In recent years, the method of using graph neural networks (GNN) to learn users’ social influence has been widely applied to social recommendation and has shown effectiveness, but several important challenges have not been well addressed: (i) Most work fails to consider the user interests (historical user-item interactions) when first building user-user social relationships, which can make it difficult to capture accurate user embedding and thus prevent the model from better exploring the users’ social influence; (ii) Most of the current methods do not build social neighbors (with the same item-user interaction) that belong to the item and do not aggregate information from the perspective of social neighbors, which makes it possible for the item to lose a lot of details when expressing the user’s interest factors. Therefore, to address the above challenges, we propose Exploring Implicit Influence for Social Recommendation Based on GNN (EIIGNN). First, we construct the initial user embedding with user-item interaction information and use the implicit modeling module in user modeling to explore the implicit influence of interest factors on users. In addition, EIIGNN models the social graph structure of item (an item-item graph) so that item can aggregate information from the perspective of their social neighbors, which helps the model learn a more accurate representation of the item. Finally, extensive experimental results on two real-world datasets clearly demonstrate the effectiveness of EIIGNN.
近年来,利用图神经网络(GNN)学习用户社交影响力的方法已被广泛应用于社交推荐,并显示出了良好的效果,但有几个重要的挑战并没有得到很好的解决:(i) 大多数工作在首次构建用户-用户社交关系时没有考虑用户兴趣(用户-物品的历史交互),这可能导致难以捕捉到准确的用户嵌入,从而使模型无法更好地探索用户的社交影响力;(ii) 目前的大多数方法没有构建属于物品的社交邻居(具有相同的物品-用户交互),也没有从社交邻居的角度进行信息聚合,这使得物品在表达用户兴趣因素时可能会丢失很多细节。因此,为了解决上述难题,我们提出了基于 GNN 的 "探索社交推荐的内隐影响"(Exploring Implicit Influence for Social Recommendation Based on GNN,EIIGNN)。首先,我们利用用户-物品交互信息构建初始用户嵌入,并利用用户建模中的隐式建模模块探索兴趣因素对用户的隐式影响。此外,EIIGNN 对项目的社交图结构(项目-项目图)进行建模,使项目可以从其社交邻居的角度聚合信息,从而帮助模型学习到更准确的项目表征。最后,在两个真实世界数据集上的大量实验结果清楚地证明了 EIIGNN 的有效性。
{"title":"Exploring implicit influence for social recommendation based on GNN","authors":"Zhewei Liu, Peilin Yang, Qingbo Hao, Wenguang Zheng, Yingyuan Xiao","doi":"10.1007/s00500-024-09898-3","DOIUrl":"https://doi.org/10.1007/s00500-024-09898-3","url":null,"abstract":"<p>In recent years, the method of using graph neural networks (GNN) to learn users’ social influence has been widely applied to social recommendation and has shown effectiveness, but several important challenges have not been well addressed: (i) Most work fails to consider the user interests (historical user-item interactions) when first building user-user social relationships, which can make it difficult to capture accurate user embedding and thus prevent the model from better exploring the users’ social influence; (ii) Most of the current methods do not build social neighbors (with the same item-user interaction) that belong to the item and do not aggregate information from the perspective of social neighbors, which makes it possible for the item to lose a lot of details when expressing the user’s interest factors. Therefore, to address the above challenges, we propose Exploring Implicit Influence for Social Recommendation Based on GNN (EIIGNN). First, we construct the initial user embedding with user-item interaction information and use the implicit modeling module in user modeling to explore the implicit influence of interest factors on users. In addition, EIIGNN models the social graph structure of item (an item-item graph) so that item can aggregate information from the perspective of their social neighbors, which helps the model learn a more accurate representation of the item. Finally, extensive experimental results on two real-world datasets clearly demonstrate the effectiveness of EIIGNN.</p>","PeriodicalId":22039,"journal":{"name":"Soft Computing","volume":"10 1","pages":""},"PeriodicalIF":4.1,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141779215","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-25DOI: 10.1007/s00500-024-09931-5
Salim Rezvani, Farhad Pourpanah, Chee Peng Lim, Q. M. Jonathan Wu
This paper presents a review on methods for class-imbalanced learning with the Support Vector Machine (SVM) and its variants. We first explain the structure of SVM and its variants and discuss their inefficiency in learning with class-imbalanced data sets. We introduce a hierarchical categorization of SVM-based models with respect to class-imbalanced learning. Specifically, we categorize SVM-based models into re-sampling, algorithmic, and fusion methods, and discuss the principles of the representative models in each category. In addition, we conduct a series of empirical evaluations to compare the performances of various representative SVM-based models in each category using benchmark imbalanced data sets, ranging from low to high imbalanced ratios. Our findings reveal that while algorithmic methods are less time-consuming owing to no data pre-processing requirements, fusion methods, which combine both re-sampling and algorithmic approaches, generally perform the best, but with a higher computational load. A discussion on research gaps and future research directions is provided.
