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Volume 27
Issue 6
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Math. Comput. Appl., Volume 27, Issue 6 (December 2022) – 25 articles

Cover Story (view full-size image): Large-scale multiobjective optimization arises in many application domains, and it deserves increasing attention from the multiobjective community, within which highly specialized algorithms have been proposed. This work elaborates on how the automatic configuration of NSGA-II with jMetal and irace allows this algorithm to properly address large-scale problems in both a real-coded benchmarking testbed and a binary-coded real-world scenario within 5G/6G networks. The figure illustrates the latter problem, showing three different base stations (BSs) usually deployed in these networks and their mapping into a binary-coded representation. One single BS may add up to 12 variables to a tentative solution, and hundreds of SBSs/km2 will be required, thus giving rise to a large-scale problem. View this paper
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27 pages, 888 KiB  
Review
MCDM, EMO and Hybrid Approaches: Tutorial and Review
by Ankur Sinha and Jyrki Wallenius
Math. Comput. Appl. 2022, 27(6), 112; https://doi.org/10.3390/mca27060112 - 19 Dec 2022
Cited by 1 | Viewed by 1875
Abstract
Most of the practical applications that require optimization often involve multiple objectives. These objectives, when conflicting in nature, pose both optimization as well as decision-making challenges. An optimization procedure for such a multi-objective problem requires computing (computer-based search) and decision making to identify [...] Read more.
Most of the practical applications that require optimization often involve multiple objectives. These objectives, when conflicting in nature, pose both optimization as well as decision-making challenges. An optimization procedure for such a multi-objective problem requires computing (computer-based search) and decision making to identify the most preferred solution. Researchers and practitioners working in various domains have integrated computing and decision-making tasks in several ways, giving rise to a variety of algorithms to handle multi-objective optimization problems. For instance, an a priori approach requires formulating (or eliciting) a decision maker’s value function and then performing a one-shot optimization of the value function, whereas an a posteriori decision-making approach requires a large number of diverse Pareto-optimal solutions to be available before a final decision is made. Alternatively, an interactive approach involves interactions with the decision maker to guide the search towards better solutions (or the most preferred solution). In our tutorial and survey paper, we first review the fundamental concepts of multi-objective optimization. Second, we discuss the classic interactive approaches from the field of Multi-Criteria Decision Making (MCDM), followed by the underlying idea and methods in the field of Evolutionary Multi-Objective Optimization (EMO). Third, we consider several promising MCDM and EMO hybrid approaches that aim to capitalize on the strengths of the two domains. We conclude with discussions on important behavioral considerations related to the use of such approaches and future work. Full article
(This article belongs to the Collection Numerical Optimization Reviews)
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22 pages, 606 KiB  
Article
A Survey on Newhouse Thickness, Fractal Intersections and Patterns
by Alexia Yavicoli
Math. Comput. Appl. 2022, 27(6), 111; https://doi.org/10.3390/mca27060111 - 14 Dec 2022
Cited by 1 | Viewed by 1406
Abstract
In this article, we introduce a notion of size for sets, called the thickness, that can be used to guarantee that two Cantor sets intersect (the Gap Lemma) and show a connection among thickness, Schmidt games and patterns. We work mostly in the [...] Read more.
In this article, we introduce a notion of size for sets, called the thickness, that can be used to guarantee that two Cantor sets intersect (the Gap Lemma) and show a connection among thickness, Schmidt games and patterns. We work mostly in the real line, but we also introduce the topic in higher dimensions. Full article
(This article belongs to the Special Issue Geometry of Deterministic and Random Fractals)
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13 pages, 4359 KiB  
Article
Go-MoS2/Water Flow over a Shrinking Cylinder with Stefan Blowing, Joule Heating, and Thermal Radiation
by Manoj Kumar Narayanaswamy, Jagan Kandasamy and Sivasankaran Sivanandam
Math. Comput. Appl. 2022, 27(6), 110; https://doi.org/10.3390/mca27060110 - 14 Dec 2022
Cited by 6 | Viewed by 1274
Abstract
The impacts of Stefan blowing along with slip and Joule heating on hybrid nanofluid (HNF) flow past a shrinking cylinder are investigated in the presence of thermal radiation. Using the suitable transformations, the governing equations are converted into ODEs, and the MATLAB tool [...] Read more.
The impacts of Stefan blowing along with slip and Joule heating on hybrid nanofluid (HNF) flow past a shrinking cylinder are investigated in the presence of thermal radiation. Using the suitable transformations, the governing equations are converted into ODEs, and the MATLAB tool bvp4c is used to solve the resulting equations. As Stefan blowing increases, temperature and concentration profiles are accelerated but the velocity profile diminishes and also the heat transfer rate improves up to 25% as thermal radiation upsurges. The mass transfer rate diminishes as increasing Stefan blowing. The Sherwood number, the Nusselt number, and the skin friction coefficient are numerically tabulated and graphs are also plotted. The outcomes are conscientiously and thoroughly discussed. Full article
(This article belongs to the Special Issue Mathematical and Computational Modeling on Fluid Flow and Heat Transfer)
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17 pages, 5824 KiB  
Article
Deep Convolutional Neural Network for Detection and Prediction of Waxy Corn Seed Viability Using Hyperspectral Reflectance Imaging
by Xiaoqing Zhao, Lei Pang, Lianming Wang, Sen Men and Lei Yan
Math. Comput. Appl. 2022, 27(6), 109; https://doi.org/10.3390/mca27060109 - 14 Dec 2022
Cited by 1 | Viewed by 1747
Abstract
This paper aimed to combine hyperspectral imaging (378–1042 nm) and a deep convolutional neural network (DCNN) to rapidly and non-destructively detect and predict the viability of waxy corn seeds. Different viability levels were set by artificial aging (aging: 0 d, 3 d, 6 [...] Read more.
