Mathematics

23 pages, 2139 KiB

Open AccessArticle

Study of Flexibility Transformation in Thermal Power Enterprises under Multi-Factor Drivers: Application of Complex-Network Evolutionary Game Theory

by Lefeng Cheng, Pan Peng, Wentian Lu, Pengrong Huang and Yang Chen

Mathematics 2024, 12(16), 2537; https://doi.org/10.3390/math12162537 - 16 Aug 2024

Abstract

With the increasing share of renewable energy in the grid and the enhanced flexibility of the future power system, it is imperative for thermal power companies to explore alternative strategies. The flexible transformation of thermal power units is an effective strategy to address [...] Read more.

With the increasing share of renewable energy in the grid and the enhanced flexibility of the future power system, it is imperative for thermal power companies to explore alternative strategies. The flexible transformation of thermal power units is an effective strategy to address the previously mentioned challenges; however, the factors influencing the diffusion of this technology merit further investigation, yet they have been seldom examined by scholars. To address this gap, this issue is examined using an evolutionary game model of multi-agent complex networks, and a more realistic group structure is established through heterogeneous group differentiation. With factors such as group relationships, diffusion paths, compensation electricity prices, and subsidy intensities as variables, several diffusion scenarios are developed for research purposes. The results indicate that when upper-level enterprises influence the decision-making of lower-level enterprises, technology diffusion is significantly accelerated, and enhanced communication among thermal power enterprises further promotes diffusion. Among thermal power enterprises, leveraging large and medium-sized enterprises to promote the flexibility transformation of units proves to be an effective strategy. With regard to factors like the compensation price for depth peak shaving, the initial application ratio of groups, and the intensity of government subsidies, the compensation price emerges as the key factor. Only with a high compensation price can the other two factors effectively contribute to promoting technology diffusion. Full article

(This article belongs to the Topic Advanced Techniques and Modeling in Business and Economics)

19 pages, 840 KiB

Open AccessArticle

Uniformly Continuous Generalized Sliding Mode Control

by Aldo Jonathan Muñoz-Vázquez and Guillermo Fernández-Anaya

Mathematics 2024, 12(16), 2536; https://doi.org/10.3390/math12162536 - 16 Aug 2024

Abstract

This paper explores a general class of singular kernels with the objective of designing new families of uniformly continuous sliding mode controllers. The proposed controller results from filtering a discontinuous switching function by means of a Sonine integral, producing a uniformly continuous control [...] Read more.

This paper explores a general class of singular kernels with the objective of designing new families of uniformly continuous sliding mode controllers. The proposed controller results from filtering a discontinuous switching function by means of a Sonine integral, producing a uniformly continuous control signal, preserving finite-time sliding motion and robustness against continuous but unknown and not necessarily integer-order differentiable disturbances. The principle of dynamic memory resetting is considered to demonstrate finite-time stability. A set of sufficient conditions to design singular kernels, preserving the above characteristics, is presented, and several examples are exposed to propose new families of continuous sliding mode approaches. Simulation results are studied to illustrate the feasibility of some of the proposed schemes. Full article

(This article belongs to the Section Dynamical Systems)

24 pages, 1874 KiB

Open AccessArticle

NIGA: A Novel Method for Investigating the Attacker–Defender Model within Critical Infrastructure Networks

by Jiaqi Ren, Jin Liu, Yibo Dong, Zhe Li and Weili Li

Mathematics 2024, 12(16), 2535; https://doi.org/10.3390/math12162535 - 16 Aug 2024

Abstract

The field of infrastructure security has garnered significant research attention. By integrating complex network theory with game theory, researchers have proposed many methods for studying the interactions between the attacker and the defender from a macroscopic viewpoint. We constructed a game model of [...] Read more.