{"title":"Methods for class-imbalanced learning with support vector machines: a review and an empirical evaluation","authors":"Salim Rezvani, Farhad Pourpanah, Chee Peng Lim, Q. M. Jonathan Wu","doi":"10.1007/s00500-024-09931-5","DOIUrl":"https://doi.org/10.1007/s00500-024-09931-5","url":null,"abstract":"<p>This paper presents a review on methods for class-imbalanced learning with the Support Vector Machine (SVM) and its variants. We first explain the structure of SVM and its variants and discuss their inefficiency in learning with class-imbalanced data sets. We introduce a hierarchical categorization of SVM-based models with respect to class-imbalanced learning. Specifically, we categorize SVM-based models into re-sampling, algorithmic, and fusion methods, and discuss the principles of the representative models in each category. In addition, we conduct a series of empirical evaluations to compare the performances of various representative SVM-based models in each category using benchmark imbalanced data sets, ranging from low to high imbalanced ratios. Our findings reveal that while algorithmic methods are less time-consuming owing to no data pre-processing requirements, fusion methods, which combine both re-sampling and algorithmic approaches, generally perform the best, but with a higher computational load. A discussion on research gaps and future research directions is provided.</p>","PeriodicalId":22039,"journal":{"name":"Soft Computing","volume":"16 1","pages":""},"PeriodicalIF":4.1,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141785936","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-24DOI: 10.1007/s00500-024-09910-w
Tran Thanh Dai, Nguyen Long Giang, Vu Duc Thi, Tran Thi Ngan, Hoang Thi Minh Chau, Le Hoang Son
Most of the current attribute reduction methods use the measure to define the reduct, such as the positive region of rough set theory (RS), information entropy, and distance. However, the size of the reduct based on the measures is still limited. To cope with this problem, we propose a new approach of attribute reduction based on using the intuitionistic fuzzy topology (IFT). Firstly, a new IFT structure based on the pre-order relation and the intuitionistic fuzzy base (IF-base) structure is introduced. Secondly, a new measure is proposed to evaluate the significance of the attribute based on the IF subbase. Finally, the new reduction algorithms based on the IF-base filter and filter-wrapper methods are presented. The theoretical and experimental results show that the proposed method is efficient in terms of size and accuracy of the reduct. Specifically, the reduct of the F_IFT algorithm has an average size of 50% smaller, and the FW_IFT algorithm has an average accuracy of 10% greater than those of the related algorithms. Significantly, the algorithm FW_IFT can very remove noisy attributes. The classification accuracy of the reduct is 15% higher than that of the original set of attributes.