This paper aimed to combine hyperspectral imaging (378–1042 nm) and a deep convolutional neural network (DCNN) to rapidly and non-destructively detect and predict the viability of waxy corn seeds. Different viability levels were set by artificial aging (aging: 0 d, 3 d, 6 d, and 9 d), and spectral data for the first 10 h of seed germination were continuously collected. Bands that were significantly correlated (SC) with moisture, protein, starch, and fat content in the seeds were selected, and another optimal combination was extracted using a successive projection algorithm (SPA). The support vector machine (SVM), k-nearest neighbor (KNN), random forest (RF), and deep convolutional neural network (DCNN) approaches were used to establish the viability detection and prediction models. During detection, with the addition of different levels, the recognition effect of the first three methods decreased, while the DCNN method remained relatively stable (always above 95%). When using the previous 2.5 h data, the prediction accuracy rate was generally higher than the detection model. Among them, SVM + full band increased the most, while DCNN + full band was the highest, reaching 98.83% accuracy. These results indicate that the combined use of hyperspectral imaging technology and the DCNN method is more conducive to the rapid detection and prediction of seed viability. Full article
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24 pages, 9994 KiB  
Article
Experimental and Numerical Investigation of the In-Plane Compression of Corrugated Paperboard Panels
by Johan Cillie and Corné Coetzee
Math. Comput. Appl. 2022, 27(6), 108; https://doi.org/10.3390/mca27060108 - 12 Dec 2022
Cited by 5 | Viewed by 1919
Abstract
Finite element analysis (FEA) has been proven as a useful design tool to model corrugated paperboard boxes, and is capable of accurately predicting load capacity. The in-plane deformation, however, is usually significantly underpredicted. To investigate this discrepancy, a panel compression test jig, that [...] Read more.
Finite element analysis (FEA) has been proven as a useful design tool to model corrugated paperboard boxes, and is capable of accurately predicting load capacity. The in-plane deformation, however, is usually significantly underpredicted. To investigate this discrepancy, a panel compression test jig, that implemented simply supported boundary conditions, was built to test individual panels. The panels were then modelled using non-linear FEA with a linear material model. The results show that the in-plane deformation was still underpredicted, but a general improvement was seen. Three discrepancies were identified. The first was that the panels showed an initial region of low stiffness that was not present in the FEA results. This was attributed to imperfections in the panels and jig. Secondly, the experimental results reported a lower stiffness than the FEA. Applying an initial imperfection in the shape of the first buckling mode shape was found to reduce the FEA stiffness. Thirdly, the panels showed a decrease in stiffness near failure, which was not seen in the FEA. A bi-linear material model was investigated and holds the potential to improve the results. Box compression tests were performed on a Regular Slotted Container (RSC) with the same dimensions as the tested panel. The box displaced 13.1 mm compared to 3.5 mm for the panel. There was an initial region of low stiffness, which accounted for 7 mm of displacement compared to 0.5 mm for the panels. Thus, box complexities such as horizontal creases should be included in finite element (FE) models to accurately predict the in-plane deformation, while a bi-linear (or any other non-linear) material model may be useful for panel compression. Full article
(This article belongs to the Special Issue Current Problems and Advances in Computational and Applied Mechanics)
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4 pages, 203 KiB  
Editorial
Preface to Numerical and Symbolic Computation: Developments and Applications—2021
by Maria Amélia R. Loja
Math. Comput. Appl. 2022, 27(6), 107; https://doi.org/10.3390/mca27060107 - 12 Dec 2022
Viewed by 803
Abstract
This is the Special Issue “Numerical and Symbolic Computation: Developments and Applications—2021”, also available at the Special Issue website https://www [...] Full article
(This article belongs to the Special Issue Numerical and Symbolic Computation: Developments and Applications 2021)
17 pages, 920 KiB  
Article
Knowledge-Driven Multi-Objective Optimization for Reconfigurable Manufacturing Systems
by Henrik Smedberg, Carlos Alberto Barrera-Diaz, Amir Nourmohammadi, Sunith Bandaru and Amos H. C. Ng
Math. Comput. Appl. 2022, 27(6), 106; https://doi.org/10.3390/mca27060106 - 09 Dec 2022
Cited by 1 | Viewed by 2237
Abstract
Current market requirements force manufacturing companies to face production changes more often than ever before. Reconfigurable manufacturing systems (RMS) are considered a key enabler in today’s manufacturing industry to cope with such dynamic and volatile markets. The literature confirms that the use of [...] Read more.
