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Algorithms

Algorithms is a peer-reviewed, open access journal which provides an advanced forum for studies related to algorithms and their applications. Algorithms is published monthly online by MDPI. The European Society for Fuzzy Logic and Technology (EUSFLAT) is affiliated with Algorithms and their members receive discounts on the article processing charges.

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 (Numerical Analysis)
Rapid Publication: manuscripts are peer-reviewed and a first decision is provided to authors approximately 17.8 days after submission; acceptance to publication is undertaken in 3.6 days (median values for papers published in this journal in the first half of 2025).
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.

Impact Factor: 2.1 (2024); 5-Year Impact Factor: 2.0 (2024)

Imprint Information Journal Flyer Open Access ISSN: 1999-4893

Latest Articles

21 pages, 1814 KB

Open AccessArticle

Data-Driven Prior Construction in Hilbert Spaces for Bayesian Optimization

by Carol Santos Almonte, Oscar Sanchez Jimenez, Eduardo Souza de Cursi and Emmanuel Pagnacco

Algorithms 2025, 18(9), 557; https://doi.org/10.3390/a18090557 - 3 Sep 2025

We propose a variant of Bayesian optimization in which probability distributions are constructed using uncertainty quantification (UQ) techniques. In this context, UQ techniques rely on a Hilbert basis expansion to infer probability distributions from limited experimental data. These distributions act as prior knowledge [...] Read more.

We propose a variant of Bayesian optimization in which probability distributions are constructed using uncertainty quantification (UQ) techniques. In this context, UQ techniques rely on a Hilbert basis expansion to infer probability distributions from limited experimental data. These distributions act as prior knowledge of the search space and are incorporated into the acquisition function to guide the selection of enrichment points more effectively. Several variants of the method are examined, depending on the distribution type (normal, log-normal, etc.), and benchmarked against traditional Bayesian optimization on test functions. The results show competitive performance, with selective improvements depending on the problem structure, and faster convergence in specific cases. As a practical application, we address a structural shape optimization problem. The initial geometry is an L-shaped plate, where the goal is to minimize the volume under a horizontal displacement constraint expressed as a penalty. Our approach first identifies a promising region while efficiently training the surrogate model. A subsequent gradient-based optimization step then refines the design using the trained surrogate, achieving a volume reduction of more than

30 %

while satisfying the displacement constraint, without requiring any additional evaluations of the objective function. Full article

(This article belongs to the Special Issue Mathematical Modelling in Engineering and Human Behaviour (3rd Edition))

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36 pages, 576 KB

Open AccessReview

A Review of Explainable Artificial Intelligence from the Perspectives of Challenges and Opportunities

by Sami Kabir, Mohammad Shahadat Hossain and Karl Andersson

Algorithms 2025, 18(9), 556; https://doi.org/10.3390/a18090556 - 3 Sep 2025

The widespread adoption of Artificial Intelligence (AI) in critical domains, such as healthcare, finance, law, and autonomous systems, has brought unprecedented societal benefits. Its black-box (sub-symbolic) nature allows AI to compute prediction without explaining the rationale to the end user, resulting in lack [...] Read more.

The widespread adoption of Artificial Intelligence (AI) in critical domains, such as healthcare, finance, law, and autonomous systems, has brought unprecedented societal benefits. Its black-box (sub-symbolic) nature allows AI to compute prediction without explaining the rationale to the end user, resulting in lack of transparency between human and machine. Concerns are growing over the opacity of such complex AI models, particularly deep learning architectures. To address this concern, explainability is of paramount importance, which has triggered the emergence of Explainable Artificial Intelligence (XAI) as a vital research area. XAI is aimed at enhancing transparency, trust, and accountability of AI models. This survey presents a comprehensive overview of XAI from the dual perspectives of challenges and opportunities. We analyze the foundational concepts, definitions, terminologies, and taxonomy of XAI methods. We then review several application domains of XAI. Special attention is given to various challenges of XAI, such as no universal definition, trade-off between accuracy and interpretability, and lack of standardized evaluation metrics. We conclude by outlining the future research directions of human-centric design, interactive explanation, and standardized evaluation frameworks. This survey serves as a resource for researchers, practitioners, and policymakers to navigate the evolving landscape of interpretable and responsible AI. Full article

(This article belongs to the Section Algorithms for Multidisciplinary Applications)

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24 pages, 3458 KB

Open AccessArticle

Output Voltage Control of a Synchronous Buck DC/DC Converter Using Artificial Neural Networks

by Juraj Šimko, Michal Praženica, Roman Koňarik, Slavomír Kaščák and Peter Klčo

Algorithms 2025, 18(9), 555; https://doi.org/10.3390/a18090555 - 2 Sep 2025

This article presents a neural network-based control method for maintaining the required output voltage of a synchronous buck converter. The goal was to replace a traditional PID controller with a neural network that calculates the duty cycle based on real-time data. Several versions [...] Read more.

