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Volume 28
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Math. Comput. Appl., Volume 28, Issue 1 (February 2023) – 27 articles

Cover Story (view full-size image): We propose a stabilized FEM for linear and nonlinear unsteady advection–diffusion–reaction (ADR) equations using a method of lines. Our approach uses a residual minimization strategy that combines time-marching and a discontinuous Galerkin (dG) formulation in space, which results in a continuous solution with on-the-fly error estimation for adaptivity. We demonstrate the effectiveness of our method on advection-dominated problems and the nonlinear Bratu equation in two dimensions, showing that it delivers stable solutions with an efficient adaptivity strategy. Our method delivers robust and reliable numerical simulations of ADR equations for various applications. View this paper
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17 pages, 3275 KiB  
Article
A Radial Hybrid Estimation of Distribution Algorithm for the Truck and Trailer Routing Problem
by Ricardo Pérez-Rodríguez and Sergio Frausto-Hernández
Math. Comput. Appl. 2023, 28(1), 27; https://doi.org/10.3390/mca28010027 - 20 Feb 2023
Cited by 1 | Viewed by 1228
Abstract
The truck and trailer routing problem (TTRP) has been widely studied under different approaches. This is due to its practical characteristic that makes its research interesting. The TTRP continues to be attractive to developing new evolutionary algorithms. This research details a new estimation [...] Read more.
The truck and trailer routing problem (TTRP) has been widely studied under different approaches. This is due to its practical characteristic that makes its research interesting. The TTRP continues to be attractive to developing new evolutionary algorithms. This research details a new estimation of the distribution algorithm coupled with a radial probability function from hydrogen. Continuous values are used in the solution representation, and every value indicates, in a hydrogen atom, the distance between the electron and the core. The key point is to exploit the radial probability distribution to construct offspring and to tackle the drawbacks of the estimation of distribution algorithms. Various instances and numerical experiments are presented to illustrate and validate this novel research. Based on the performance of the proposed scheme, we can make the conclusion that incorporating radial probability distributions helps to improve the estimation of distribution algorithms. Full article
(This article belongs to the Special Issue Numerical and Evolutionary Optimization 2022)
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20 pages, 821 KiB  
Article
Single-Loop Multi-Objective Reliability-Based Design Optimization Using Chaos Control Theory and Shifting Vector with Differential Evolution
by Raktim Biswas and Deepak Sharma
Math. Comput. Appl. 2023, 28(1), 26; https://doi.org/10.3390/mca28010026 - 17 Feb 2023
Viewed by 1202
Abstract
Multi-objective reliability-based design optimization (MORBDO) is an efficient tool for generating reliable Pareto-optimal (PO) solutions. However, generating such PO solutions requires many function evaluations for reliability analysis, thereby increasing the computational cost. In this paper, a single-loop multi-objective reliability-based design optimization formulation is [...] Read more.
Multi-objective reliability-based design optimization (MORBDO) is an efficient tool for generating reliable Pareto-optimal (PO) solutions. However, generating such PO solutions requires many function evaluations for reliability analysis, thereby increasing the computational cost. In this paper, a single-loop multi-objective reliability-based design optimization formulation is proposed that approximates reliability analysis using Karush-Kuhn Tucker (KKT) optimality conditions. Further, chaos control theory is used for updating the point that is estimated through KKT conditions for avoiding any convergence issues. In order to generate the reliable point in the feasible region, the proposed formulation also incorporates the shifting vector approach. The proposed MORBDO formulation is solved using differential evolution (DE) that uses a heuristic convergence parameter based on hypervolume indicator for performing different mutation operators. DE incorporating the proposed formulation is tested on two mathematical and one engineering examples. The results demonstrate the generation of a better set of reliable PO solutions using the proposed method over the double-loop variant of multi-objective DE. Moreover, the proposed method requires 6×–377× less functional evaluations than the double-loop-based DE. 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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25 pages, 3248 KiB  
Article
The Arctan Power Distribution: Properties, Quantile and Modal Regressions with Applications to Biomedical Data
by Suleman Nasiru, Abdul Ghaniyyu Abubakari and Christophe Chesneau
Math. Comput. Appl. 2023, 28(1), 25; https://doi.org/10.3390/mca28010025 - 14 Feb 2023
Cited by 2 | Viewed by 1655
Abstract
The usefulness of (probability) distributions in the field of biomedical science cannot be underestimated. Hence, several distributions have been used in this field to perform statistical analyses and make inferences. In this study, we develop the arctan power (AP) distribution and illustrate its [...] Read more.