Current market requirements force manufacturing companies to face production changes more often than ever before. Reconfigurable manufacturing systems (RMS) are considered a key enabler in today’s manufacturing industry to cope with such dynamic and volatile markets. The literature confirms that the use of simulation-based multi-objective optimization offers a promising approach that leads to improvements in RMS. However, due to the dynamic behavior of real-world RMS, applying conventional optimization approaches can be very time-consuming, specifically when there is no general knowledge about the quality of solutions. Meanwhile, Pareto-optimal solutions may share some common design principles that can be discovered with data mining and machine learning methods and exploited by the optimization. In this study, the authors investigate a novel knowledge-driven optimization (KDO) approach to speed up the convergence in RMS applications. This approach generates generalized knowledge from previous scenarios, which is then applied to improve the efficiency of the optimization of new scenarios. This study applied the proposed approach to a multi-part flow line RMS that considers scalable capacities while addressing the tasks assignment to workstations and the buffer allocation problems. The results demonstrate how a KDO approach leads to convergence rate improvements in a real-world RMS case. Full article
(This article belongs to the Special Issue Evolutionary Multi-objective Optimization: An Honorary Issue Dedicated to Professor Kalyanmoy Deb)
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27 pages, 4189 KiB  
Article
New Lifetime Distribution for Modeling Data on the Unit Interval: Properties, Applications and Quantile Regression
by Suleman Nasiru, Abdul Ghaniyyu Abubakari and Christophe Chesneau
Math. Comput. Appl. 2022, 27(6), 105; https://doi.org/10.3390/mca27060105 - 03 Dec 2022
Cited by 3 | Viewed by 1610
Abstract
Probability distributions are very useful in modeling lifetime datasets. However, no specific distribution is suitable for all kinds of datasets. In this study, the bounded truncated Cauchy power exponential distribution is proposed for modeling datasets on the unit interval. The probability density function [...] Read more.
Probability distributions are very useful in modeling lifetime datasets. However, no specific distribution is suitable for all kinds of datasets. In this study, the bounded truncated Cauchy power exponential distribution is proposed for modeling datasets on the unit interval. The probability density function exhibits desirable shapes, such as left-skewed, right-skewed, reversed J, and bathtub shapes, whereas the hazard rate function displays J and bathtub shapes. For the purpose of modeling dependence between measures in a dataset, a bivariate extension of the proposed distribution is developed. The bivariate probability density function displays monotonic and non-monotonic shapes, making it suitable for modeling complex bivariate relations. Subsequently, the applications of the distribution are illustrated using COVID-19 data. The results revealed that the new distribution provides a better fit to the datasets compared to other existing distributions. Finally, a new quantile regression model is developed and its application demonstrated. The generated quantile regression model offers a decent fit to the data, according to the residual analysis. Full article
(This article belongs to the Special Issue Statistical Inference in Linear Models)
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23 pages, 4958 KiB  
Article
Flexible Parametric Accelerated Hazard Model: Simulation and Application to Censored Lifetime Data with Crossing Survival Curves
by Abdisalam Hassan Muse, Christophe Chesneau, Oscar Ngesa and Samuel Mwalili
Math. Comput. Appl. 2022, 27(6), 104; https://doi.org/10.3390/mca27060104 - 30 Nov 2022
Cited by 3 | Viewed by 1793
Abstract
This study aims to propose a flexible, fully parametric hazard-based regression model for censored time-to-event data with crossing survival curves. We call it the accelerated hazard (AH) model. The AH model can be written with or without a baseline distribution for lifetimes. The [...] Read more.
This study aims to propose a flexible, fully parametric hazard-based regression model for censored time-to-event data with crossing survival curves. We call it the accelerated hazard (AH) model. The AH model can be written with or without a baseline distribution for lifetimes. The former assumption results in parametric regression models, whereas the latter results in semi-parametric regression models, which are by far the most commonly used in time-to-event analysis. However, under certain conditions, a parametric hazard-based regression model may produce more efficient estimates than a semi-parametric model. The parametric AH model, on the other hand, is inappropriate when the baseline distribution is exponential because it is constant over time; similarly, when the baseline distribution is the Weibull distribution, the AH model coincides with the accelerated failure time (AFT) and proportional hazard (PH) models. The use of a versatile parametric baseline distribution (generalized log-logistic distribution) for modeling the baseline hazard rate function is investigated. For the parameters of the proposed AH model, the classical (via maximum likelihood estimation) and Bayesian approaches using noninformative priors are discussed. A comprehensive simulation study was conducted to assess the performance of the proposed model’s estimators. A real-life right-censored gastric cancer dataset with crossover survival curves is used to demonstrate the tractability and utility of the proposed fully parametric AH model. The study concluded that the parametric AH model is effective and could be useful for assessing a variety of survival data types with crossover survival curves. Full article
(This article belongs to the Special Issue Statistical Inference in Linear Models)
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17 pages, 929 KiB  
Article
Is NSGA-II Ready for Large-Scale Multi-Objective Optimization?
by Antonio J. Nebro, Jesús Galeano-Brajones, Francisco Luna and Carlos A. Coello Coello
Math. Comput. Appl. 2022, 27(6), 103; https://doi.org/10.3390/mca27060103 - 30 Nov 2022
Cited by 3 | Viewed by 3403
Abstract
NSGA-II is, by far, the most popular metaheuristic that has been adopted for solving multi-objective optimization problems. However, its most common usage, particularly when dealing with continuous problems, is circumscribed to a standard algorithmic configuration similar to the one described in its seminal [...] Read more.