This article presents a neural network-based control method for maintaining the required output voltage of a synchronous buck converter. The goal was to replace a traditional PID controller with a neural network that calculates the duty cycle based on real-time data. Several versions of the neural network were tested. The final version, which included the input voltage, reference, and output current as inputs and compensated for dead time, was successfully validated on real hardware. It was able to respond to changes in load and input voltage within a limited operating range. Full article

(This article belongs to the Collection Feature Papers in Evolutionary Algorithms and Machine Learning)

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33 pages, 1985 KB

Open AccessArticle

Future Skills in the GenAI Era: A Labor Market Classification System Using Kolmogorov–Arnold Networks and Explainable AI

by Dimitrios Christos Kavargyris, Konstantinos Georgiou, Eleanna Papaioannou, Theodoros Moysiadis, Nikolaos Mittas and Lefteris Angelis

Algorithms 2025, 18(9), 554; https://doi.org/10.3390/a18090554 - 2 Sep 2025

Generative Artificial Intelligence (GenAI) is widely recognized for its profound impact on labor market demand, supply, and skill dynamics. However, due to its transformative nature, GenAI increasingly overlaps with traditional AI roles, blurring boundaries and intensifying the need to reassess workforce competencies. To [...] Read more.

Generative Artificial Intelligence (GenAI) is widely recognized for its profound impact on labor market demand, supply, and skill dynamics. However, due to its transformative nature, GenAI increasingly overlaps with traditional AI roles, blurring boundaries and intensifying the need to reassess workforce competencies. To address this challenge, this paper introduces KANVAS (Kolmogorov–Arnold Network Versatile Algorithmic Solution)—a framework based on Kolmogorov–Arnold Networks (KANs), which utilize B-spline-based, compact, and interpretable neural units—to distinguish between traditional AI roles and emerging GenAI-related positions. The aim of the study is to develop a reliable and interpretable labor market classification system that differentiates these roles using explainable machine learning. Unlike prior studies that emphasize predictive performance, our work is the first to employ KANs as an explanatory tool for labor classification, to reveal how GenAI-related and European Skills, Competences, Qualifications, and Occupations (ESCO)-aligned skills differentially contribute to distinguishing modern from traditional AI job roles. Using raw job vacancy data from two labor market platforms, KANVAS implements a hybrid pipeline combining a state-of-the-art Large Language Model (LLM) with Explainable AI (XAI) techniques, including Shapley Additive Explanations (SHAP), to enhance model transparency. The framework achieves approximately 80% classification consistency between traditional and GenAI-aligned roles, while also identifying the most influential skills contributing to each category. Our findings indicate that GenAI positions prioritize competencies such as prompt engineering and LLM integration, whereas traditional roles emphasize statistical modeling and legacy toolkits. By surfacing these distinctions, the framework offers actionable insights for curriculum design, targeted reskilling programs, and workforce policy development. Overall, KANVAS contributes a novel, interpretable approach to understanding how GenAI reshapes job roles and skill requirements in a rapidly evolving labor market. Finally, the open-source implementation of KANVAS is flexible and well-suited for HR managers and relevant stakeholders. Full article

(This article belongs to the Collection Feature Papers on Artificial Intelligence Algorithms and Their Applications)

17 pages, 569 KB

Open AccessArticle

AI-Driven Optimization of Functional Feature Placement in Automotive CAD

by Ardian Kelmendi and George Pappas

Algorithms 2025, 18(9), 553; https://doi.org/10.3390/a18090553 - 2 Sep 2025

The automotive industry increasingly relies on 3D modeling technologies to design and manufacture vehicle components with high precision. One critical challenge is optimizing the placement of latches that secure the dashboard side paneling, as these placements vary between models and must maintain minimal [...] Read more.

The automotive industry increasingly relies on 3D modeling technologies to design and manufacture vehicle components with high precision. One critical challenge is optimizing the placement of latches that secure the dashboard side paneling, as these placements vary between models and must maintain minimal tolerance for movement to ensure durability. While generative artificial intelligence (AI) has advanced rapidly in generating text, images, and video, its application to creating accurate 3D CAD models remains limited. This paper proposes a novel framework that integrates a PointNet deep learning model with Python-based CAD automation to predict optimal clip placements and surface thickness for dashboard side panels. Unlike prior studies that focus on general-purpose CAD generation, this work specifically targets automotive interior components and demonstrates a practical method for automating part design. The approach involves generating placement data—potentially via generative AI—and importing it into the CAD environment to produce fully parameterized 3D models. Experimental results show that the prototype achieved a 75% success rate across six of eight test surfaces, indicating strong potential despite the limited sample size. This research highlights a clear pathway for applying generative AI to part design automation in the automotive sector and offers a foundation for scaling to broader design applications. Full article

