% parameter increment compared to ResNet18.
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(This article belongs to the Section Algorithms and Mathematical Models for Computer-Assisted Diagnostic Systems)
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Automatic Modulation Recognition Based on Adaptive Wavelet Enhancement and Dynamic Graph Construction
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Shunyong Zhou, Yingying Liu, Yizhong Li, Zhaoxu Che and Lehui Xie
Algorithms 2026, 19(9), 714; https://doi.org/10.3390/a19090714 - 26 Aug 2026
Abstract
Automatic modulation recognition (AMR) is essential for cognitive radio and intelligent wireless communication, yet its performance degrades markedly under low signal-to-noise ratio (SNR) conditions because weak local structures are corrupted and class boundaries become less separable. To address this problem, we propose ADGNet,
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Automatic modulation recognition (AMR) is essential for cognitive radio and intelligent wireless communication, yet its performance degrades markedly under low signal-to-noise ratio (SNR) conditions because weak local structures are corrupted and class boundaries become less separable. To address this problem, we propose ADGNet, an automatic modulation recognition network based on adaptive wavelet enhancement and dynamic graph construction. ADGNet adopts a dual-branch architecture in which the main branch extracts time-domain amplitude–phase features from raw in-phase/quadrature sequences, while the auxiliary branch combines short-time Fourier transform features with adaptive wavelet features to capture complementary frequency–energy distributions and multi-scale transient details. A dual-domain adaptive encoder then recalibrates and fuses the two branches, suppressing redundant and noise-contaminated responses. In addition, a G2 dynamic topology module constructs sample-adaptive top-k adjacency matrices from node features and fuses them with the original graph structure to improve temporal relation modeling. Experiments on RadioML2016.10a and RadioML2016.10b show average accuracies of 64.23% and 69.69%, respectively. On RadioML2016.10b, ADGNet achieves 63.48% average accuracy from −12 dB to 0 dB, compared with 59.51% for the baseline. With approximately 0.13 million parameters, ADGNet provides a favorable balance between low-SNR robustness and model complexity.
Full article
(This article belongs to the Special Issue Signal Processing, Intelligent Analysis, and Optimization for Communication and Electronic Systems)
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Hierarchical Modeling of AI-Supported Mathematical Problem Solving, Student Diagnostic Reasoning, and Mathematics Achievement
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Ines Bula Bunjaku, Edmond Muhaxheri and Edin Bula
Algorithms 2026, 19(9), 713; https://doi.org/10.3390/a19090713 - 25 Aug 2026
Abstract
This study develops and empirically evaluates a multilevel analytical framework linking AI-generated mathematical reasoning, students’ diagnostic reasoning, and mathematics achievement in AI-supported mathematical problem solving. A classroom intervention with 76 undergraduate Calculus A students generated 380 repeated student–problem observations across five mathematical tasks
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This study develops and empirically evaluates a multilevel analytical framework linking AI-generated mathematical reasoning, students’ diagnostic reasoning, and mathematics achievement in AI-supported mathematical problem solving. A classroom intervention with 76 undergraduate Calculus A students generated 380 repeated student–problem observations across five mathematical tasks and three instructional formulations. Students evaluated AI-generated solutions for final-answer correctness, methodological correctness, and procedural completeness, identified mathematical errors, and proposed corrections before completing an individual posttest. Hierarchical mixed-effects models and student-level achievement analyses were used to examine successive stages of the learning process. Instructional formulation was not significantly associated with the quality of AI-generated mathematical reasoning. Final-answer correctness, methodological correctness, and procedural completeness showed substantial task-specific variation. Instructional formulation was significantly associated with students’ error detection, with higher detection performance under Instruction Types B and C than under Type A, while AI-generated response quality remained comparable across instructional formulations. Baseline mathematical proficiency was the strongest predictor of posttest performance. Students’ Mean Error-Detection Event Rate was positively associated with posttest achievement. No robust overall independent association between instructional formulation and posttest achievement was identified after baseline adjustment. Students’ diagnostic engagement with AI-generated mathematical reasoning was associated with subsequent mathematics achievement, supporting the analysis of diagnostic reasoning as a distinct component of AI-supported mathematics learning.