The field of infrastructure security has garnered significant research attention. By integrating complex network theory with game theory, researchers have proposed many methods for studying the interactions between the attacker and the defender from a macroscopic viewpoint. We constructed a game model of infrastructure networks to analyze attacker-defender confrontations. To address the challenge of finding the Nash equilibrium, we developed a novel algorithm—node-incremental greedy algorithm (NIGA)—which uses less strategy space to solve the problem. The experiments performed further showed that NIGA has better optimization ability than other traditional algorithms. The optimal defense strategies under different conditions of initial strategy ratios and attacker-defender resources were analyzed in this study. Using intelligent computing to solve the Nash equilibrium is a new approach by which for researchers to analyze attacker-defender confrontations. Full article

20 pages, 630 KiB

Open AccessArticle

Progressive Archive in Adaptive jSO Algorithm

by Petr Bujok

Mathematics 2024, 12(16), 2534; https://doi.org/10.3390/math12162534 - 16 Aug 2024

Abstract

The problem of optimisation methods is the stagnation of population P, which results in a local solution for the task. This problem can be solved by employing an archive for good historical solutions outperformed by the new better offspring. The archive A [...] Read more.

The problem of optimisation methods is the stagnation of population P, which results in a local solution for the task. This problem can be solved by employing an archive for good historical solutions outperformed by the new better offspring. The archive A was introduced with the variant of adaptive differential evolution (DE), and it was successfully applied in many adaptive DE variants including the efficient jSO algorithm. In the original jSO, the historical good individuals replace the random existing positions in A. It causes that outperformed historical solution from P with lower quality to replace the stored solution in A with better quality. In this paper, a new approach to replace individuals in archive A more progressively is proposed. Outperformed individuals from P replace solutions in the worse part of A based on the function value. The portion of A selected for replacement is controlled by the input parameter, and its setting is studied in this experiment. The proposed progressive archive is employed in the original jSO. Moreover, the Eigenvector transformation of the individuals for crossover is applied to increase the efficiency for the rotated optimisation problems. The efficiency of the proposed progressive archive and the Eigen crossover are evaluated using the set of 29 optimisation problems for CEC 2024 and various dimensionality. All the experiments were performed on a standard PC, and the results were compared using the standard statistical methods. The newly proposed algorithm with the progressive archive approach performs substantially better than the original jSO, especially when 20 or

40 %

of the worse individuals of A are set for replacement. The Eigen crossover increases the performance of the proposed jSO algorithm with the progressive archive approach. The estimated time complexity illustrates the low computational demands of the proposed archive approach. Full article

(This article belongs to the Section Computational and Applied Mathematics)

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23 pages, 1398 KiB

Open AccessArticle

Continuum–Discontinuum Bonded-Block Model for Simulating Mixed-Mode Fractures

by Yue Sun, Tao Chen, Longquan Yong and Qian Chen

Mathematics 2024, 12(16), 2533; https://doi.org/10.3390/math12162533 - 16 Aug 2024

Abstract

In this study, an improved discontinuous deformation analysis method with sub-block strategy is introduced to numerically simulate mixed-mode fractures. This approach partitions the material domain into continuum and potential discontinuum regions, applying specialized modeling techniques to each. In the continuum region, penalty-like bonding [...] Read more.

In this study, an improved discontinuous deformation analysis method with sub-block strategy is introduced to numerically simulate mixed-mode fractures. This approach partitions the material domain into continuum and potential discontinuum regions, applying specialized modeling techniques to each. In the continuum region, penalty-like bonding springs are employed to glue the sub-blocks together to capture the elastic behavior of the material. In the potential discontinuum region, the cohesive springs with the stiffness based on the cohesive zone model are implemented between sub-blocks to reproduce the process of crack nucleation and propagation. The primary advantage of this method is its capability to effectively model the transition of quasi-brittle solids from a continuous to a discontinuous stage through the degradation of cohesive springs. This accurately represents material failure while maintaining stability and consistency along uncracked interfaces. Another significant benefit is the method’s efficiency, as it avoids complex contact operations along sub-block interfaces before the cohesive spring between them fails. Validation through various benchmark numerical examples, such as cantilever beam-bending and diverse fracture simulations, demonstrates the method’s accuracy and robustness by comparing the results with analytical solutions. These comparisons show that the proposed method effectively captures the interplay between tensile and shear traction components in the mixed-mode crack propagation process. Full article

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28 pages, 8515 KiB

Open AccessArticle

Signaling Security Games with Attack Planner Deception

by Santing He, Mingchu Li and Runfa Zhang

Mathematics 2024, 12(16), 2532; https://doi.org/10.3390/math12162532 - 16 Aug 2024

Abstract

This paper studies a class of attack behavior in which adversaries assume the role of initiators, orchestrating and implementing attacks by hiring executors. We examine the dynamics of strategic attacks, modeling the initiator as an attack planner and constructing the interaction with the [...] Read more.