(This article belongs to the Section Evolutionary Algorithms and Machine Learning)

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22 pages, 8021 KB

Open AccessArticle

Multi-Task Semi-Supervised Approach for Counting Cones in Adaptive Optics Images

by Vidya Bommanapally, Amir Akhavanrezayat, Parvathi Chundi, Quan Dong Nguyen and Mahadevan Subramaniam

Algorithms 2025, 18(9), 552; https://doi.org/10.3390/a18090552 - 2 Sep 2025

Counting and density estimation of cone cells using adaptive optics (AO) imaging plays an important role in the clinical management of retinal diseases. A novel deep learning approach for the cone counting task with minimal manual labeling of cone cells in AO images [...] Read more.

Counting and density estimation of cone cells using adaptive optics (AO) imaging plays an important role in the clinical management of retinal diseases. A novel deep learning approach for the cone counting task with minimal manual labeling of cone cells in AO images is described in this paper. We propose a hybrid multi-task semi-supervised learning (MTSSL) framework that simultaneously trains on unlabeled and labeled data. On the unlabeled images, the model learns structural and relational features by employing two self-supervised pretext tasks—image inpainting (IP) and learning-to-rank (L2R). At the same time, it leverages a small set of labeled examples to supervise a density estimation head for cone counting. By jointly minimizing the image reconstruction loss, the ranking loss, and the supervised density-map loss, our approach harnesses the rich information in unlabeled data to learn feature representations and directly incorporates ground-truth annotations to guide accurate density prediction and counts. Experiments were conducted on a dataset of AO images of 120 subjects captured using a device with a retinal camera (rtx1) with a wide field-of-view. MTSSL gains strengths from hybrid self-supervised pretext tasks of generative and predictive pretraining that aid in learning global and local context required for counting cones. The results show that the proposed MTSSL approach significantly outperforms the individual self-supervised pipelines with an RMSE score improved by a factor of 2 for cone counting. Full article

(This article belongs to the Special Issue Advanced Machine Learning Algorithms for Image Processing)

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19 pages, 17084 KB

Open AccessArticle

SPADE: Superpixel Adjacency Driven Embedding for Three-Class Melanoma Segmentation

by Pablo Ordóñez, Ying Xie, Xinyue Zhang, Chloe Yixin Xie, Santiago Acosta and Issac Guitierrez

Algorithms 2025, 18(9), 551; https://doi.org/10.3390/a18090551 - 2 Sep 2025

The accurate segmentation of pigmented skin lesions is a critical prerequisite for reliable melanoma detection, yet approximately 30% of lesions exhibit fuzzy or poorly defined borders. This ambiguity makes the definition of a single contour unreliable and limits the effectiveness of computer-assisted diagnosis [...] Read more.

The accurate segmentation of pigmented skin lesions is a critical prerequisite for reliable melanoma detection, yet approximately 30% of lesions exhibit fuzzy or poorly defined borders. This ambiguity makes the definition of a single contour unreliable and limits the effectiveness of computer-assisted diagnosis (CAD) systems. While clinical assessment based on the ABCDE criteria (asymmetry, border, color, diameter, and evolution), dermoscopic imaging, and scoring systems remains the standard, these methods are inherently subjective and vary with clinician experience. We address this challenge by reframing segmentation into three distinct regions: background, border, and lesion core. These regions are delineated using superpixels generated via the Simple Linear Iterative Clustering (SLIC) algorithm, which provides meaningful structural units for analysis. Our contributions are fourfold: (1) redefining lesion borders as regions, rather than sharp lines; (2) generating superpixel-level embeddings with a transformer-based autoencoder; (3) incorporating these embeddings as features for superpixel classification; and (4) integrating neighborhood information to construct enhanced feature vectors. Unlike pixel-level algorithms that often overlook boundary context, our pipeline fuses global class information with local spatial relationships, significantly improving precision and recall in challenging border regions. An evaluation on the HAM10000 melanoma dataset demonstrates that our superpixel–RAG–transformer (region adjacency graph) pipeline achieves exceptional performance (100% F1 score, accuracy, and precision) in classifying background, border, and lesion core superpixels. By transforming raw dermoscopic images into region-based structured representations, the proposed method generates more informative inputs for downstream deep learning models. This strategy not only advances melanoma analysis but also provides a generalizable framework for other medical image segmentation and classification tasks. Full article

(This article belongs to the Special Issue Algorithms and Applications of Machine Learning Techniques for Healthcare)

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19 pages, 641 KB

Open AccessArticle

Lightweight Hash Function Design for the Internet of Things: Structure and SAT-Based Cryptanalysis

by Kairat Sakan, Kunbolat Algazy, Nursulu Kapalova and Andrey Varennikov

Algorithms 2025, 18(9), 550; https://doi.org/10.3390/a18090550 - 1 Sep 2025

This paper introduces a lightweight cryptographic hash algorithm, LWH-128, developed using a sponge-based construction and specifically adapted for operation under constrained computational and energy conditions typical of embedded systems and Internet of Things devices. The algorithm employs a two-layer processing structure based on [...] Read more.