The usefulness of (probability) distributions in the field of biomedical science cannot be underestimated. Hence, several distributions have been used in this field to perform statistical analyses and make inferences. In this study, we develop the arctan power (AP) distribution and illustrate its application using biomedical data. The distribution is flexible in the sense that its probability density function exhibits characteristics such as left-skewedness, right-skewedness, and J and reversed-J shapes. The characteristic of the corresponding hazard rate function also suggests that the distribution is capable of modeling data with monotonic and non-monotonic failure rates. A bivariate extension of the AP distribution is also created to model the interdependence of two random variables or pairs of data. The application reveals that the AP distribution provides a better fit to the biomedical data than other existing distributions. The parameters of the distribution can also be fairly accurately estimated using a Bayesian approach, which is also elaborated. To end the study, the quantile and modal regression models based on the AP distribution provided better fits to the biomedical data than other existing regression models. Full article
(This article belongs to the Special Issue Statistical Inference in Linear Models)
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23 pages, 939 KiB  
Article
Stability Analysis of Caputo Fractional Order Viral Dynamics of Hepatitis B Cellular Infection
by Michael O. Opoku, Eric N. Wiah, Eric Okyere, Albert L. Sackitey, Emmanuel K. Essel and Stephen E. Moore
Math. Comput. Appl. 2023, 28(1), 24; https://doi.org/10.3390/mca28010024 - 09 Feb 2023
Cited by 2 | Viewed by 1302
Abstract
We present a Caputo fractional order mathematical model that describes the cellular infection of the Hepatitis B virus and the immune response of the body with Holling type II functional response. We study the existence of unique positive solutions and the local and [...] Read more.
We present a Caputo fractional order mathematical model that describes the cellular infection of the Hepatitis B virus and the immune response of the body with Holling type II functional response. We study the existence of unique positive solutions and the local and global stability of virus-free and endemic equilibria. Finally, we present numerical results using the Adam-type predictor–corrector iterative scheme. Full article
(This article belongs to the Special Issue Ghana Numerical Analysis Day)
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15 pages, 3974 KiB  
Article
Higher-Order Multiplicative Derivative Iterative Scheme to Solve the Nonlinear Problems
by Gurjeet Singh, Sonia Bhalla and Ramandeep Behl
Math. Comput. Appl. 2023, 28(1), 23; https://doi.org/10.3390/mca28010023 - 09 Feb 2023
Cited by 1 | Viewed by 1319
Abstract
Grossman and Katz (five decades ago) suggested a new definition of differential and integral calculus which utilizes the multiplicative and division operator as compared to addition and subtraction. Multiplicative calculus is a vital part of applied mathematics because of its application in the [...] Read more.
Grossman and Katz (five decades ago) suggested a new definition of differential and integral calculus which utilizes the multiplicative and division operator as compared to addition and subtraction. Multiplicative calculus is a vital part of applied mathematics because of its application in the areas of biology, science and finance, biomedical, economic, etc. Therefore, we used a multiplicative calculus approach to develop a new fourth-order iterative scheme for multiple roots based on the well-known King’s method. In addition, we also propose a detailed convergence analysis of our scheme with the help of a multiplicative calculus approach rather than the normal one. Different kinds of numerical comparisons have been suggested and analyzed. The obtained results (from line graphs, bar graphs and tables) are very impressive compared to the earlier iterative methods of the same order with the ordinary derivative. Finally, the convergence of our technique is also analyzed by the basin of attractions, which also supports the theoretical aspects. Full article
(This article belongs to the Special Issue Mathematical and Computational Modeling on Fluid Flow and Heat Transfer)
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16 pages, 1710 KiB  
Article
Hand–Eye Calibration Using a Tablet Computer
by Junya Sato
Math. Comput. Appl. 2023, 28(1), 22; https://doi.org/10.3390/mca28010022 - 08 Feb 2023
Cited by 1 | Viewed by 1163
Abstract
Many approaches have been developed to solve the hand–eye calibration problem. The traditional approach involves a precise mathematical model, which has advantages and disadvantages. For example, mathematical representations can provide numerical and quantitative results to users and researchers. Thus, it is possible to [...] Read more.