This paper studies a class of attack behavior in which adversaries assume the role of initiators, orchestrating and implementing attacks by hiring executors. We examine the dynamics of strategic attacks, modeling the initiator as an attack planner and constructing the interaction with the defender within a defender–attack planner framework. The individuals tasked with executing the attacks are identified as attackers. To ensure the attackers’ adherence to the planner’s directives, we concurrently consider the interests of each attacker by formulating a multi-objective problem. Furthermore, acknowledging the information asymmetry where defenders have incomplete knowledge of the planners’ payments and the attackers’ profiles, and recognizing the planner’s potential to exploit this for strategic deception, we develop a defender–attack planner model with deception based on signaling games. Subsequently, through the analysis of the interaction between the defender and planner, we refine the model into a tri-level programming problem. To address this, we introduce an effective decomposition algorithm leveraging genetic algorithms. Ultimately, our numerical experiments substantiate that the attack planner’s deceptive strategy indeed yield greater benefits. Full article

(This article belongs to the Special Issue Intelligent Computing and Mathematical Physics: Robots, Security Games, Quantum Algorithms and Symbolic Computing)

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21 pages, 1493 KiB

Open AccessArticle

A Distorted-Image Quality Assessment Algorithm Based on a Sparse Structure and Subjective Perception

by Yang Yang, Chang Liu, Hui Wu and Dingguo Yu

Mathematics 2024, 12(16), 2531; https://doi.org/10.3390/math12162531 - 16 Aug 2024

Abstract

Most image quality assessment (IQA) algorithms based on sparse representation primarily focus on amplitude information, often overlooking the structural composition of images. However, structural composition is closely linked to perceived image quality, a connection that existing methods do not adequately address. To fill [...] Read more.

Most image quality assessment (IQA) algorithms based on sparse representation primarily focus on amplitude information, often overlooking the structural composition of images. However, structural composition is closely linked to perceived image quality, a connection that existing methods do not adequately address. To fill this gap, this paper proposes a novel distorted-image quality assessment algorithm based on a sparse structure and subjective perception (IQA-SSSP). This algorithm evaluates the quality of distorted images by measuring the sparse structure similarity between a reference and distorted images. The proposed method has several advantages. First, the sparse structure algorithm operates with reduced computational complexity, leading to faster processing speeds, which makes it suitable for practical applications. Additionally, it efficiently handles large-scale data, further enhancing the assessment process. Experimental results validate the effectiveness of the algorithm, showing that it achieves a high correlation with human visual perception, as reflected in both objective and subjective evaluations. Specifically, the algorithm yielded a Pearson correlation coefficient of 0.929 and a mean squared error of 8.003, demonstrating its robustness and efficiency. By addressing the limitations of existing IQA methods and introducing a more holistic approach, this paper offers new perspectives on IQA. The proposed algorithm not only provides reliable quality assessment results but also closely aligns with human visual experience, thereby enhancing both the objectivity and accuracy of image quality evaluations. This research offers significant theoretical support for the advancement of sparse representation in IQA. Full article

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20 pages, 9374 KiB

Open AccessArticle

A Numerical Investigation of Activation Energy Impact on MHD Water-Based Fe₃O₄ and CoFe₂O₄ Flow between the Rotating Cone and Expanding Disc

by Kandavkovi Mallikarjuna Nihaal, Ulavathi Shettar Mahabaleshwar, Nedunchezhian Swaminathan, David Laroze and Igor V. Shevchuk

Mathematics 2024, 12(16), 2530; https://doi.org/10.3390/math12162530 - 16 Aug 2024

Abstract

Hybrid nanofluids have caught the attention of scholars and investigators in the present technological period due to their improved thermophysical features and the desire to boost heat transfer rates compared to those of conventional fluids. The present paper is mainly concerned with heat [...] Read more.