This paper introduces a lightweight cryptographic hash algorithm, LWH-128, developed using a sponge-based construction and specifically adapted for operation under constrained computational and energy conditions typical of embedded systems and Internet of Things devices. The algorithm employs a two-layer processing structure based on simple logical operations (XOR, cyclic shifts, and S-boxes) and incorporates a preliminary diffusion transformation function G, along with the Davis–Meyer compression scheme, to enhance irreversibility and improve cryptographic robustness. A comparative analysis of hardware implementation demonstrates that LWH-128 exhibits balanced characteristics in terms of circuit complexity, memory usage, and processing speed, making it competitive with existing lightweight hash algorithms. As part of the cryptanalytic evaluation, a Boolean SATisfiability (SAT) Problem-based model of the compression function is constructed in the form of a conjunctive normal form of Boolean variables. Experimental results using the Parkissat SAT solver show an exponential increase in computational time as the number of unknown input bits increased. These findings support the conclusion that the LWH-128 algorithm exhibits strong resistance to preimage attacks based on SAT-solving techniques. Full article

(This article belongs to the Section Combinatorial Optimization, Graph, and Network Algorithms)

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20 pages, 3333 KB

Open AccessArticle

A New Hybrid Intelligent System for Predicting Bottom-Hole Pressure in Vertical Oil Wells: A Case Study

by Kheireddine Redouane and Ashkan Jahanbani Ghahfarokhi

Algorithms 2025, 18(9), 549; https://doi.org/10.3390/a18090549 - 1 Sep 2025

The evaluation of pressure drops across the length of production wells is a crucial task, as it influences both the cost-effective selection of tubing and the development of an efficient production strategy, both of which are vital for maximizing oil recovery while minimizing [...] Read more.

The evaluation of pressure drops across the length of production wells is a crucial task, as it influences both the cost-effective selection of tubing and the development of an efficient production strategy, both of which are vital for maximizing oil recovery while minimizing operational expenses. To address this, our study proposes an innovative hybrid intelligent system designed to predict bottom-hole flowing pressure in vertical multiphase conditions with superior accuracy compared to existing methods using a data set of 150 field measurements amassed from Algerian fields. In this work, the applied hybrid framework is the Adaptive Neuro-Fuzzy Inference System (ANFIS), which integrates artificial neural networks (ANN) with fuzzy logic (FL). The ANFIS model was constructed using a subtractive clustering technique after data filtering, and then its outcomes were evaluated against the most widely utilized correlations and mechanistic models. Graphical inspection and error statistics confirmed that ANFIS consistently outperformed all other approaches in terms of precision, reliability, and effectiveness. For further improvement of the ANFIS performance, a particle swarm optimization (PSO) algorithm is employed to refine the model and optimize the design of the antecedent Gaussian memberships along with the consequent linear coefficient vector. The results achieved by the hybrid ANFIS-PSO model demonstrated greater accuracy in bottom-hole pressure estimation than the conventional hybrid approach. Full article

(This article belongs to the Special Issue AI and Computational Methods in Engineering and Science)

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13 pages, 685 KB

Open AccessArticle

Comparison of Linear MPC and Explicit MPC for Battery Cell Balancing Control

by Wanqun Yang and Jun Chen

Algorithms 2025, 18(9), 548; https://doi.org/10.3390/a18090548 - 1 Sep 2025

This paper presents and compares two model predictive control (MPC) approaches for battery cell state-of-charge (SOC) balancing. In both approaches, a linearized discrete-time model that takes into account individual cell capacities is used. The first approach is a linear MPC controller that effectively [...] Read more.