NSGA-II is, by far, the most popular metaheuristic that has been adopted for solving multi-objective optimization problems. However, its most common usage, particularly when dealing with continuous problems, is circumscribed to a standard algorithmic configuration similar to the one described in its seminal paper. In this work, our aim is to show that the performance of NSGA-II, when properly configured, can be significantly improved in the context of large-scale optimization. It leverages a combination of tools for automated algorithmic tuning called irace, and a highly configurable version of NSGA-II available in the jMetal framework. Two scenarios are devised: first, by solving the Zitzler–Deb–Thiele (ZDT) test problems, and second, when dealing with a binary real-world problem of the telecommunications domain. Our experiments reveal that an auto-configured version of NSGA-II can properly address test problems ZDT1 and ZDT2 with up to 217=131,072 decision variables. The same methodology, when applied to the telecommunications problem, shows that significant improvements can be obtained with respect to the original NSGA-II algorithm when solving problems with thousands of bits. Full article
(This article belongs to the Special Issue Evolutionary Multi-objective Optimization: An Honorary Issue Dedicated to Professor Kalyanmoy Deb)
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18 pages, 8351 KiB  
Article
Role of Nanoparticles and Heat Source/Sink on MHD Flow of Cu-H2O Nanofluid Flow Past a Vertical Plate with Soret and Dufour Effects
by Ramesh Kune, Hari Singh Naik, Borra Shashidar Reddy and Christophe Chesneau
Math. Comput. Appl. 2022, 27(6), 102; https://doi.org/10.3390/mca27060102 - 28 Nov 2022
Cited by 5 | Viewed by 1507
Abstract
The study is devoted to investigating the effect of an unsteady non-Newtonian Casson fluid over a vertical plate. A mathematical analysis is presented for a Casson fluid by taking into consideration Soret and Dufour effects, heat generation, heat radiation, and chemical reaction. The [...] Read more.
The study is devoted to investigating the effect of an unsteady non-Newtonian Casson fluid over a vertical plate. A mathematical analysis is presented for a Casson fluid by taking into consideration Soret and Dufour effects, heat generation, heat radiation, and chemical reaction. The novelty of the problem is the physical interpretation of Casson fluid before and after adding copper water-based nanoparticles to the governing flow. It is found that velocity was decreased and the temperature profile was enhanced. A similarity transformation is used to convert the linked partial differential equations that control flow into non-linear coupled ordinary differential equations. The momentum, energy, and concentration formulations are cracked by means of the finite element method. The thermal and solute layer thickness growth is due to the nanoparticles’ thermo-diffusion. The effects of relevant parameters such as the Casson fluid parameter, radiation, Soret and Dufour effects, chemical reaction, and Prandtl number are discussed. A correlation of the average Nusselt number and Sherwood number corresponding to active parameters is presented. It can be noticed that increasing the Dufour number leads to an uplift in heat transfer. Fluid velocity increases with Grashof number and decreases with magnetic effect. The impact of heat sources and radiation is to increase the thermal conductivity. Concentration decreases with the Schmidt number. Full article
(This article belongs to the Special Issue Mathematical and Computational Modeling on Fluid Flow and Heat Transfer)
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24 pages, 3782 KiB  
Article
A Large Group Emergency Decision-Making Method Based on Uncertain Linguistic Cloud Similarity Method
by Gang Chen, Lihua Wei, Jiangyue Fu, Chengjiang Li and Gang Zhao
Math. Comput. Appl. 2022, 27(6), 101; https://doi.org/10.3390/mca27060101 - 24 Nov 2022
Cited by 1 | Viewed by 1100
Abstract
In recent years, the consensus-reaching process of large group decision making has attracted much attention in the research society, especially in emergency environment area. However, the decision information is always limited and inaccurate. The trust relationship among decision makers has been proven to [...] Read more.
In recent years, the consensus-reaching process of large group decision making has attracted much attention in the research society, especially in emergency environment area. However, the decision information is always limited and inaccurate. The trust relationship among decision makers has been proven to exert important impacts on group consensus. In this study, we proposed a novel uncertain linguistic cloud similarity method based on trust update and the opinion interaction mechanism. Firstly, we transformed the linguistic preferences into clouds and used cloud similarity to divide large-scale decision makers into several groups. Secondly, an improved PageRank algorithm based on the trust relationship was developed to calculate the weights of decision makers. A combined weighting method considering the similarity and group size was also presented to calculate the weights of groups. Thirdly, a trust updating mechanism based on cloud similarity, consensus level, and cooperation willingness was developed to speed up the consensus-reaching process, and an opinion interaction mechanism was constructed to measure the consensus level of decision makers. Finally, a numerical experiment effectively illustrated the feasibility of the proposed method. The proposed method was proven to maximally retain the randomness and fuzziness of the decision information during a consensus-reaching process with fast convergent speed and good practicality. Full article
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29 pages, 1082 KiB  
Article
Scarce Sample-Based Reliability Estimation and Optimization Using Importance Sampling
by Kiran Pannerselvam, Deepanshu Yadav and Palaniappan Ramu
Math. Comput. Appl. 2022, 27(6), 99; https://doi.org/10.3390/mca27060099 - 22 Nov 2022
Cited by 2 | Viewed by 1863
Abstract
Importance sampling is a variance reduction technique that is used to improve the efficiency of Monte Carlo estimation. Importance sampling uses the trick of sampling from a distribution, which is located around the zone of interest of the primary distribution thereby reducing the [...] Read more.