Hybrid nanofluids have caught the attention of scholars and investigators in the present technological period due to their improved thermophysical features and the desire to boost heat transfer rates compared to those of conventional fluids. The present paper is mainly concerned with heat transmission in cone-disk geometry in the presence of a magnetic field, activation energy, and non-uniform heat absorption/generation. In this work, the cone-disk (CD) apparatus is considered to have a rotating cone (RC) and a stretching disk, along with iron oxide and cobalt ferrite-based hybrid nanofluid. Appropriate similarity transformations are employed to change the physically modeled equations into ordinary differential equations (ODEs). Heat transfer rates at both surfaces are estimated by implementing a modified energy equation with non-uniform heat absorption/generation. The outcomes illustrated that the inclusion of such physical streamwise heat conduction variables in the energy equation has a significant impact on the well-known conclusions of heat transfer rates. To understand flow profile behavior, we have resorted to the RKF-45 method and the shooting method, which are illustrated using graphs. The findings provide conclusive evidence that wall stretching alters the flow, heat, and mass profile characteristics within the conical gap. The wall deformation caused by disk stretching was found to have a potential impact of modifying the centripetal/centrifugal flow characteristics of the disk, increasing the flow velocity and swirling angles. A rise in activation energy leads to an improved concentration field. Full article

(This article belongs to the Special Issue Computational Fluid Dynamics with Applications)

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22 pages, 4062 KiB

Open AccessArticle

Comparative Evaluation of Model Accuracy for Predicting Selected Attributes in Agile Project Management

by Emira Mustafa Moamer Alzeyani and Csaba Szabó

Mathematics 2024, 12(16), 2529; https://doi.org/10.3390/math12162529 - 16 Aug 2024

Abstract

In this study, we evaluate predictive modelling techniques within project management, employing diverse architectures such as the LSTM, CNN, CNN-LSTM, GRU, MLP, and RNN models. The primary focus is on assessing the precision and consistency of predictions for crucial project parameters, including completion [...] Read more.

In this study, we evaluate predictive modelling techniques within project management, employing diverse architectures such as the LSTM, CNN, CNN-LSTM, GRU, MLP, and RNN models. The primary focus is on assessing the precision and consistency of predictions for crucial project parameters, including completion time, required personnel, and estimated costs. Our analysis utilises a comprehensive dataset that encapsulates the complexities inherent in real-world projects, providing a robust basis for evaluating model performance. The findings, presented through detailed tables and comparative charts, underscore the collective success of the models. The LSTM model stands out for its exceptional performance in consistently predicting completion time, personnel requirements, and estimated costs. Quantitative evaluation metrics, including Mean Absolute Error (MAE), Mean Squared Error (MSE), and Mean Absolute Percentage Error (MAPE), corroborate the efficacy of the models. This study offers insights into the success observed, reflecting the potential for further refinement and continuous exploration to enhance the accuracy of predictive models in the ever-evolving landscape of project management. Full article

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16 pages, 644 KiB

Open AccessArticle

Large-Scale Group Decision-Making Method with Public Participation and Its Application in Urban Management

by Xiuhong Niu, Yongming Song and Zhongwen Xu

Mathematics 2024, 12(16), 2528; https://doi.org/10.3390/math12162528 - 15 Aug 2024

Abstract

Civic participation is of great significance to urban management decision-making. In order to facilitate citizens to participate in city management decision-making, this paper proposes a large-scale group decision-making (LSGDM) method based on multi-granular probabilistic linguistic preference relations (MG-PLPRs). First, each decision maker selects [...] Read more.