This paper presents and compares two model predictive control (MPC) approaches for battery cell state-of-charge (SOC) balancing. In both approaches, a linearized discrete-time model that takes into account individual cell capacities is used. The first approach is a linear MPC controller that effectively regulates multiple cells to track a target SOC level while satisfying physical constraints. The second approach is based on explicit MPC implementation to reduce online computation while achieving a comparable performance. The simulation results suggest that explicit MPC can deliver the same balancing performance as linear MPC, while achieving faster online execution. Specifically, explicit MPC reduces the computation time by

37.3 %

in a five-cell battery example, with the cost of higher offline computation. However, simulation results also reveal a significant limitation for explicit MPC for battery systems with a larger number of cells. As the number of cells increases and/or the prediction horizon increases, the computational requirements grow exponentially, making its application to SOC balancing for large battery systems impractical. To the best of the authors’ knowledge, this is the first study that compares MPC and explicit MPC algorithms in the context of battery cell balancing. Full article

(This article belongs to the Special Issue Advanced Artificial Intelligence/Machine Learning Techniques for Safe Operation and Control in Power and Sustainable Energy Systems)

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16 pages, 1007 KB

Open AccessArticle

Learning SMILES Semantics: Word2Vec and Transformer Embeddings for Molecular Property Prediction

by Saya Hashemian, Zak Khan, Pulkit Kalhan and Yang Liu

Algorithms 2025, 18(9), 547; https://doi.org/10.3390/a18090547 - 1 Sep 2025

This paper investigates the effectiveness of Word2Vec-based molecular representation learning on SMILES (Simplified Molecular Input Line Entry System) strings for a downstream prediction task related to the market approvability of chemical compounds. Here, market approvability is treated as a proxy classification label derived [...] Read more.

This paper investigates the effectiveness of Word2Vec-based molecular representation learning on SMILES (Simplified Molecular Input Line Entry System) strings for a downstream prediction task related to the market approvability of chemical compounds. Here, market approvability is treated as a proxy classification label derived from approval status, where only the molecular structure is analyzed. We train character-level embeddings using Continuous Bag of Words (CBOW) and Skip-Gram with Negative Sampling architectures and apply the resulting embeddings in a downstream classification task using a multi-layer perceptron (MLP). To evaluate the utility of these lightweight embedding techniques, we conduct experiments on a curated SMILES dataset labeled by approval status under both imbalanced and SMOTE-balanced training conditions. In addition to our Word2Vec-based models, we include a ChemBERTa-based baseline using the pretrained ChemBERTa-77M model. Our findings show that while ChemBERTa achieves a higher performance, the Word2Vec-based models offer a favorable trade-off between accuracy and computational efficiency. This efficiency is especially relevant in large-scale compound screening, where rapid exploration of the chemical space can support early-stage cheminformatics workflows. These results suggest that traditional embedding models can serve as viable alternatives for scalable and interpretable cheminformatics pipelines, particularly in resource-constrained environments. Full article

(This article belongs to the Special Issue Mathematical Modelling in Engineering and Human Behaviour (3rd Edition))

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25 pages, 11853 KB

Open AccessArticle

Mixed 1D/2D Simplicial Approximation of Volumetric Medial Axis by Direct Palpation of Shape Diameter Function

by Andres F. Puentes-Atencio, Daniel Mejia-Parra, Ander Arbelaiz, Carlos Cadavid and Oscar Ruiz-Salguero

Algorithms 2025, 18(9), 546; https://doi.org/10.3390/a18090546 - 31 Aug 2025

In the domain of Shape Encoding, the approximation of the Medial Axis of a solid region in

R^{3}

with Boundary Representation M, is relevant because the Medial Axis is an efficient encoding for M in Design, Manufacturing, and Shape Learning. Existing [...] Read more.

In the domain of Shape Encoding, the approximation of the Medial Axis of a solid region in

R^{3}

with Boundary Representation M, is relevant because the Medial Axis is an efficient encoding for M in Design, Manufacturing, and Shape Learning. Existing Medial Axis approximations include (a) full Voronoi and (b) and partial Shape Diameter Function (SDF)-based ones. Methods (a) produce large high-frequency data, which must then be pruned. Methods (b) reduce computing expenses at the price of not handling some shapes (e.g., prismatic), and currently, they only synthesize 1D Medial Axes. To partially overcome these limitations, this investigation performs a direct synthesis of a 1D and 2D simplex-based Medial Axis approximation by a combination of stochastic geometric reasoning and graph operations on the SDF-originated point cloud. Our method covers one- and two-dimensional Simplicial Complex Medial Axes, thus improving on 1D Medial Axes approximation methods. Our approach avoids the expensive full computing plus pruning of Medial Axis based on Voronoi methods. Future work is needed in the synthesis of Medial Axis approximation for high-frequency neighborhoods of mesh M. Full article

(This article belongs to the Section Analysis of Algorithms and Complexity Theory)

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24 pages, 2159 KB

Open AccessArticle

Agentic RAG-Driven Multi-Omics Analysis for PI3K/AKT Pathway Deregulation in Precision Medicine

by Micheal Olaolu Arowolo, Sulaiman Olaniyi Abdulsalam, Rafiu Mope Isiaka, Kingsley Theophilus Igulu, Bukola Fatimah Balogun, Mihail Popescu and Dong Xu

Algorithms 2025, 18(9), 545; https://doi.org/10.3390/a18090545 - 30 Aug 2025

The phosphoinositide 3-kinase (PI3K)/AKT signaling pathway is a crucial regulator of cellular metabolism, proliferation, and survival. It is frequently dysregulated in metabolic, cardiovascular, and neoplastic disorders. Despite the advancements in multi-omics technology, existing methods often fail to provide real-time, pathway-specific insights for precision [...] Read more.