目前的属性还原方法大多使用度量来定义还原,如粗糙集理论(RS)的正区域、信息熵和距离。然而,基于度量的还原规模仍然有限。针对这一问题,我们提出了一种基于直觉模糊拓扑(IFT)的属性还原新方法。首先,我们引入了一种基于前序关系和直觉模糊基(IF-base)结构的新 IFT 结构。其次,提出了一种新的度量方法,用于评估基于 IF 子基的属性的重要性。最后,介绍了基于 IF 基滤波器和滤波器包装器方法的新还原算法。理论和实验结果表明,所提出的方法在还原的规模和准确性方面都很有效。具体来说,与相关算法相比,F_IFT 算法的还原规模平均缩小了 50%,FW_IFT 算法的平均精度提高了 10%。值得注意的是,FW_IFT 算法可以很好地去除噪声属性。还原后的分类准确率比原始属性集的分类准确率高 15%。
{"title":"A new approach for attribute reduction from decision table based on intuitionistic fuzzy topology","authors":"Tran Thanh Dai, Nguyen Long Giang, Vu Duc Thi, Tran Thi Ngan, Hoang Thi Minh Chau, Le Hoang Son","doi":"10.1007/s00500-024-09910-w","DOIUrl":"https://doi.org/10.1007/s00500-024-09910-w","url":null,"abstract":"<p>Most of the current attribute reduction methods use the measure to define the reduct, such as the positive region of rough set theory (RS), information entropy, and distance. However, the size of the reduct based on the measures is still limited. To cope with this problem, we propose a new approach of attribute reduction based on using the intuitionistic fuzzy topology (IFT). Firstly, a new IFT structure based on the pre-order relation and the intuitionistic fuzzy base (IF-base) structure is introduced. Secondly, a new measure is proposed to evaluate the significance of the attribute based on the IF subbase. Finally, the new reduction algorithms based on the IF-base filter and filter-wrapper methods are presented. The theoretical and experimental results show that the proposed method is efficient in terms of size and accuracy of the reduct. Specifically, the reduct of the F_IFT algorithm has an average size of 50% smaller, and the FW_IFT algorithm has an average accuracy of 10% greater than those of the related algorithms. Significantly, the algorithm FW_IFT can very remove noisy attributes. The classification accuracy of the reduct is 15% higher than that of the original set of attributes.</p>","PeriodicalId":22039,"journal":{"name":"Soft Computing","volume":"63 1","pages":""},"PeriodicalIF":4.1,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141779221","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-24DOI: 10.1007/s00500-024-09847-0
Banghee So, Emiliano A. Valdez
Classification predictive modeling involves the accurate assignment of observations in a dataset to target classes or categories. Real-world classification problems with severely imbalanced class distributions have increased substantially in recent years. In such cases, significantly fewer observations are available for minority classes to learn from than for majority classes. Despite this sparsity, the minority class is often considered as the more interesting class, yet the development of a scientific learning algorithm that is suitable for these observations presents numerous challenges. In this study, we further explore the merits of an effective multi-class classification algorithm known as SAMME.C2 that is specialized for handling severely imbalanced classes. This innovative method blends the flexible mechanics of the boosting techniques from the SAMME algorithm, which is a multi-class classifier, and the Ada.C2 algorithm, which is a cost-sensitive binary classifier that is designed to address highly imbalanced classes. We establish a scientific and statistical formulation of the SAMME.C2 algorithm, together with providing and explaining the resulting procedure. We demonstrate the consistently superior performance of this algorithm through numerical experiments as well as empirical studies.
分类预测建模涉及将数据集中的观测结果准确分配到目标类或类别中。近年来,现实世界中严重失衡类分布的分类问题大幅增加。在这种情况下,少数类可用于学习的观测数据明显少于多数类。尽管存在这种稀缺性,少数类往往被认为是更有趣的类,但开发适合这些观察结果的科学学习算法却面临诸多挑战。在本研究中,我们进一步探索了一种名为 SAMME.C2 的有效多类分类算法的优点,该算法专门用于处理严重不平衡的类。这种创新方法融合了 SAMME 算法(一种多类分类器)和 Ada.C2 算法(一种成本敏感的二进制分类器,专为处理高度不平衡类而设计)中提升技术的灵活机制。我们对 SAMME.C2 算法进行了科学的统计表述,并提供和解释了由此产生的程序。我们通过数值实验和实证研究证明了该算法始终如一的卓越性能。
{"title":"SAMME.C2 algorithm for imbalanced multi-class classification","authors":"Banghee So, Emiliano A. Valdez","doi":"10.1007/s00500-024-09847-0","DOIUrl":"https://doi.org/10.1007/s00500-024-09847-0","url":null,"abstract":"<p>Classification predictive modeling involves the accurate assignment of observations in a dataset to target classes or categories. Real-world classification problems with severely imbalanced class distributions have increased substantially in recent years. In such cases, significantly fewer observations are available for minority classes to learn from than for majority classes. Despite this sparsity, the minority class is often considered as the more interesting class, yet the development of a scientific learning algorithm that is suitable for these observations presents numerous