Many approaches have been developed to solve the hand–eye calibration problem. The traditional approach involves a precise mathematical model, which has advantages and disadvantages. For example, mathematical representations can provide numerical and quantitative results to users and researchers. Thus, it is possible to explain and understand the calibration results. However, information about the end-effector, such as the position attached to the robot and its dimensions, is not considered in the calibration process. If there is no CAD model, additional calibration is required for accurate manipulation, especially for a handmade end-effector. A neural network-based method is used as the solution to this problem. By training a neural network model using data created via the attached end-effector, additional calibration can be avoided. Moreover, it is not necessary to develop a precise and complex mathematical model. However, it is difficult to provide quantitative information because a neural network is a black box. Hence, a method with both advantages is proposed in this study. A mathematical model was developed and optimized using the data created by the attached end-effector. To acquire accurate data and evaluate the calibration results, a tablet computer was utilized. The established method achieved a mean positioning error of 1.0 mm. Full article
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20 pages, 4615 KiB  
Article
Chemical MHD Hiemenz Flow over a Nonlinear Stretching Sheet and Brownian Motion Effects of Nanoparticles through a Porous Medium with Radiation Effect
by Faisal Salah, Abdelmgid O. M. Sidahmed and K. K. Viswanathan
Math. Comput. Appl. 2023, 28(1), 21; https://doi.org/10.3390/mca28010021 - 07 Feb 2023
Cited by 3 | Viewed by 1421
Abstract
In this paper, the numerical solutions for magneto-hydrodynamic Hiemenz fluid over a nonlinear stretching sheet and the Brownian motion effects of nanoparticles through a porous medium with chemical reaction and radiation are studied. The repercussions of thermophoresis and mass transfer at the stagnation [...] Read more.
In this paper, the numerical solutions for magneto-hydrodynamic Hiemenz fluid over a nonlinear stretching sheet and the Brownian motion effects of nanoparticles through a porous medium with chemical reaction and radiation are studied. The repercussions of thermophoresis and mass transfer at the stagnation point flow are discussed. The plate progresses in the contrary direction or in the free stream orientation. The underlying PDEs are reshaped into a set of ordinary differential equations employing precise transformation. They are addressed numerically using the successive linearization method, which is an efficient systematic process. The main goal of this study is to compare the solutions obtained using the successive linearization method to solve the velocity and temperature equations in the presence of m changes, thereby demonstrating its accuracy and suitability for solving nonlinear differential equations. For comparison, tables containing the results are presented. This contrast is significant because it demonstrates the accuracy with which a set of nonlinear differential equations can be solved using the successive linearization method. The resulting solution is examined and discussed with respect to a number of engineering parameters. Graphs exemplify the simulation of distinct parameters that govern the motion factors. Full article
(This article belongs to the Special Issue Mathematical and Computational Modeling on Fluid Flow and Heat Transfer)
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21 pages, 636 KiB  
Article
Numerical Computation of Ag/Al2O3 Nanofluid over a Riga Plate with Heat Sink/Source and Non-Fourier Heat Flux Model
by S. Divya, S. Eswaramoorthi and Karuppusamy Loganathan
Math. Comput. Appl. 2023, 28(1), 20; https://doi.org/10.3390/mca28010020 - 03 Feb 2023
Cited by 3 | Viewed by 1490
Abstract
The main goal of the current research is to investigate the numerical computation of Ag/Al2O3 nanofluid over a Riga plate with injection/suction. The energy equation is formulated using the Cattaneo–Christov heat flux, non-linear thermal radiation, and heat sink/source. [...] Read more.