The phosphoinositide 3-kinase (PI3K)/AKT signaling pathway is a crucial regulator of cellular metabolism, proliferation, and survival. It is frequently dysregulated in metabolic, cardiovascular, and neoplastic disorders. Despite the advancements in multi-omics technology, existing methods often fail to provide real-time, pathway-specific insights for precision medicine and drug repurposing. We offer Agentic RAG-Driven Multi-Omics Analysis (ARMOA), an autonomous, hypothesis-driven system that integrates retrieval-augmented generation (RAG), large language models (LLMs), and agentic AI to thoroughly analyze genomic, transcriptomic, proteomic, and metabolomic data. Through the use of graph neural networks (GNNs) to model complex interactions within the PI3K/AKT pathway, ARMOA enables the discovery of novel biomarkers, probable candidates for drug repurposing, and customized therapy responses to address the complexities of PI3K/AKT dysregulation in disease states. ARMOA dynamically gathers and synthesizes knowledge from multiple sources, including KEGG, TCGA, and DrugBank, to guarantee context-aware insights. Through adaptive reasoning, it gradually enhances predictions, achieving 91% accuracy in external testing and 92% accuracy in cross-validation. Case studies in breast cancer and type 2 diabetes demonstrate that ARMOA can identify synergistic drug combinations with high clinical relevance and predict therapeutic outcomes specific to each patient. The framework’s interpretability and scalability are greatly enhanced by its use of multi-omics data fusion and real-time hypothesis creation. ARMOA provides a cutting-edge example for precision medicine by integrating multi-omics data, clinical judgment, and AI agents. Its ability to provide valuable insights on its own makes it a powerful tool for advancing biomedical research and treatment development. Full article

(This article belongs to the Special Issue Advanced Algorithms for Biomedical Data Analysis)

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21 pages, 914 KB

Open AccessArticle

Modeling How the Different Parts of the Immune System Fight Viruses

by Benito Chen-Charpentier

Algorithms 2025, 18(9), 544; https://doi.org/10.3390/a18090544 - 29 Aug 2025

Viruses cause a large number of diseases. After penetrating into a host, the virus starts infecting healthy cells. Then it uses the RNA or DNA of the cell to replicate and afterward it explodes the infected cell, letting out many copies of the [...] Read more.

Viruses cause a large number of diseases. After penetrating into a host, the virus starts infecting healthy cells. Then it uses the RNA or DNA of the cell to replicate and afterward it explodes the infected cell, letting out many copies of the virus that can infect new cells. The innate and adaptive parts of the immune system defend the body by eliminating both the free viruses and the infected cells. Neutrophils, macrophages, natural killer cells, helper T cells (CD4+) and cytotoxic T lymphocytes (CD8+) are among the participating immune cells. The interactions are complex and not fully understood. In this paper, we present and study three mathematical models based on ordinary differential equations of virus and immune system interactions with different complexities, and also introduce possible treatments. We discuss the advantages and disadvantages of each model. We do global sensitivity analysis and numerical simulations. Finally, we present conclusions including comments about the complexity of mathematical models. Full article

(This article belongs to the Special Issue Mathematical Modelling in Engineering and Human Behaviour (3rd Edition))

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20 pages, 2367 KB

Open AccessArticle

Hybrid Machine Learning Model for Blast-Induced Peak Particle Velocity Estimation in Surface Mining: Application of Sparrow Search Algorithm in ANN Optimization

by Kesalopa Gaopale, Takashi Sasaoka, Akihiro Hamanaka and Hideki Shimada

Algorithms 2025, 18(9), 543; https://doi.org/10.3390/a18090543 - 27 Aug 2025

Blast-induced ground vibrations present substantial safety and environmental hazards in surface mining operations. This study proposes and evaluates the Sparrow Search Algorithm-optimized ANN (SSA-ANN) against artificial neural network (ANN), Genetic Algorithm-optimized ANN (GA-ANN), and empirical formula (USBM) to estimate peak particle velocity (PPV). [...] Read more.