challenges. In this study, we further explore the merits of an effective multi-class classification algorithm known as <span>SAMME.C2</span> that is specialized for handling severely imbalanced classes. This innovative method blends the flexible mechanics of the boosting techniques from the <span>SAMME</span> algorithm, which is a multi-class classifier, and the <span>Ada.C2</span> algorithm, which is a cost-sensitive binary classifier that is designed to address highly imbalanced classes. We establish a scientific and statistical formulation of the <span>SAMME.C2</span> algorithm, together with providing and explaining the resulting procedure. We demonstrate the consistently superior performance of this algorithm through numerical experiments as well as empirical studies.</p>","PeriodicalId":22039,"journal":{"name":"Soft Computing","volume":"51 1","pages":""},"PeriodicalIF":4.1,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141785950","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Community detection is a valuable tool for studying the function and dynamic structure of most real-world networks. Existing techniques either concentrate on the network's topological structure or node properties without adequately addressing the dynamic aspect. As a result, in this research, we present a unique technique called Multi-Objective Optimization Overlapping Dynamic Community Detection (MOOODCD) that leverages both the topological structure and node attributes of dynamic networks. By incorporating the Dirichlet distribution to control network dynamics, we formulate dynamic community detection as a non-negative matrix factorization problem. The block coordinate ascent method is used to estimate the latent elements of the model. Our experiments on artificial and real networks indicate that MOOODCD detects overlapping communities in dynamic networks with acceptable precision and scalability.
{"title":"A multi-objective optimization approach for overlapping dynamic community detection","authors":"Sondos Bahadori, Mansooreh Mirzaie, Maryam Nooraei Abadeh","doi":"10.1007/s00500-024-09895-6","DOIUrl":"https://doi.org/10.1007/s00500-024-09895-6","url":null,"abstract":"<p>Community detection is a valuable tool for studying the function and dynamic structure of most real-world networks. Existing techniques either concentrate on the network's topological structure or node properties without adequately addressing the dynamic aspect. As a result, in this research, we present a unique technique called Multi-Objective Optimization Overlapping Dynamic Community Detection (MOOODCD) that leverages both the topological structure and node attributes of dynamic networks. By incorporating the Dirichlet distribution to control network dynamics, we formulate dynamic community detection as a non-negative matrix factorization problem. The block coordinate ascent method is used to estimate the latent elements of the model. Our experiments on artificial and real networks indicate that MOOODCD detects overlapping communities in dynamic networks with acceptable precision and scalability.</p>","PeriodicalId":22039,"journal":{"name":"Soft Computing","volume":"73 1","pages":""},"PeriodicalIF":4.1,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141785954","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-24DOI: 10.1007/s00500-024-09892-9
Kadir Karakaya
In various applied disciplines, the modeling of continuous data often requires the use of flexible continuous distributions. Meeting this demand calls for the introduction of new continuous distributions that possess desirable characteristics. This paper introduces a new continuous distribution. Several estimators for estimating the unknown parameters of the new distribution are discussed and their efficiency is assessed through Monte Carlo simulations. Furthermore, the process capability index (S_{pmk}) is examined when the underlying distribution is the proposed distribution. The maximum likelihood estimation of the (S_{pmk}) is also studied. The asymptotic confidence interval is also constructed for (S_{pmk}). The simulation results indicate that estimators for both the unknown parameters of the new distribution and the (S_{pmk}) provide reasonable results. Some practical analyses are also performed on both the new distribution and the (S_{pmk}). The results of the conducted data analysis indicate that the new distribution yields effective outcomes in modeling lifetime data in the literature. Similarly, the data analyses performed for (S_{pmk}) illustrate that the new distribution can be utilized for process capability indices by quality controllers.