Importance sampling is a variance reduction technique that is used to improve the efficiency of Monte Carlo estimation. Importance sampling uses the trick of sampling from a distribution, which is located around the zone of interest of the primary distribution thereby reducing the number of realizations required for an estimate. In the context of reliability-based structural design, the limit state is usually separable and is of the form Capacity (C)–Response (R). The zone of interest for importance sampling is observed to be the region where these distributions overlap each other. However, often the distribution information of C and R themselves are not known, and one has only scarce realizations of them. In this work, we propose approximating the probability density function and the cumulative distribution function using kernel functions and employ these approximations to find the parameters of the importance sampling density (ISD) to eventually estimate the reliability. In the proposed approach, in addition to ISD parameters, the approximations also played a critical role in affecting the accuracy of the probability estimates. We assume an ISD which follows a normal distribution whose mean is defined by the most probable point (MPP) of failure, and the standard deviation is empirically chosen such that most of the importance sample realizations lie within the means of R and C. Since the probability estimate depends on the approximation, which in turn depends on the underlying samples, we use bootstrap to quantify the variation associated with the low failure probability estimate. The method is investigated with different tailed distributions of R and C. Based on the observations, a modified Hill estimator is utilized to address scenarios with heavy-tailed distributions where the distribution approximations perform poorly. The proposed approach is tested on benchmark reliability examples and along with surrogate modeling techniques is implemented on four reliability-based design optimization examples of which one is a multi-objective optimization problem. Full article
(This article belongs to the Special Issue Evolutionary Multi-objective Optimization: An Honorary Issue Dedicated to Professor Kalyanmoy Deb)
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7 pages, 283 KiB  
Article
Modeling of Perforated Piezoelectric Plates
by Houari Mechkour
Math. Comput. Appl. 2022, 27(6), 100; https://doi.org/10.3390/mca27060100 - 22 Nov 2022
Cited by 1 | Viewed by 1096
Abstract
In this article, we are interested in the behavior of a three-dimensional model of periodic perforated piezoelectric plate, when the thickness h of the plate and the size ε of the holes are small. We study the dependence of displacements and electric potential [...] Read more.
In this article, we are interested in the behavior of a three-dimensional model of periodic perforated piezoelectric plate, when the thickness h of the plate and the size ε of the holes are small. We study the dependence of displacements and electric potential on h and ε, and give equivalent limits when h and ε tend towards zero. We compute analytical formulae for all effective properties of the periodic perforated piezoelectric plate. Full article
(This article belongs to the Special Issue Mathematical and Computational Modelling in Mechanics of Materials and Structures)
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14 pages, 583 KiB  
Article
Three-Dimensional Non-Linearly Thermally Radiated Flow of Jeffrey Nanoliquid towards a Stretchy Surface with Convective Boundary and Cattaneo–Christov Flux
by Kandasamy Jagan and Sivanandam Sivasankaran
Math. Comput. Appl. 2022, 27(6), 98; https://doi.org/10.3390/mca27060098 - 19 Nov 2022
Cited by 7 | Viewed by 1048
Abstract
The objective of this paper is to investigate the 3D non-linearly thermally radiated flow of a Jeffrey nanofluid towards a stretchy surface with the Cattaneo–Christov heat flux (CCHF) model in the presence of a convective boundary condition.The Homotopy Analysis Method (HAM) is used [...] Read more.
The objective of this paper is to investigate the 3D non-linearly thermally radiated flow of a Jeffrey nanofluid towards a stretchy surface with the Cattaneo–Christov heat flux (CCHF) model in the presence of a convective boundary condition.The Homotopy Analysis Method (HAM) is used to solve the ordinary differential equation that is obtained by reforming the governing equation using suitable transformations. The equations obtained from HAM are plotted graphically for different parameters. In addition, the skin-friction coefficient, local Nusselt number, and Sherwood number for various parameters are calculated and discussed. The velocity profile along the x- and y-directions decrease with a raise in the ratio of relaxation to retardation times. The concentration and temperature profile rises while magnifying the ratio of relaxation to retardation times. While raising the ratio parameter, the x-direction velocity, temperature, and concentration profile diminishes, whereas the y-direction velocity profile magnifies. Magnifying the Deborah number results in a rise in the velocity profile along the x- and y-directions, and a decline in the temperature and concentration profile. Full article
(This article belongs to the Special Issue Mathematical and Computational Modeling on Fluid Flow and Heat Transfer)
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18 pages, 1290 KiB  
Article
An Efficient Two-Step Iterative Family Adaptive with Memory for Solving Nonlinear Equations and Their Applications
by Himani Sharma, Munish Kansal and Ramandeep Behl
Math. Comput. Appl. 2022, 27(6), 97; https://doi.org/10.3390/mca27060097 - 18 Nov 2022
Cited by 1 | Viewed by 1316
Abstract
We propose a new iterative scheme without memory for solving nonlinear equations. The proposed scheme is based on a cubically convergent Hansen–Patrick-type method. The beauty of our techniques is that they work even though the derivative is very small in the vicinity of [...] Read more.