The main goal of the current research is to investigate the numerical computation of Ag/Al2O3 nanofluid over a Riga plate with injection/suction. The energy equation is formulated using the Cattaneo–Christov heat flux, non-linear thermal radiation, and heat sink/source. The leading equations are non-dimensionalized by employing the suitable transformations, and the numerical results are achieved by using the MATLAB bvp4c technique. The fluctuations of fluid flow and heat transfer on porosity, Forchheimer number, radiation, suction/injection, velocity slip, and nanoparticle volume fraction are investigated. Furthermore, the local skin friction coefficient (SFC), and local Nusselt number (LNN) are also addressed. Compared to previously reported studies, our computational results exactly coincided with the outcomes of the previous reports. We noticed that the Forchheimer number, suction/injection, slip, and nanoparticle volume fraction factors slow the velocity profile. We also noted that with improving rates of thermal radiation and convective heating, the heat transfer gradient decreases. The 40% presence of the Hartmann number leads to improved drag force by 14% and heat transfer gradient by 0.5%. The 20% presence of nanoparticle volume fraction leads to a decrement in heat transfer gradient for 21% of Ag nanoparticles and 18% of Al2O3 nanoparticles. Full article
(This article belongs to the Special Issue Significance of Mathematical Modelling and Control in Real-World Problems: New Developments and Applications)
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15 pages, 1203 KiB  
Article
Forecasting Financial and Macroeconomic Variables Using an Adaptive Parameter VAR-KF Model
by Nat Promma and Nawinda Chutsagulprom
Math. Comput. Appl. 2023, 28(1), 19; https://doi.org/10.3390/mca28010019 - 02 Feb 2023
Cited by 2 | Viewed by 1463
Abstract
The primary objective of this article is to present an adaptive parameter VAR-KF technique (APVAR-KF) to forecast stock market performance and macroeconomic factors. The method exploits a vector autoregressive model as a system identification technique, and the Kalman filter is served as a [...] Read more.
The primary objective of this article is to present an adaptive parameter VAR-KF technique (APVAR-KF) to forecast stock market performance and macroeconomic factors. The method exploits a vector autoregressive model as a system identification technique, and the Kalman filter is served as a recursive state parameter estimation tool. A further development was designed by incorporating the GARCH model to quantify an automatic observation covariance matrix in the Kalman filter step. To verify the efficiency of our proposed method, we conducted an experimental simulation applied to the main stock exchange index, real effective exchange rate and consumer price index of Thailand and Indonesia from January 1997 to May 2021. The APVAR-KF method is generally shown to have a superior performance relative to the conventional VAR(1) model and the VAR-KF model with constant parameters. Full article
(This article belongs to the Special Issue Statistical Inference in Linear Models)
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15 pages, 5282 KiB  
Article
Entropy Generation of Cu–Al2O3/Water Flow with Convective Boundary Conditions through a Porous Stretching Sheet with Slip Effect, Joule Heating and Chemical Reaction
by Maria Immaculate Joyce, Jagan Kandasamy and Sivasankaran Sivanandam
Math. Comput. Appl. 2023, 28(1), 18; https://doi.org/10.3390/mca28010018 - 02 Feb 2023
Cited by 6 | Viewed by 1701
Abstract
Currently, the efficiency of heat exchange is not only determined by enhancements in the rate of heat transfer but also by economic and accompanying considerations. Responding to this demand, many scientists have been involved in improving heat transfer performance, which is referred to [...] Read more.