{"title":"Inference on process capability index $$S_{pmk}$$ for a new lifetime distribution","authors":"Kadir Karakaya","doi":"10.1007/s00500-024-09892-9","DOIUrl":"https://doi.org/10.1007/s00500-024-09892-9","url":null,"abstract":"<p>In various applied disciplines, the modeling of continuous data often requires the use of flexible continuous distributions. Meeting this demand calls for the introduction of new continuous distributions that possess desirable characteristics. This paper introduces a new continuous distribution. Several estimators for estimating the unknown parameters of the new distribution are discussed and their efficiency is assessed through Monte Carlo simulations. Furthermore, the process capability index <span>(S_{pmk})</span> is examined when the underlying distribution is the proposed distribution. The maximum likelihood estimation of the <span>(S_{pmk})</span> is also studied. The asymptotic confidence interval is also constructed for <span>(S_{pmk})</span>. The simulation results indicate that estimators for both the unknown parameters of the new distribution and the <span>(S_{pmk})</span> provide reasonable results. Some practical analyses are also performed on both the new distribution and the <span>(S_{pmk})</span>. The results of the conducted data analysis indicate that the new distribution yields effective outcomes in modeling lifetime data in the literature. Similarly, the data analyses performed for <span>(S_{pmk})</span> illustrate that the new distribution can be utilized for process capability indices by quality controllers.</p>","PeriodicalId":22039,"journal":{"name":"Soft Computing","volume":"821 1","pages":""},"PeriodicalIF":4.1,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141779090","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-24DOI: 10.1007/s00500-024-09950-2
Francisco Javier Maldonado Carrascosa, Doraid Seddiki, Antonio Jiménez Sánchez, Sebastián García Galán, Manuel Valverde Ibáñez, Adam Marchewka
Workload migration among cloud data centers is currently an evolving task that requires substantial advancements. The incorporation of fuzzy systems holds potential for enhancing performance and efficiency within cloud computing. This study addresses a multi-objective problem wherein the goal is to maximize the interpretability and the percentage of renewable energy consumed by a fuzzy meta-scheduler system in cloud scenarios. To accomplish this objective, the present research proposes a novel approach utilizing a multi-objective Knowledge Acquisition with a Swarm Intelligence Approach algorithm. Additionally, it takes advantage of a framework built on CloudSim, which includes virtual machine migration capabilities based on an expert system. Furthermore, a hierarchical fuzzy system is employed to assess rule base interpretability, along with another multi-objective algorithm, named Non-dominated Sorting Genetic Algorithm II. The framework and hierarchical system are employed to perform various simulation results concerning renewable energy and interpretability, while the algorithms aim to enhance the system’s performance and interpretability. Empirical results demonstrate that it is possible to improve the performance of cloud data centers while improving the interpretability of the corresponding fuzzy rule-based system. The proposed multi-objective algorithm shows comparable or superior performance to the genetic algorithm across diverse scenarios. The simulation results indicate that improvements in cloud data center performance can be achieved while enhancing system interpretability. The average improvement in the interpretability index ranges from 0.6 to 6%, with a corresponding increase in renewable energy utilization ranging from 5 to 6%.
{"title":"Multi-objective optimization of virtual machine migration among cloud data centers","authors":"Francisco Javier Maldonado Carrascosa, Doraid Seddiki, Antonio Jiménez Sánchez, Sebastián García Galán, Manuel Valverde Ibáñez, Adam Marchewka","doi":"10.1007/s00500-024-09950-2","DOIUrl":"https://doi.org/10.1007/s00500-024-09950-2","url":null,"abstract":"<p>Workload migration among cloud data centers is currently an evolving task that requires substantial advancements. The incorporation of fuzzy systems holds potential for enhancing performance and efficiency within cloud computing. This study addresses a multi-objective problem wherein the goal is to maximize the interpretability and the percentage of renewable energy consumed by a fuzzy meta-scheduler system in cloud scenarios. To accomplish this objective, the present research proposes a novel approach utilizing a multi-objective Knowledge Acquisition with a Swarm Intelligence Approach algorithm. Additionally, it takes advantage of a framework built on CloudSim, which includes virtual machine migration capabilities based on an expert system. Furthermore, a hierarchical fuzzy system is employed to assess rule base interpretability, along with another multi-objective algorithm, named Non-dominated Sorting Genetic Algorithm II. The framework and hierarchical system are employed to perform various simulation results concerning renewable energy and interpretability, while the algorithms aim to enhance the system’s performance and interpretability. Empirical results demonstrate that it is possible to improve the performance of cloud data centers while improving the interpretability of the corresponding fuzzy rule-based system. The proposed multi-objective algorithm shows comparable or superior performance to the genetic algorithm across diverse scenarios. The simulation results indicate that improvements in cloud data center performance can be achieved while enhancing system interpretability. The average improvement in the interpretability index ranges from 0.6 to 6%, with a corresponding increase in renewable energy utilization ranging from 5 to 6%.</p>","PeriodicalId":22039,"journal":{"name":"Soft Computing","volume":"43 1","pages":""},"PeriodicalIF":4.1,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141779223","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Learning high order non-oscillatory polynomial approximation procedures which form the backbone of high order numerical solution of partial differential equations is challenging. The major issue is to pose these procedures as a learning problem and generate suitable synthetic data set which suffice learning it with small neural networks. In this work, we pose an arc-length based essentially non-oscillatory (ENOL) reconstruction algorithm as machine learning problem. A novel way to construct the synthetic data using ENOL algorithm along with basic smooth and piece-wise continuous functions is given. Small vanilla regression and classification neural networks are trained to learn third order (ENOL) polynomial approximation procedure. The metric of trained ENO classification and regression networks is presented and commented. These trained models are implemented in numerical solver to compute the solution of test problems of hyperbolic conservation laws. The presented numerical results show that ENO classification network gives results comparable to the exact ENOL reconstruction whereas ENO regression network performs poorly both in terms of convergence and resolving the discontinuities.