We propose a new iterative scheme without memory for solving nonlinear equations. The proposed scheme is based on a cubically convergent Hansen–Patrick-type method. The beauty of our techniques is that they work even though the derivative is very small in the vicinity of the required root or f′(x)=0. On the contrary, the previous modifications either diverge or fail to work. In addition, we also extended the same idea for an iterative method with memory. Numerical examples and comparisons with some of the existing methods are included to confirm the theoretical results. Furthermore, basins of attraction are included to describe a clear picture of the convergence of the proposed method as well as that of some of the existing methods. Numerical experiments are performed on engineering problems, such as fractional conversion in a chemical reactor, Planck’s radiation law problem, Van der Waal’s problem, trajectory of an electron in between two parallel plates. The numerical results reveal that the proposed schemes are of utmost importance to be applied on various real–life problems. Basins of attraction also support this aspect. Full article
(This article belongs to the Special Issue Mathematical and Computational Modeling on Fluid Flow and Heat Transfer)
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28 pages, 7117 KiB  
Article
Multi-Strategy Improved Sparrow Search Algorithm and Application
by Xiangdong Liu, Yan Bai, Cunhui Yu, Hailong Yang, Haoning Gao, Jing Wang, Qing Chang and Xiaodong Wen
Math. Comput. Appl. 2022, 27(6), 96; https://doi.org/10.3390/mca27060096 - 17 Nov 2022
Cited by 4 | Viewed by 1777
Abstract
The sparrow search algorithm (SSA) is a metaheuristic algorithm developed based on the foraging and anti-predatory behavior of sparrow populations. Compared with other metaheuristic algorithms, SSA also suffers from poor population diversity, has weak global comprehensive search ability, and easily falls into local [...] Read more.
The sparrow search algorithm (SSA) is a metaheuristic algorithm developed based on the foraging and anti-predatory behavior of sparrow populations. Compared with other metaheuristic algorithms, SSA also suffers from poor population diversity, has weak global comprehensive search ability, and easily falls into local optimality. To address the problems whereby the sparrow search algorithm tends to fall into local optimum and the population diversity decreases in the later stage of the search, an improved sparrow search algorithm (PGL-SSA) based on piecewise chaotic mapping, Gaussian difference variation, and linear differential decreasing inertia weight fusion is proposed. Firstly, we analyze the improvement of six chaotic mappings on the overall performance of the sparrow search algorithm, and we finally determine the initialization of the population by piecewise chaotic mapping to increase the initial population richness and improve the initial solution quality. Secondly, we introduce Gaussian difference variation in the process of individual iterative update and use Gaussian difference variation to perturb the individuals to generate a diversity of individuals so that the algorithm can converge quickly and avoid falling into localization. Finally, linear differential decreasing inertia weights are introduced globally to adjust the weights so that the algorithm can fully traverse the solution space with larger weights in the first iteration to avoid falling into local optimum, and we enhance the local search ability with smaller weights in the later iteration to improve the search accuracy of the optimal solution. The results show that the proposed algorithm has a faster convergence speed and higher search accuracy than the comparison algorithm, the global search capability is significantly enhanced, and it is easier to jump out of the local optimum. The improved algorithm is also applied to the Heating, Ventilation and Air Conditioning (HVAC) system control optimization direction, and the improved algorithm is used to optimize the parameters of the HVAC system Proportion Integral Differential (PID) controller. The results show that the PID controller optimized by the improved algorithm has higher control accuracy and system stability, which verifies the feasibility of the improved algorithm in practical engineering applications. Full article
(This article belongs to the Special Issue Setting the Future of Smart Industry 4.0 with Metaheuristic Algorithms)
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16 pages, 471 KiB  
Article
Four-Parameter Guessing Model and Related Item Response Models
by Alexander Robitzsch
Math. Comput. Appl. 2022, 27(6), 95; https://doi.org/10.3390/mca27060095 - 17 Nov 2022
Cited by 1 | Viewed by 2076
Abstract
Guessing effects frequently occur in testing data in educational or psychological applications. Different item response models have been proposed to handle guessing effects in dichotomous test items. However, it has been pointed out in the literature that the often employed three-parameter logistic model [...] Read more.
Guessing effects frequently occur in testing data in educational or psychological applications. Different item response models have been proposed to handle guessing effects in dichotomous test items. However, it has been pointed out in the literature that the often employed three-parameter logistic model poses implausible assumptions regarding the guessing process. The four-parameter guessing model has been proposed as an alternative to circumvent these conceptual issues. In this article, the four-parameter guessing model is compared with alternative item response models for handling guessing effects through a simulation study and an empirical example. It turns out that model selection for item response models should be rather based on the AIC than the BIC. However, the RMSD item fit statistic used with typical cutoff values was found to be ineffective in detecting misspecified item response models. Furthermore, sufficiently large sample sizes are required for sufficiently precise item parameter estimation. Moreover, it is argued that the criterion of the statistical model fit should not be the sole criterion of model choice. The item response model used in operational practice should be valid with respect to the meaning of the ability variable and the underlying model assumptions. In this sense, the four-parameter guessing model could be the model of choice in educational large-scale assessment studies. Full article
(This article belongs to the Section Social Sciences)
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13 pages, 2123 KiB  
Article
Multi-Objective Optimization of an Elastic Rod with Viscous Termination
by Siyuan Xing and Jian-Qiao Sun
Math. Comput. Appl. 2022, 27(6), 94; https://doi.org/10.3390/mca27060094 - 15 Nov 2022
Viewed by 1098
Abstract
In this paper, we study the multi-objective optimization of the viscous boundary condition of an elastic rod using a hybrid method combining a genetic algorithm and simple cell mapping (GA-SCM). The method proceeds with the NSGAII algorithm to seek a rough Pareto set, [...] Read more.