Civic participation is of great significance to urban management decision-making. In order to facilitate citizens to participate in city management decision-making, this paper proposes a large-scale group decision-making (LSGDM) method based on multi-granular probabilistic linguistic preference relations (MG-PLPRs). First, each decision maker selects a language terms set from the multi-granularity language terms set to represent individual preference relations, and the MG-PLPRs are obtained by statistical calculation to represent sub-group’s preferences information. Then, an optimization model based on the expected consistency of PLPR and consensus measure of groups is established for achieving consensus-reaching processes, which can ensure satisfactory individual consistency and group consensus. Finally, the validity and applicability of the proposed method is verified by a case of a city “shared garden” site selection with the participation of citizens. Full article

(This article belongs to the Special Issue Advances and Application of Fuzzy Sets, Decision Making and Soft Computing)

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19 pages, 1891 KiB

Open AccessArticle

Extrapolation of Physics-Inspired Deep Networks in Learning Robot Inverse Dynamics

by Zhiming Li, Shuangshuang Wu, Wenbai Chen and Fuchun Sun

Mathematics 2024, 12(16), 2527; https://doi.org/10.3390/math12162527 - 15 Aug 2024

Abstract

Accurate robot dynamics models are crucial for safe and stable control as well as for generalization to new conditions. Data-driven methods are increasingly used in robotics dynamics modeling for their superior approximation, with extrapolation performance being a critical efficacy indicator. While deep learning [...] Read more.

Accurate robot dynamics models are crucial for safe and stable control as well as for generalization to new conditions. Data-driven methods are increasingly used in robotics dynamics modeling for their superior approximation, with extrapolation performance being a critical efficacy indicator. While deep learning is widely used, it often overlooks essential physical principles, leading to weaker extrapolation capabilities. Recent innovations have introduced physics-inspired deep networks that integrate deep learning with physics, leading to improved extrapolation due to their informed structure, but potentially to underfitting in real-world scenarios due to the presence of unmodeled phenomena. This paper presents an experimental framework to assess the extrapolation capabilities of data-driven methods. Using this framework, physics-inspired deep networks are applied to learn the inverse dynamics models of a simulated robotic manipulator and two real physical systems. The results show that under ideal observation conditions physics-inspired models can learn the system’s underlying structure and demonstrate strong extrapolation capabilities, indicating a promising direction in robotics by offering more accurate and interpretable models. However, in real systems their extrapolation often falls short because the physical priors do not capture all dynamic phenomena, indicating room for improvement in practical applications. Full article

(This article belongs to the Special Issue Advancement of Mathematical Methods in Feature Representation Learning for Artificial Intelligence, Data Mining and Robotics, 2nd Edition)

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26 pages, 12562 KiB

Open AccessArticle

A Study on the Performance of Adaptive Neural Networks for Haze Reduction with a Focus on Precision

by Ahmed Alshahir, Khaled Kaaniche, Ghulam Abbas, Paolo Mercorelli, Mohammed Albekairi and Meshari D. Alanazi

Mathematics 2024, 12(16), 2526; https://doi.org/10.3390/math12162526 - 15 Aug 2024

Abstract

Visual clarity is significantly compromised, and the efficacy of numerous computer vision tasks is impeded by the widespread presence of haze in images. Innovative approaches to accurately minimize haze while keeping image features are needed to address this difficulty. The difficulties of current [...] Read more.

Visual clarity is significantly compromised, and the efficacy of numerous computer vision tasks is impeded by the widespread presence of haze in images. Innovative approaches to accurately minimize haze while keeping image features are needed to address this difficulty. The difficulties of current methods and the need to create better ones are brought to light in this investigation of the haze removal problem. The main goal is to provide a region-specific haze reduction approach by utilizing an Adaptive Neural Training Net (ANTN). The suggested technique uses adaptive training procedures with external haze images, pixel-segregated images, and haze-reduced images. Iteratively comparing spectral differences in hazy and non-hazy areas improves accuracy and decreases haze reduction errors. This study shows that the recommended strategy significantly improves upon the existing training ratio, region differentiation, and precision methods. The results demonstrate that the proposed method is effective, with a 9.83% drop in mistake rate and a 14.55% drop in differentiating time. This study’s findings highlight the value of adaptable neural networks for haze reduction without losing image quality. The research concludes with a positive outlook on the future of haze reduction methods, which should lead to better visual clarity and overall performance across a wide range of computer vision applications. Full article

(This article belongs to the Special Issue Advanced Topics in Nonlinear Programming and Its Application in Robotic Control)

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21 pages, 4350 KiB

Open AccessArticle

Generalized Framework for Liquid Neural Network upon Sequential and Non-Sequential Tasks

by Prakash Kumar Karn, Iman Ardekani and Waleed H. Abdulla

Mathematics 2024, 12(16), 2525; https://doi.org/10.3390/math12162525 - 15 Aug 2024

Abstract

This paper introduces a novel approach to neural networks: a Generalized Liquid Neural Network (GLNN) framework. This design excels at handling both sequential and non-sequential tasks. By leveraging the Runge Kutta DOPRI method, the GLNN enables dynamic simulation of complex systems across diverse [...] Read more.