Blast-induced ground vibrations present substantial safety and environmental hazards in surface mining operations. This study proposes and evaluates the Sparrow Search Algorithm-optimized ANN (SSA-ANN) against artificial neural network (ANN), Genetic Algorithm-optimized ANN (GA-ANN), and empirical formula (USBM) to estimate peak particle velocity (PPV). In addition, the input parameters include key blasting design parameters and rock mass features (GSI and UCS). The SSA-ANN demonstrated superior prediction accuracy, attaining an average R² of 0.51 using bootstrap validation, surpassing GA-ANN (0.41) and standard ANN (0.26). Furthermore, the incorporation of GSI enhanced the model’s geotechnical sensitivity. These results illustrate that the application of SSA-ANN alongside comprehensive rock mass characteristics can substantially decrease uncertainty in PPV prediction, therefore enhancing safety within the blast area and improving vibration control methods in blasting operations. Full article

(This article belongs to the Special Issue Mathematical Modelling in Engineering and Human Behaviour (3rd Edition))

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32 pages, 3707 KB

Open AccessArticle

Performance Optimization of a Silica Gel–Water Adsorption Chiller Using Grey Wolf-Based Multi-Objective Algorithms and Regression Analysis

by Patricia Kwakye-Boateng, Lagouge Tartibu and Jen Tien-Chien

Algorithms 2025, 18(9), 542; https://doi.org/10.3390/a18090542 - 26 Aug 2025

The growing need for cooling, combined with the environmental concerns surrounding conventional mechanical vapour compression (MVC) systems, has accelerated research for sustainable cooling solutions driven by low-grade heat. Single-stage dual-bed adsorption chillers (ADCs) using silica gel and water provide a promising approach due [...] Read more.

The growing need for cooling, combined with the environmental concerns surrounding conventional mechanical vapour compression (MVC) systems, has accelerated research for sustainable cooling solutions driven by low-grade heat. Single-stage dual-bed adsorption chillers (ADCs) using silica gel and water provide a promising approach due to their continuous cooling output, lower complexity, and the use of environmentally safe working fluids. However, limitations in their performance, specifically in the coefficient of performance (COP), cooling capacity (Q_cc), and waste heat recovery efficiency (η_e), necessitate improvement through optimization. This study employs statistically validated regression-based objective functions to optimize ten decision variables using the single Grey Wolf Optimizer (GWO) and its multi-objective variant, Muilti-Objective Grey Wolf Optimization (MOGWO), for a silica gel–water single-stage dual-bed ADC. The results from the single-objective optimization showed a maximum coefficient of performance (COP) of 0.697, cooling capacity (Q_cc) of 20.76 kW, and waste heat recovery efficiency (η_e) of 0.125. The values from the Pareto-optimal solutions for the MOGWO ranged from 0.5123 to 0.6859 for COP, 12.45 to 20.73 kW for Q_ccand 8.24% to 12.48% for η_e, demonstrating superior performance compared to existing benchmarks. A one-at-a-time sensitivity analysis revealed non-linear and non-monotonic impacts of variables, confirming the robustness and physical realism of the MOGWO model. The developed MOGWO framework effectively enhances the performance of the single-stage dual-bed ADC and improves low-grade heat utilization, offering a robust decision-support tool for system design and optimization. Full article

(This article belongs to the Section Combinatorial Optimization, Graph, and Network Algorithms)

17 pages, 723 KB

Open AccessArticle

Accelerating Subgraph Matching Through Advanced Compression and Label Filtering

by Yanfeng Chai, Jiashu Li and Qiang Zhang

Algorithms 2025, 18(9), 541; https://doi.org/10.3390/a18090541 - 26 Aug 2025

Efficiently identifying subgraphs that match a given query graph within large-scale graphs has become a critical focus in both academic and industrial research. Subgraph matching, a fundamental problem in graph algorithms, facilitates the effective querying of graph data and is fundamentally based on [...] Read more.

Efficiently identifying subgraphs that match a given query graph within large-scale graphs has become a critical focus in both academic and industrial research. Subgraph matching, a fundamental problem in graph algorithms, facilitates the effective querying of graph data and is fundamentally based on the subgraph isomorphism problem, which is known to be NP-complete. Among the various stages of subgraph matching, the filtering phase is particularly crucial as it directly affects the overall efficiency of the algorithm. A robust filtering mechanism can rapidly identify candidate nodes that satisfy the query criteria, thereby significantly reducing computational costs in the subsequent stages. The analysis of existing subgraph matching techniques reveals several challenges in the filtering stage: (1) redundant enumeration of equivalent nodes; (2) incomplete filtering due to structural limitations; and (3) excessive redundant validations during the verification phase. To overcome these issues, we propose an adaptive subgraph matching (ASM) framework that integrates efficient compressed graph nodes (CGNs) and a novel label count filter (LCF) algorithm. These innovations enhance the filtering process, resulting in significant improvements in query processing performance. Experimental evaluations demonstrate that our approach achieves substantial gains, outperforming state-of-the-art subgraph search and matching algorithms by several orders of magnitude in query processing time. Full article