Currently, the efficiency of heat exchange is not only determined by enhancements in the rate of heat transfer but also by economic and accompanying considerations. Responding to this demand, many scientists have been involved in improving heat transfer performance, which is referred to as heat transfer enhancement, augmentation, or intensification. This study deals with the influence on hybrid Cu–Al2CO3/water nanofluidic flows on a porous stretched sheet of velocity slip, convective boundary conditions, Joule heating, and chemical reactions using an adapted Tiwari–Das model. Nonlinear fundamental equations such as continuity, momentum, energy, and concentration are transmuted into a non-dimensional ordinary nonlinear differential equation by similarity transformations. Numerical calculations are performed using HAM and the outcomes are traced on graphs such as velocity, temperature, and concentration. Temperature and concentration profiles are elevated as porosity is increased, whereas velocity is decreased. The Biot number increases the temperature profile. The rate of entropy is enhanced as the Brinkman number is raised. A decrease in the velocity is seen as the slip increases. Full article
(This article belongs to the Special Issue Mathematical and Computational Modeling on Fluid Flow and Heat Transfer)
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19 pages, 4005 KiB  
Article
Many-Objectives Optimization: A Machine Learning Approach for Reducing the Number of Objectives
by António Gaspar-Cunha, Paulo Costa, Francisco Monaco and Alexandre Delbem
Math. Comput. Appl. 2023, 28(1), 17; https://doi.org/10.3390/mca28010017 - 30 Jan 2023
Cited by 1 | Viewed by 3116
Abstract
Solving real-world multi-objective optimization problems using Multi-Objective Optimization Algorithms becomes difficult when the number of objectives is high since the types of algorithms generally used to solve these problems are based on the concept of non-dominance, which ceases to work as the number [...] Read more.
Solving real-world multi-objective optimization problems using Multi-Objective Optimization Algorithms becomes difficult when the number of objectives is high since the types of algorithms generally used to solve these problems are based on the concept of non-dominance, which ceases to work as the number of objectives grows. This problem is known as the curse of dimensionality. Simultaneously, the existence of many objectives, a characteristic of practical optimization problems, makes choosing a solution to the problem very difficult. Different approaches are being used in the literature to reduce the number of objectives required for optimization. This work aims to propose a machine learning methodology, designated by FS-OPA, to tackle this problem. The proposed methodology was assessed using DTLZ benchmarks problems suggested in the literature and compared with similar algorithms, showing a good performance. In the end, the methodology was applied to a difficult real problem in polymer processing, showing its effectiveness. The algorithm proposed has some advantages when compared with a similar algorithm in the literature based on machine learning (NL-MVU-PCA), namely, the possibility for establishing variable–variable and objective–variable relations (not only objective–objective), and the elimination of the need to define/chose a kernel neither to optimize algorithm parameters. The collaboration with the DM(s) allows for the obtainment of explainable solutions. 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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3 pages, 177 KiB  
Editorial
Feature Paper Collection of Mathematical and Computational Applications—2022
by Gianluigi Rozza, Oliver Schütze and Nicholas Fantuzzi
Math. Comput. Appl. 2023, 28(1), 16; https://doi.org/10.3390/mca28010016 - 28 Jan 2023
Viewed by 1087
Abstract
This Special Issue comprises the first collection of papers submitted by the Editorial Board Members (EBMs) of the journal Mathematical and Computational Applications (MCA), as well as outstanding scholars working in the core research fields of MCA [...] Full article
(This article belongs to the Collection Feature Papers in Mathematical and Computational Applications)
4 pages, 181 KiB  
Editorial
Acknowledgment to the Reviewers of MCA in 2022
by MCA Editorial Office
Math. Comput. Appl. 2023, 28(1), 15; https://doi.org/10.3390/mca28010015 - 18 Jan 2023
Viewed by 738
Abstract
High-quality academic publishing is built on rigorous peer review [...] Full article
13 pages, 457 KiB  
Article
Knowledge Transfer Based on Particle Filters for Multi-Objective Optimization
by Xilu Wang and Yaochu Jin
Math. Comput. Appl. 2023, 28(1), 14; https://doi.org/10.3390/mca28010014 - 18 Jan 2023
Viewed by 1480
Abstract
Particle filters, also known as sequential Monte Carlo (SMC) methods, constitute a class of importance sampling and resampling techniques designed to use simulations to perform on-line filtering. Recently, particle filters have been extended for optimization by utilizing the ability to track a sequence [...] Read more.