高阶非振荡多项式近似程序是偏微分方程高阶数值解法的基础,学习这些程序具有挑战性。主要的问题是将这些程序作为一个学习问题,并生成合适的合成数据集,以便用小型神经网络学习这些程序。在这项工作中,我们将基于弧长的本质非振荡(ENOL)重构算法作为机器学习问题。我们给出了一种使用 ENOL 算法以及基本平滑和片断连续函数构建合成数据的新方法。通过训练小香草回归和分类神经网络来学习三阶(ENOL)多项式近似程序。介绍并评论了经过训练的 ENO 分类和回归网络的度量。这些训练有素的模型在数值求解器中实施,以计算双曲守恒定律测试问题的解决方案。给出的数值结果表明,ENO 分类网络给出的结果与精确的 ENOL 重建结果相当,而 ENO 回归网络在收敛性和解决不连续性方面表现不佳。
{"title":"Eno classification and regression neural networks for numerical approximation of discontinuous flow problems","authors":"Vikas Kumar Jayswal, Prashant Kumar Pandey, Ritesh Kumar Dubey","doi":"10.1007/s00500-024-09944-0","DOIUrl":"https://doi.org/10.1007/s00500-024-09944-0","url":null,"abstract":"<p>Learning high order non-oscillatory polynomial approximation procedures which form the backbone of high order numerical solution of partial differential equations is challenging. The major issue is to pose these procedures as a learning problem and generate suitable synthetic data set which suffice learning it with small neural networks. In this work, we pose an arc-length based essentially non-oscillatory (ENOL) reconstruction algorithm as machine learning problem. A novel way to construct the synthetic data using ENOL algorithm along with basic smooth and piece-wise continuous functions is given. Small vanilla regression and classification neural networks are trained to learn third order (ENOL) polynomial approximation procedure. The metric of trained ENO classification and regression networks is presented and commented. These trained models are implemented in numerical solver to compute the solution of test problems of hyperbolic conservation laws. The presented numerical results show that ENO classification network gives results comparable to the exact ENOL reconstruction whereas ENO regression network performs poorly both in terms of convergence and resolving the discontinuities.</p>","PeriodicalId":22039,"journal":{"name":"Soft Computing","volume":"43 1","pages":""},"PeriodicalIF":4.1,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141785948","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-24DOI: 10.1007/s00500-024-09925-3
Saumya Ranjan Jena, Archana Senapati
This study uses the cubic spline method to solve the one-dimensional (1D) (one spatial and one temporal dimension) heat problem (a parametric linear partial differential equation) numerically using both explicit and implicit strategies. The set of simultaneous equations acquired in both the explicit and implicit method may be solved using the Thomas algorithm from the tridiagonal dominating matrix, and the spline offers a continuous solution. The results are implemented with very fine meshes and with relatively small-time steps. Using mesh refinement, it was possible to find better temperature distribution in the thin bar. Five numerical examples are used to support the efficiency and accuracy of the current scheme. The findings are also compared with analytical results and other results in terms of error and error norms ({L}_{2}) and ({L}_{infty }). The Von-Neuman technique is used to analyse stability. The truncation error of both systems is calculated and determined to have a convergence of order (Oleft( {h + Delta t^{2} } right).)