This paper introduces a novel approach to neural networks: a Generalized Liquid Neural Network (GLNN) framework. This design excels at handling both sequential and non-sequential tasks. By leveraging the Runge Kutta DOPRI method, the GLNN enables dynamic simulation of complex systems across diverse fields. Our research demonstrates the framework’s capabilities through three key applications. In predicting damped sinusoidal trajectories, the Generalized LNN outperforms the neural ODE by approximately 46.03% and the conventional LNN by 57.88%. Modelling non-linear RLC circuits shows a 20% improvement in precision. Finally, in medical diagnosis through Optical Coherence Tomography (OCT) image analysis, our approach achieves an F1 score of 0.98, surpassing the classical LNN by 10%. These advancements signify a significant shift, opening new possibilities for neural networks in complex system modelling and healthcare diagnostics. This research advances the field by introducing a versatile and reliable neural network architecture. Full article

(This article belongs to the Special Issue Machine-Learning-Based Process and Analysis of Medical Images)

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17 pages, 1195 KiB

Open AccessArticle

Separable CenterNet Detection Network Based on MobileNetV3—An Optimization Approach for Small-Object and Occlusion Issues

by Zhengkuo Jiao, Heng Dong and Naizhe Diao

Mathematics 2024, 12(16), 2524; https://doi.org/10.3390/math12162524 - 15 Aug 2024

Abstract

This paper proposes a novel object detection method to address the challenges posed by small objects and occlusion in object detection. This work is performed within the CenterNet framework, leveraging the MobileNetV3 backbone to model the input image’s abstract representation in a lightweight [...] Read more.

This paper proposes a novel object detection method to address the challenges posed by small objects and occlusion in object detection. This work is performed within the CenterNet framework, leveraging the MobileNetV3 backbone to model the input image’s abstract representation in a lightweight manner. A sparse convolutional skip connection is introduced in the bottleneck of MobileNetV3, specifically designed to adaptively suppress redundant and interfering information, thus enhancing feature extraction capabilities. A Dual-Path Bidirectional Feature Pyramid Network (DBi-FPN) is incorporated, allowing for high-level feature fusion through bidirectional flow and significantly improving the detection capabilities for small objects and occlusions. Task heads are applied within the feature space of multi-scale information merged by DBi-FPN, facilitating comprehensive consideration of multi-level representations. A bounding box-area loss function is also introduced, aimed at enhancing the model’s adaptability to object morphologies and geometric distortions. Extensive experiments on the PASCAL VOC 2007 and MS COCO 2017 datasets validate the competitiveness of our proposed method, particularly in real-time applications on resource-constrained devices. Our contributions offer promising avenues for enhancing the accuracy and robustness of object detection systems in complex scenarios. Full article

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16 pages, 596 KiB

Open AccessArticle

Modifications to the Jarque–Bera Test

by Vladimir Glinskiy, Yulia Ismayilova, Sergey Khrushchev, Artem Logachov, Olga Logachova, Lyudmila Serga, Anatoly Yambartsev and Kirill Zaykov

Mathematics 2024, 12(16), 2523; https://doi.org/10.3390/math12162523 - 15 Aug 2024

Abstract

The Jarque–Bera test is commonly used in statistics and econometrics to test the hypothesis that sample elements adhere to a normal distribution with an unknown mean and variance. This paper proposes several modifications to this test, allowing for testing hypotheses that the considered [...] Read more.