Particle filters, also known as sequential Monte Carlo (SMC) methods, constitute a class of importance sampling and resampling techniques designed to use simulations to perform on-line filtering. Recently, particle filters have been extended for optimization by utilizing the ability to track a sequence of distributions. In this work, we incorporate transfer learning capabilities into the optimizer by using particle filters. To achieve this, we propose a novel particle-filter-based multi-objective optimization algorithm (PF-MOA) by transferring knowledge acquired from the search experience. The key insight adopted here is that, if we can construct a sequence of target distributions that can balance the multiple objectives and make the degree of the balance controllable, we can approximate the Pareto optimal solutions by simulating each target distribution via particle filters. As the importance weight updating step takes the previous target distribution as the proposal distribution and takes the current target distribution as the target distribution, the knowledge acquired from the previous run can be utilized in the current run by carefully designing the set of target distributions. The experimental results on the DTLZ and WFG test suites show that the proposed PF-MOA achieves competitive performance compared with state-of-the-art multi-objective evolutionary algorithms on most test instances. 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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16 pages, 360 KiB  
Article
Controllability Criteria for Nonlinear Impulsive Fractional Differential Systems with Distributed Delays in Controls
by Amar Debbouche, Bhaskar Sundara Vadivoo, Vladimir E. Fedorov and Valery Antonov
Math. Comput. Appl. 2023, 28(1), 13; https://doi.org/10.3390/mca28010013 - 15 Jan 2023
Cited by 3 | Viewed by 1124
Abstract
We establish a class of nonlinear fractional differential systems with distributed time delays in the controls and impulse effects. We discuss the controllability criteria for both linear and nonlinear systems. The main results required a suitable Gramian matrix defined by the Mittag–Leffler function, [...] Read more.
We establish a class of nonlinear fractional differential systems with distributed time delays in the controls and impulse effects. We discuss the controllability criteria for both linear and nonlinear systems. The main results required a suitable Gramian matrix defined by the Mittag–Leffler function, using the standard Laplace transform and Schauder fixed-point techniques. Further, we provide an illustrative example supported by graphical representations to show the validity of the obtained abstract results. Full article
(This article belongs to the Special Issue Significance of Mathematical Modelling and Control in Real-World Problems: New Developments and Applications)
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15 pages, 1293 KiB  
Article
COVID-19 Data Analysis with a Multi-Objective Evolutionary Algorithm for Causal Association Rule Mining
by Santiago Sinisterra-Sierra, Salvador Godoy-Calderón and Miriam Pescador-Rojas
Math. Comput. Appl. 2023, 28(1), 12; https://doi.org/10.3390/mca28010012 - 13 Jan 2023
Viewed by 1606
Abstract
Association rule mining plays a crucial role in the medical area in discovering interesting relationships among the attributes of a data set. Traditional association rule mining algorithms such as Apriori, FP growth, or Eclat require considerable computational resources and generate large volumes [...] Read more.
Association rule mining plays a crucial role in the medical area in discovering interesting relationships among the attributes of a data set. Traditional association rule mining algorithms such as Apriori, FP growth, or Eclat require considerable computational resources and generate large volumes of rules. Moreover, these techniques depend on user-defined thresholds which can inadvertently cause the algorithm to omit some interesting rules. In order to solve such challenges, we propose an evolutionary multi-objective algorithm based on NSGA-II to guide the mining process in a data set composed of 15.5 million records with official data describing the COVID-19 pandemic in Mexico. We tested different scenarios optimizing classical and causal estimation measures in four waves, defined as the periods of time where the number of people with COVID-19 increased. The proposed contributions generate, recombine, and evaluate patterns, focusing on recovering promising high-quality rules with actionable cause–effect relationships among the attributes to identify which groups are more susceptible to disease or what combinations of conditions are necessary to receive certain types of medical care. 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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14 pages, 1410 KiB  
Article
Pseudo-Poisson Distributions with Concomitant Variables
by Barry C. Arnold and Bangalore G. Manjunath
Math. Comput. Appl. 2023, 28(1), 11; https://doi.org/10.3390/mca28010011 - 12 Jan 2023
Viewed by 1403
Abstract
It has been argued in Arnold and Manjunath (2021) that the bivariate pseudo-Poisson distribution will be the model of choice for bivariate data with one equidispersed marginal and the other marginal over-dispersed. This is due to its simple structure, straightforward parameter estimation and [...] Read more.