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(This article belongs to the Special Issue Artificial Intelligence in Education: Innovations and Implications)
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Open AccessArticle
Critical Evaluation of Weighted Similarity Measures and Algorithmic Solutions in Fuzzy Pattern Recognition
by
Yung-Ning Cheng, Ching-Wen Yeh and Kuo-Chen Hung
Algorithms 2026, 19(9), 712; https://doi.org/10.3390/a19090712 - 24 Aug 2026
Abstract
This study re-examines several published weighted similarity measures for intuitionistic fuzzy pattern recognition problems. This study constructs four counterexamples, each involving two candidate patterns and one sample, to test whether the measure can consistently produce a unique classification decision. The examples show that
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This study re-examines several published weighted similarity measures for intuitionistic fuzzy pattern recognition problems. This study constructs four counterexamples, each involving two candidate patterns and one sample, to test whether the measure can consistently produce a unique classification decision. The examples show that distinct patterns can receive identical similarity scores under the published formulation; therefore, the measure does not always resolve class assignment in the cases considered here. We then analyze why weighting alone does not necessarily eliminate this difficulty and discuss multi-measure algorithmic alternatives for selected discrete cases. The contribution of this study is, therefore, a counterexample-based critique of the discriminative limitations of weighted similarity measures.
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(This article belongs to the Section Algorithms for Multidisciplinary Applications)
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Open AccessSystematic Review
Intelligent Algorithms in Inventory Management: A Systematic Literature Review
by
Daniel Mauricio Beltrán Del Hierro, Denysse Marisol Castillo Martínez and Argenis Lissander Heredia Campaña
Algorithms 2026, 19(9), 711; https://doi.org/10.3390/a19090711 - 24 Aug 2026
Abstract
In recent years, interest in artificial intelligence has grown significantly, particularly in the development of advanced computational models for supply chain decision-making. Inventory management is one of the areas in which intelligent algorithms can support demand forecasting, replenishment, stock control, and operational optimization
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In recent years, interest in artificial intelligence has grown significantly, particularly in the development of advanced computational models for supply chain decision-making. Inventory management is one of the areas in which intelligent algorithms can support demand forecasting, replenishment, stock control, and operational optimization under uncertainty. This study presents an updated systematic literature review of intelligent algorithms applied to inventory management. The review followed PRISMA 2020 guidelines and combined database searches in Scopus, ScienceDirect, Web of Science, IEEE Xplore, SpringerLink, Taylor & Francis, and complementary manual searching. The original search covering January 2020 to December 2024 was updated in July 2026 to include studies published or available online up to June 2026. After applying strict eligibility criteria, 37 primary studies with quantitative evidence were included. The updated corpus confirms the predominance of deep learning, reinforcement learning, and hybrid intelligent models, while also showing the recent emergence of Transformer-based, graph neural network, multi-agent reinforcement learning, and prescriptive analytics approaches. The most frequent application areas were inventory control, inventory optimization, replenishment decision-making, and demand forecasting. Reported improvements were mainly associated with cost efficiency, service level, stockout reduction, and system performance; however, the magnitude of improvement varied across algorithms, data sources, sectors, and simulation or real-world settings. Overall, intelligent algorithms represent a relevant tool for improving inventory management, but their adoption requires careful validation, transparent reporting, and alignment with the operational context.
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(This article belongs to the Section Algorithms for Multidisciplinary Applications)
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Open AccessArticle
A Hybrid Particle Swarm Optimization and Differential Evolution Algorithm with Adaptive Population and Dynamic Parameter Allocation
by
Yaopei Wang, Yufeng Wang and Ke Liu
Algorithms 2026, 19(9), 710; https://doi.org/10.3390/a19090710 - 24 Aug 2026
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Traditional particle swarm optimization (PSO) easily falls into premature convergence, while differential evolution (DE) is highly sensitive to fixed control parameters. Existing PSO-DE hybrid frameworks suffer from static population sizes and insufficient cross-population information exchange. This paper proposes PSO-DE-ADP, a hybrid optimizer with
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Traditional particle swarm optimization (PSO) easily falls into premature convergence, while differential evolution (DE) is highly sensitive to fixed control parameters. Existing PSO-DE hybrid frameworks suffer from static population sizes and insufficient cross-population information exchange. This paper proposes PSO-DE-ADP, a hybrid optimizer with sinusoidal adaptive parameters, elite-guided mutation, ring neighborhood-weighted PSO and fitness-driven dynamic dual-population allocation. Four complementary mechanisms are integrated: (i) sine-wave perturbation superimposed on linear decay adaptively adjusts PSO inertia weight, acceleration factors and DE scaling/crossover coefficients to balance search stages; (ii) global elite individuals are embedded into DE mutation to reduce blind random search; (iii) ring topology with weighted learning realizes bidirectional information interaction between PSO and DE subpopulations; (iv) the proportion of PSO/DE individuals is dynamically adjusted according to elite ratio to allocate computing resources. Experiments adopt the CEC2017 30-dimensional benchmark with 30 test functions covering unimodal, multimodal, hybrid and composite landscapes. Compared with 8 state-of-the-art metaheuristics, PSO-DE-ADP achieves the lowest Friedman rank (1.08 vs. 2.23–4.90 for PSO variants; 1.53 vs. 2.07–5.00 for non-PSO algorithms). Ablation tests prove each component significantly boosts accuracy; The algorithm only costs 0.172 s average runtime, superior to all competitors. Statistical Wilcoxon and Friedman tests verify its significant superiority. Future work extends this method to multi-objective, constrained and real engineering optimization tasks.