The Jarque–Bera test is commonly used in statistics and econometrics to test the hypothesis that sample elements adhere to a normal distribution with an unknown mean and variance. This paper proposes several modifications to this test, allowing for testing hypotheses that the considered sample comes from: a normal distribution with a known mean (variance unknown); a normal distribution with a known variance (mean unknown); a normal distribution with a known mean and variance. For given significance levels,

α = 0.05

and

α = 0.01

, we compare the power of our normality test with the most well-known and popular tests using the Monte Carlo method: Kolmogorov–Smirnov (KS), Anderson–Darling (AD), Cramér–von Mises (CVM), Lilliefors (LF), and Shapiro–Wilk (SW) tests. Under the specific distributions, 1000 datasets were generated with the sample sizes

n = 25, 50, 75, 100, 150, 200, 250, 500,

and 1000. The simulation study showed that the suggested tests often have the best power properties. Our study also has a methodological nature, providing detailed proofs accessible to undergraduate students in statistics and probability, unlike the works of Jarque and Bera. Full article

(This article belongs to the Special Issue Mathematical Modeling and Applications in Industrial Organization)

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20 pages, 372 KiB

Open AccessArticle

Single-Machine Scheduling with Simultaneous Learning Effects and Delivery Times

by Zheng Liu and Ji-Bo Wang

Mathematics 2024, 12(16), 2522; https://doi.org/10.3390/math12162522 - 15 Aug 2024

Abstract

This paper studies the single-machine scheduling problem with truncated learning effect, time-dependent processing time, and past-sequence-dependent delivery time. The delivery time is the time that the job is delivered to the customer after processing is complete. The goal is to determine an optimal [...] Read more.

This paper studies the single-machine scheduling problem with truncated learning effect, time-dependent processing time, and past-sequence-dependent delivery time. The delivery time is the time that the job is delivered to the customer after processing is complete. The goal is to determine an optimal job schedule to minimize the total weighted completion time and maximum tardiness. In order to solve the general situation of the problem, we propose a branch-and-bound algorithm and other heuristic algorithms. Computational experiments also prove the effectiveness of the given algorithms. Full article

(This article belongs to the Special Issue Mathematical Methods and Operations Research in Planning, Scheduling and Supply Chain)

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31 pages, 1024 KiB

Open AccessArticle

Hybrid Bio-Optimized Algorithms for Hyperparameter Tuning in Machine Learning Models: A Software Defect Prediction Case Study

by Madhusmita Das, Biju R. Mohan, Ram Mohana Reddy Guddeti and Nandini Prasad

Mathematics 2024, 12(16), 2521; https://doi.org/10.3390/math12162521 - 15 Aug 2024

Abstract

Addressing real-time optimization problems becomes increasingly challenging as their complexity continues to escalate over time. So bio-optimization algorithms (BoAs) come into the picture to solve such problems due to their global search capability, adaptability, versatility, parallelism, and robustness. This article aims to perform [...] Read more.

Addressing real-time optimization problems becomes increasingly challenging as their complexity continues to escalate over time. So bio-optimization algorithms (BoAs) come into the picture to solve such problems due to their global search capability, adaptability, versatility, parallelism, and robustness. This article aims to perform hyperparameter tuning of machine learning (ML) models by integrating them with BoAs. Aiming to maximize the accuracy of the hybrid bio-optimized defect prediction (HBoDP) model, this research paper develops four novel hybrid BoAs named the gravitational force Lévy flight grasshopper optimization algorithm (GFLFGOA), the gravitational force Lévy flight grasshopper optimization algorithm–sparrow search algorithm (GFLFGOA-SSA), the gravitational force grasshopper optimization algorithm–sparrow search algorithm (GFGOA-SSA), and the Lévy flight grasshopper optimization algorithm–sparrow search algorithm (LFGOA-SSA). These aforementioned algorithms are proposed by integrating the good exploration capacity of the SSA with the faster convergence of the LFGOA and GFGOA. The performances of the GFLFGOA, GFLFGOA-SSA, GFGOA-SSA, and LFGOA-SSA are verified by conducting two different experiments. Firstly, the experimentation was conducted on nine benchmark functions (BFs) to assess the mean, standard deviation (SD), and convergence rate. The second experiment focuses on boosting the accuracy of the HBoDP model through the fine-tuning of the hyperparameters in the artificial neural network (ANN) and XGBOOST (XGB) models. To justify the effectiveness and performance of these hybrid novel algorithms, we compared them with four base algorithms, namely the grasshopper optimization algorithm (GOA), the sparrow search algorithm (SSA), the gravitational force grasshopper optimization algorithm (GFGOA), and the Lévy flight grasshopper optimization algorithm (LFGOA). Our findings illuminate the effectiveness of this hybrid approach in enhancing the convergence rate and accuracy. The experimental results show a faster convergence rate for BFs and improvements in software defect prediction accuracy for the NASA defect datasets by comparing them with some baseline methods. Full article