In this paper, we study the multi-objective optimization of the viscous boundary condition of an elastic rod using a hybrid method combining a genetic algorithm and simple cell mapping (GA-SCM). The method proceeds with the NSGAII algorithm to seek a rough Pareto set, followed by a local recovery process based on one-step simple cell mapping to complete the branch of the Pareto set. To accelerate computation, the rod response under impulsive loading is calculated with a particular solution method that provides accurate structural responses with less computational effort. The Pareto set and Pareto front of a case study are obtained with the GA-SCM hybrid method. Optimal designs of each objective function are illustrated through numerical simulations. Full article
(This article belongs to the Special Issue Evolutionary Multi-objective Optimization: An Honorary Issue Dedicated to Professor Kalyanmoy Deb)
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20 pages, 1031 KiB  
Article
Stochastic Capital–Labor Lévy Jump Model with the Precariat Labor Force
by Jaouad Danane
Math. Comput. Appl. 2022, 27(6), 93; https://doi.org/10.3390/mca27060093 - 10 Nov 2022
Cited by 1 | Viewed by 1094
Abstract
In this work, we study a capital–labor model by considering the interaction between the new proposed and the confirmed free jobs, the precariat labor force, and the mature labor force by introducing Brownian motion and Lévy noise. Moreover, we illustrate the well-posedness of [...] Read more.
In this work, we study a capital–labor model by considering the interaction between the new proposed and the confirmed free jobs, the precariat labor force, and the mature labor force by introducing Brownian motion and Lévy noise. Moreover, we illustrate the well-posedness of the solution. In addition, we establish the conditions of the extinction of both the free jobs and labor force; subsequently, we prove the persistence of only the free jobs, and we also show the conditions of the persistence of both the free jobs and labor force. Finally, we validate our theoretical finding by numerical simulation by building a new stochastic Runge–Kutta method. Full article
(This article belongs to the Special Issue Ghana Numerical Analysis Day)
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16 pages, 968 KiB  
Article
A New Material Model for Agglomerated Cork
by Gabriel Thomaz de Aquino Pereira, Ricardo J. Alves de Sousa, I-Shih Liu, Marcello Goulart Teixeira and Fábio A. O. Fernandes
Math. Comput. Appl. 2022, 27(6), 92; https://doi.org/10.3390/mca27060092 - 09 Nov 2022
Cited by 1 | Viewed by 1114
Abstract
It is increasingly necessary to promote means of production that are less polluting and less harmful to the environment following the UN 2030 agenda for sustainable development. Using natural cellular materials in structural applications can be essential for enabling a future in this [...] Read more.
It is increasingly necessary to promote means of production that are less polluting and less harmful to the environment following the UN 2030 agenda for sustainable development. Using natural cellular materials in structural applications can be essential for enabling a future in this direction. Cork is a natural cellular material with an excellent energy absorption capacity. Its use in engineering applications and products has grown over time, so predicting its mechanical response through numerical tools is crucial. Classical cork modeling uses a model developed for foam material, including an adjustment function that does not have a clear physical interpretation. This work presents a new material model for an agglomerated cork based solely on well-known hypotheses of continuum mechanics using fewer parameters than the classical model and further a finite element framework to validate the new model against experimental data. Full article
(This article belongs to the Collection Feature Papers in Mathematical and Computational Applications)
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14 pages, 10766 KiB  
Article
Impacts of Stefan Blowing on Hybrid Nanofluid Flow over a Stretching Cylinder with Thermal Radiation and Dufour and Soret Effect
by Manoj Kumar Narayanaswamy, Jagan Kandasamy and Sivasankaran Sivanandam
Math. Comput. Appl. 2022, 27(6), 91; https://doi.org/10.3390/mca27060091 - 02 Nov 2022
Cited by 5 | Viewed by 1616
Abstract
The focal interest in this article is to investigate the Stefan blowing and Dufour and Soret effects on hybrid nanofluid (HNF) flow towards a stretching cylinder with thermal radiation. The governing equations are converted into ODE by using suitable transformations. The boundary value [...] Read more.
The focal interest in this article is to investigate the Stefan blowing and Dufour and Soret effects on hybrid nanofluid (HNF) flow towards a stretching cylinder with thermal radiation. The governing equations are converted into ODE by using suitable transformations. The boundary value problem solver (bvp4c), which is a package in the MATLAB, is used to solve the resulting ODE equations. Results show that rise in the Stefan blowing enhances velocity, temperature, and concentration profiles. Heat transfer rate increases by up to 10% in the presence of 4% nanoparticle/HNF but mass transfer rate diminishes. Additionally, skin friction coefficient, Nusselt number and Sherwood number are examined for many parameters entangled in this article. Additionally, results are deliberatively discussed in detail. Full article
(This article belongs to the Special Issue Mathematical and Computational Modeling on Fluid Flow and Heat Transfer)
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9 pages, 2939 KiB  
Article
Increased Material Density within a New Biomechanism
by Carlos Aurelio Andreucci, Elza M. M. Fonseca and Renato N. Jorge
Math. Comput. Appl. 2022, 27(6), 90; https://doi.org/10.3390/mca27060090 - 02 Nov 2022
Cited by 8 | Viewed by 1636
Abstract
A new mechanism, applied in this study as a biomechanical device, known as a Bioactive Kinetic Screw (BKS) for bone implants is described. The BKS was designed as a bone implant, in which the bone particles, blood, cells, and protein molecules removed during [...] Read more.