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Open AccessArticle
Ultrasonic Lamb Wave Denoising Algorithm for Aluminum Plates Based on ICPO-VMD Combined Improvement of Wavelet Threshold
by
Haoyuan Chen, Songsong Li, Qiaozhen Zhou, Shidong Li, Meide Liu and Xiaoming Chen
Algorithms 2026, 19(9), 709; https://doi.org/10.3390/a19090709 - 23 Aug 2026
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In ultrasonic Lamb wave non-destructive testing of aluminum plates, Lamb wave signals are susceptible to industrial interference, which may obscure useful information. To address this issue, this paper developed a signal denoising method combining Improved Crested Porcupine Optimizer (ICPO) and Variational Mode Decomposition
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In ultrasonic Lamb wave non-destructive testing of aluminum plates, Lamb wave signals are susceptible to industrial interference, which may obscure useful information. To address this issue, this paper developed a signal denoising method combining Improved Crested Porcupine Optimizer (ICPO) and Variational Mode Decomposition (VMD) with an improved wavelet threshold. The ICPO algorithm optimizes VMD parameters using fuzzy entropy as the fitness function. The decomposed modes are categorized into signal-dominant, mixed, and noise-dominant modes by the correlation coefficient method. The mixed modes are denoised using wavelet thresholding, and the final signal is reconstructed from the signal-dominant modes and the denoised mixed modes. Compared with VMD, direct wavelet thresholding, and ICPO-VMD combined with soft or hard thresholding, the proposed method outperforms the compared methods in both quantitative metrics and waveform preservation. These results confirm the effectiveness of the proposed method for aluminum plate Lamb wave denoising under the tested conditions.
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Open AccessArticle
Computational Modeling and Intelligent Simulation of PEMFC Parameter Identification: Design and Technical Validation of a Virtual Teaching Experiment Using an Enhanced LRSAO Algorithm
by
Chu Zhang, Tongrui Feng, Qianlong Liu, Tian Peng and Huanyu Zhao
Algorithms 2026, 19(9), 708; https://doi.org/10.3390/a19090708 - 23 Aug 2026
Abstract
Proton exchange membrane fuel cell (PEMFC) parameter identification is a nonlinear computational modeling problem involving strongly coupled electrochemical parameters and partially unobservable polarization processes. Its experimental teaching is further constrained by the cost of fuel cell stacks and the safety requirements associated with
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Proton exchange membrane fuel cell (PEMFC) parameter identification is a nonlinear computational modeling problem involving strongly coupled electrochemical parameters and partially unobservable polarization processes. Its experimental teaching is further constrained by the cost of fuel cell stacks and the safety requirements associated with hydrogen operation. To address these challenges, this study develops a computational modeling and intelligent simulation framework for a virtual teaching experiment on PEMFC parameter identification. A semi-empirical output-voltage model is established, and the sum of squared errors (SSE) between measured and simulated voltages is formulated as the optimization objective. An enhanced Logistic–Tent reverse snow ablation optimizer (LRSAO), termed RLFDB-LRSAO, is introduced by integrating roulette-wheel-selection-enhanced fitness-distance balance and Lévy flight perturbation. Its methodological novelty lies in the stage-wise coordination of population-diversity enhancement, candidate-selection guidance, and search perturbation within the LRSAO framework, rather than in the individual component strategies themselves. The framework organizes the identification process into mechanism interpretation, model construction, algorithm implementation, parameter configuration, visualization, comparative evaluation, and reflective analysis. Case studies using the NedStack PS6 and Modular SR-12 stacks yield best SSE values of 1.2173340 and 6.13503904, respectively. A small-scale qualitative teaching evaluation involving 20 postgraduate students indicated that the framework supported programming practice, strengthened conceptual understanding of PEMFC parameter identification and intelligent optimization, and provided useful support for research-oriented skills such as engineering problem analysis, technical writing, and innovation-oriented project development. These results provide preliminary evidence of technical and educational feasibility while supporting a cautious, problem-dependent interpretation of the optimizer.
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(This article belongs to the Special Issue Computational Modeling and Intelligent Simulation of Next-Generation Energy Systems)
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