(This article belongs to the Section Randomized, Online, and Approximation Algorithms)

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21 pages, 327 KB

Open AccessArticle

Algorithm for Determining the Strong Fuzzy Grade of a Hypergroup

by Yuming Feng and Violeta Leoreanu-Fotea

Algorithms 2025, 18(9), 540; https://doi.org/10.3390/a18090540 - 26 Aug 2025

In this paper, we present an algorithm for determining the strong fuzzy grade of a hypergroup, considering a particular class of hypergroups associated with genetics. A study is carried out depending on the cardinality of the initial hypergroup. The last paragraph of this [...] Read more.

In this paper, we present an algorithm for determining the strong fuzzy grade of a hypergroup, considering a particular class of hypergroups associated with genetics. A study is carried out depending on the cardinality of the initial hypergroup. The last paragraph of this paper contains the MATLAB R2018b program for the fuzzy grade for cardinals

3, 4, 5, 6, 8

. Full article

(This article belongs to the Collection Feature Papers in Algorithms for Multidisciplinary Applications)

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27 pages, 1880 KB

Open AccessArticle

Optimal Choice of the Shape Parameter for the Radial Basis Functions Method in One-Dimensional Parabolic Inverse Problems

by Sanduni Wasana and Upeksha Perera

Algorithms 2025, 18(9), 539; https://doi.org/10.3390/a18090539 - 25 Aug 2025

Inverse problems have numerous important applications in science, engineering, medicine, and other disciplines. In this study, we present a numerical solution for a one-dimensional parabolic inverse problem with energy overspecification at a fixed spatial point, using the radial basis function (RBF) method. The [...] Read more.

Inverse problems have numerous important applications in science, engineering, medicine, and other disciplines. In this study, we present a numerical solution for a one-dimensional parabolic inverse problem with energy overspecification at a fixed spatial point, using the radial basis function (RBF) method. The collocation matrix arising in RBF-based approaches is typically highly ill-conditioned, and the method’s performance is strongly influenced by the choice of the radial basis function and its shape parameter. Unlike previous studies that focused primarily on Gaussian radial basis functions, this work investigates and compares the performance of three RBF types—Gaussian (GRBF), Multiquadrics (MQRBF), and Inverse Multiquadrics (IMQRBF). By transforming the inverse problem into an equivalent direct problem, we apply the RBF collocation method in both space and time. Numerical experiments on two test problems with known analytical solutions are conducted to evaluate the approximation error, optimal shape parameters, and matrix conditioning. Results indicate that both MQRBF and IMQRBF generally provide better accuracy than GRBF. Furthermore, IMQRBF enhances numerical stability due to its lower condition number, making it a more robust choice for solving ill-posed inverse problems where both stability and accuracy are critical. Full article

(This article belongs to the Section Analysis of Algorithms and Complexity Theory)

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17 pages, 3896 KB

Open AccessArticle

HFGAD: Hierarchical Fine-Grained Attention Decoder for Gaze Estimation

by Shaojie Huang, Tianzhong Wang, Weiquan Liu, Yingchao Piao, Jinhe Su, Guorong Cai and Huilin Xu

Algorithms 2025, 18(9), 538; https://doi.org/10.3390/a18090538 - 24 Aug 2025

Gaze estimation is a cornerstone of applications such as human–computer interaction and behavioral analysis, e.g., for intelligent transport systems. Nevertheless, existing methods predominantly rely on coarse-grained features from deep layers of visual encoders, overlooking the critical role that fine-grained details from shallow layers [...] Read more.

Gaze estimation is a cornerstone of applications such as human–computer interaction and behavioral analysis, e.g., for intelligent transport systems. Nevertheless, existing methods predominantly rely on coarse-grained features from deep layers of visual encoders, overlooking the critical role that fine-grained details from shallow layers play in gaze estimation. To address this gap, we propose a novel Hierarchical Fine-Grained Attention Decoder (HFGAD), a lightweight fine-grained decoder that emphasizes the importance of shallow-layer information in gaze estimation. Specifically, HFGAD integrates a fine-grained amplifier MSCSA that employs multi-scale spatial-channel attention to direct focus toward gaze-relevant regions, and also incorporates a shallow-to-deep fusion module SFM to facilitate interaction between coarse-grained and fine-grained information. Extensive experiments on three benchmark datasets demonstrate the superiority of HFGAD over existing methods, achieving a remarkable 1.13° improvement in gaze estimation accuracy for in-car scenarios. Full article

(This article belongs to the Topic Applications of NLP, AI, and ML in Software Engineering)

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