{"title":"Explicit and implicit numerical investigations of one-dimensional heat equation based on spline collocation and Thomas algorithm","authors":"Saumya Ranjan Jena, Archana Senapati","doi":"10.1007/s00500-024-09925-3","DOIUrl":"https://doi.org/10.1007/s00500-024-09925-3","url":null,"abstract":"<p>This study uses the cubic spline method to solve the one-dimensional (1D) (one spatial and one temporal dimension) heat problem (a parametric linear partial differential equation) numerically using both explicit and implicit strategies. The set of simultaneous equations acquired in both the explicit and implicit method may be solved using the Thomas algorithm from the tridiagonal dominating matrix, and the spline offers a continuous solution. The results are implemented with very fine meshes and with relatively small-time steps. Using mesh refinement, it was possible to find better temperature distribution in the thin bar. Five numerical examples are used to support the efficiency and accuracy of the current scheme. The findings are also compared with analytical results and other results in terms of error and error norms <span>({L}_{2})</span> and <span>({L}_{infty })</span>. The Von-Neuman technique is used to analyse stability. The truncation error of both systems is calculated and determined to have a convergence of order <span>(Oleft( {h + Delta t^{2} } right).)</span></p>","PeriodicalId":22039,"journal":{"name":"Soft Computing","volume":"178 1","pages":""},"PeriodicalIF":4.1,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141785949","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-24DOI: 10.1007/s00500-024-09893-8
Peixin Huang, Guo Zhou, Yongquan Zhou, Qifang Luo
Optimization problem involving interval parameters and multiple conflicting objectives are called multi-objective optimization problems with interval parameters (IMOPs), which are common and hard to be solved effectively in practical applications. An interval multi-objective honey badger algorithm (IMOHBA) is proposed to address the IMOPs in this paper. Firstly, the (mu) metric is employed to assess the Pareto dominance relationship among interval individuals, which reflects the quality of the optimal solutions. Secondly, the crowding distance suitable for the interval objective is utilized to reflect the distribution of the optimal solution. Finally, the candidate solutions are ranked and selected by the non-dominated sorting method. To validate the performance of IMOHBA, it is tested on 19 benchmark IMOPs as well as an interval multi-objective scheduling problem for underwater wireless sensor networks and compared with three state-of-the-art algorithms. The experimental results demonstrate the superiority and strong competitiveness of IMOHBA in addressing IMOPs, exhibiting improved convergence and broader exploration capabilities of the solution space. These findings further validate the effectiveness and feasibility of IMOHBA, highlighting its unique advantage in solving IMOPs.
{"title":"Interval-based multi-objective metaheuristic honey badger algorithm","authors":"Peixin Huang, Guo Zhou, Yongquan Zhou, Qifang Luo","doi":"10.1007/s00500-024-09893-8","DOIUrl":"https://doi.org/10.1007/s00500-024-09893-8","url":null,"abstract":"<p>Optimization problem involving interval parameters and multiple conflicting objectives are called multi-objective optimization problems with interval parameters (IMOPs), which are common and hard to be solved effectively in practical applications. An interval multi-objective honey badger algorithm (IMOHBA) is proposed to address the IMOPs in this paper. Firstly, the <span>(mu)</span> metric is employed to assess the Pareto dominance relationship among interval individuals, which reflects the quality of the optimal solutions. Secondly, the crowding distance suitable for the interval objective is utilized to reflect the distribution of the optimal solution. Finally, the candidate solutions are ranked and selected by the non-dominated sorting method. To validate the performance of IMOHBA, it is tested on 19 benchmark IMOPs as well as an interval multi-objective scheduling problem for underwater wireless sensor networks and compared with three state-of-the-art algorithms. The experimental results demonstrate the superiority and strong competitiveness of IMOHBA in addressing IMOPs, exhibiting improved convergence and broader exploration capabilities of the solution space. These findings further validate the effectiveness and feasibility of IMOHBA, highlighting its unique advantage in solving IMOPs.</p>","PeriodicalId":22039,"journal":{"name":"Soft Computing","volume":"1 1","pages":""},"PeriodicalIF":4.1,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141785952","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}