A new mechanism, applied in this study as a biomechanical device, known as a Bioactive Kinetic Screw (BKS) for bone implants is described. The BKS was designed as a bone implant, in which the bone particles, blood, cells, and protein molecules removed during bone drilling are used as a homogeneous autogenous transplant at the same implant site, aiming to optimize the healing process and simplify the surgical procedure. In this work, the amount of bone that will be compacted inside and around the new biomechanism was studied, based on the density of the bone applied. This study allows us to analyze the average bone density in humans (1.85 mg/mm3 or 1850 µg/mm³) with four different synthetic bone densities (Sawbones PCF 10, 20, 30 and 40). The results show that across all four different synthetic bones densities, the bone within the new model is 3.45 times denser. After a pilot drill (with 10 mm length and 1.8 mm diameter), in cases where a guide hole is required, the increase in ratio is equal to 2.7 times inside and around the new biomechanism. The in vitro test validated the mathematical results, describing that in two different materials, the same compact factor of 3.45 was determined with the new biomechanical device. It was possible to describe that BKS can become a powerful tool in the diagnosis and treatment of natural bone conditions and any type of disease. Full article
(This article belongs to the Special Issue Numerical and Symbolic Computation: Developments and Applications 2021)
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32 pages, 8839 KiB  
Article
Shadowed Type-2 Fuzzy Sets in Dynamic Parameter Adaption in Cuckoo Search and Flower Pollination Algorithms for Optimal Design of Fuzzy Fault-Tolerant Controllers
by Himanshukumar R. Patel and Vipul A. Shah
Math. Comput. Appl. 2022, 27(6), 89; https://doi.org/10.3390/mca27060089 - 28 Oct 2022
Cited by 10 | Viewed by 1407
Abstract
In recent, various metaheuristic algorithms have shown significant results in control engineering problems; moreover, fuzzy sets (FSs) and theories were frequently used for dynamic parameter adaption in metaheuristic algorithms. The primary reason for this is that fuzzy inference system (FISs) can be designed [...] Read more.
In recent, various metaheuristic algorithms have shown significant results in control engineering problems; moreover, fuzzy sets (FSs) and theories were frequently used for dynamic parameter adaption in metaheuristic algorithms. The primary reason for this is that fuzzy inference system (FISs) can be designed using human knowledge, allowing for intelligent dynamic adaptations of metaheuristic parameters. To accomplish these tasks, we proposed shadowed type-2 fuzzy inference systems (ST2FISs) for two metaheuristic algorithms, namely cuckoo search (CS) and flower pollination (FP). Furthermore, with the advent of shadowed type-2 fuzzy logic, the abilities of uncertainty handling offer an appealing improved performance for dynamic parameter adaptation in metaheuristic methods; moreover, the use of ST2FISs has been shown in recent works to provide better results than type-1 fuzzy inference systems (T1FISs). As a result, ST2FISs are proposed for adjusting the Lèvy flight (P) and switching probability (P′) parameters in the original cuckoo search (CS) and flower pollination (FP) algorithms, respectively. Our approach investigated trapezoidal types of membership functions (MFs), such as ST2FSs. The proposed method was used to optimize the precursors and implications of a two-tank non-interacting conical frustum tank level (TTNCFTL) process using an interval type-2 fuzzy controller (IT2FLC). To ensure that the implementation is efficient compared with the original CS and FP algorithms, simulation results were obtained without and then with uncertainty in the main actuator (CV1) and system component (leak) at the bottom of frustum tank two of the TTNCFLT process. In addition, the statistical z-test and non-parametric Friedman test are performed to analyze and deliver the findings for the best metaheuristic algorithm. The reported findings highlight the benefits of employing this approach over traditional general type-2 fuzzy inference systems since we get superior performance in the majority of cases while using minimal computational resources. Full article
(This article belongs to the Special Issue Setting the Future of Smart Industry 4.0 with Metaheuristic Algorithms)
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22 pages, 14309 KiB  
Article
The Modification of the Dynamic Behaviour of the Cyclonic Flow in a Hydrocyclone under Surging Conditions
by Muaaz Bhamjee, Simon H. Connell and André Leon Nel
Math. Comput. Appl. 2022, 27(6), 88; https://doi.org/10.3390/mca27060088 - 22 Oct 2022
Viewed by 1513
Abstract
The aim in this study was to determine how surging modifies the dynamic behaviour of the cyclonic flow in a hydrocyclone using computational fluid and granular dynamics models. The Volume-of-Fluid model was used to model the air-core formation. Fluid–particle, particle–particle, and particle–wall interactions [...] Read more.
The aim in this study was to determine how surging modifies the dynamic behaviour of the cyclonic flow in a hydrocyclone using computational fluid and granular dynamics models. The Volume-of-Fluid model was used to model the air-core formation. Fluid–particle, particle–particle, and particle–wall interactions were modelled using an unsteady two-way coupled Discrete Element Method. Turbulence was modelled using both the Reynold’s Stress Model and the Large Eddy Simulation. The model predictions indicate that the phenomenon of surging modifies the dynamics of the cyclonic flow in hydrocyclones and subsequently impacts separation. The results reveal that the primary cyclonic separation mechanisms break down during surging and result in air-core suppression. The flow and primary separation mechanism in the core of the hydrocyclone is driven by the pressure drop and the flow and primary separation mechanism near the wall is primarily driven by the gravitational and centrifugal force-induced momentum. However, surging causes a breakdown in this mechanism by swapping this primary flow and separation behaviour, where the pressure drop becomes the primary driver of the flow near the walls and gravitational and centrifugal force-induced momentum primarily drives the flow in the core of the hydrocyclone. Full article
(This article belongs to the Special Issue Current Problems and Advances in Computational and Applied Mechanics)
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