(This article belongs to the Section Mathematics and Computer Science)

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17 pages, 31026 KiB

Open AccessArticle

Addressing Noisy Pixels in Weakly Supervised Semantic Segmentation with Weights Assigned

by Feng Qian, Juan Yang, Sipeng Tang, Gao Chen and Jingwen Yan

Mathematics 2024, 12(16), 2520; https://doi.org/10.3390/math12162520 - 15 Aug 2024

Abstract

Weakly supervised semantic segmentation (WSSS) aims to segment objects without a heavy burden of dense annotations. Pseudo-masks serve as supervisory information for training segmentation models, which is crucial to the performance of segmentation models. However, the generated pseudo-masks contain significant noisy labels, which [...] Read more.

Weakly supervised semantic segmentation (WSSS) aims to segment objects without a heavy burden of dense annotations. Pseudo-masks serve as supervisory information for training segmentation models, which is crucial to the performance of segmentation models. However, the generated pseudo-masks contain significant noisy labels, which leads to poor performance of the segmentation models trained on these pseudo-masks. Few studies address this issue, as these noisy labels remain inevitable even after the pseudo-masks are improved. In this paper, we propose an uncertainty-weight transform module to mitigate the impact of noisy labels on model performance. It is noteworthy that our approach is not aimed at eliminating noisy labels but rather enhancing the robustness of the model to noisy labels. The proposed method adopts a frequency-based approach to estimate pixel uncertainty. Moreover, the uncertainty of pixels is transformed into loss weights through a set of well-designed functions. After dynamically assigning weights, the model allocates attention to each pixel in a significantly differentiated manner. Meanwhile, the impact of noisy labels on model performance is weakened. Experiments validate the effectiveness of the proposed method, achieving state-of-the-art results of 69.3% on PASCAL VOC 2012 and 39.3% on MS COCO 2014, respectively. Full article

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20 pages, 351 KiB

Open AccessArticle

Finite Element Method for a Fractional-Order Filtration Equation with a Transient Filtration Law

by Nurlana Alimbekova, Abdumauvlen Berdyshev, Muratkan Madiyarov and Yerlan Yergaliyev

Mathematics 2024, 12(16), 2519; https://doi.org/10.3390/math12162519 - 15 Aug 2024

Abstract

In this article, a numerical method is proposed and investigated for an initial boundary value problem governed by a fractional differential generalization of the nonlinear transient filtration law which describes fluid motion in a porous medium. This type of equation is widely used [...] Read more.

In this article, a numerical method is proposed and investigated for an initial boundary value problem governed by a fractional differential generalization of the nonlinear transient filtration law which describes fluid motion in a porous medium. This type of equation is widely used to describe complex filtration processes such as fluid movement in horizontal wells in fractured geological formations. To construct the numerical method, a high-order approximation formula for the fractional derivative in the sense of Caputo is applied, and a combination of the finite difference method with the finite element method is used. The article proves the uniqueness and continuous dependence of the solution on the input data in differential form, as well as the stability and convergence of the proposed numerical scheme. The linearization of nonlinear terms is carried out by the Newton method, which allows for achieving high accuracy in solving complex problems. The research results are confirmed by a series of numerical tests that demonstrate the applicability of the developed method in real engineering problems. The practical significance of the presented approach lies in its ability to accurately and effectively model filtration processes in shale formations, which allows engineers and geologists to make more informed decisions when designing and operating oil fields. Full article

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