It has been argued in Arnold and Manjunath (2021) that the bivariate pseudo-Poisson distribution will be the model of choice for bivariate data with one equidispersed marginal and the other marginal over-dispersed. This is due to its simple structure, straightforward parameter estimation and fast computation. In the current note, we introduce the effects of concomitant variables on the bivariate pseudo-Poisson parameters and explore the distributional and inferential aspects of the augmented models. We also include a small simulation study and an example of application to real-life data. Full article
(This article belongs to the Special Issue Statistical Inference in Linear Models)
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22 pages, 1297 KiB  
Article
The Hypervolume Newton Method for Constrained Multi-Objective Optimization Problems
by Hao Wang, Michael Emmerich, André Deutz, Víctor Adrián Sosa Hernández and Oliver Schütze
Math. Comput. Appl. 2023, 28(1), 10; https://doi.org/10.3390/mca28010010 - 09 Jan 2023
Viewed by 2400
Abstract
Recently, the Hypervolume Newton Method (HVN) has been proposed as a fast and precise indicator-based method for solving unconstrained bi-objective optimization problems with objective functions. The HVN is defined on the space of (vectorized) fixed cardinality sets of decision space vectors for a [...] Read more.
Recently, the Hypervolume Newton Method (HVN) has been proposed as a fast and precise indicator-based method for solving unconstrained bi-objective optimization problems with objective functions. The HVN is defined on the space of (vectorized) fixed cardinality sets of decision space vectors for a given multi-objective optimization problem (MOP) and seeks to maximize the hypervolume indicator adopting the Newton–Raphson method for deterministic numerical optimization. To extend its scope to non-convex optimization problems, the HVN method was hybridized with a multi-objective evolutionary algorithm (MOEA), which resulted in a competitive solver for continuous unconstrained bi-objective optimization problems. In this paper, we extend the HVN to constrained MOPs with in principle any number of objectives. Similar to the original variant, the first- and second-order derivatives of the involved functions have to be given either analytically or numerically. We demonstrate the applicability of the extended HVN on a set of challenging benchmark problems and show that the new method can be readily applied to solve equality constraints with high precision and to some extent also inequalities. We finally use HVN as a local search engine within an MOEA and show the benefit of this hybrid method on several benchmark problems. 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, 579 KiB  
Article
Global Stability of Multi-Strain SEIR Epidemic Model with Vaccination Strategy
by Zakaria Yaagoub and Karam Allali
Math. Comput. Appl. 2023, 28(1), 9; https://doi.org/10.3390/mca28010009 - 07 Jan 2023
Cited by 8 | Viewed by 1762
Abstract
A three-strain SEIR epidemic model with a vaccination strategy is suggested and studied in this work. This model is represented by a system of nine nonlinear ordinary differential equations that describe the interaction between susceptible individuals, strain-1-vaccinated individuals, strain-1-exposed individuals, strain-2-exposed individuals, strain-3-exposed [...] Read more.
A three-strain SEIR epidemic model with a vaccination strategy is suggested and studied in this work. This model is represented by a system of nine nonlinear ordinary differential equations that describe the interaction between susceptible individuals, strain-1-vaccinated individuals, strain-1-exposed individuals, strain-2-exposed individuals, strain-3-exposed individuals, strain-1-infected individuals, strain-2-infected individuals, strain-3-infected individuals, and recovered individuals. We start our analysis of this model by establishing the existence, positivity, and boundedness of all the solutions. In order to show global stability, the model has five equilibrium points: The first one stands for the disease-free equilibrium, the second stands for the strain-1 endemic equilibrium, the third one describes the strain-2 equilibrium, the fourth one represents the strain-3 equilibrium point, and the last one is called the total endemic equilibrium. We establish the global stability of each equilibrium point using some suitable Lyapunov function. This stability depends on the strain-1 reproduction number R01, the strain-2 basic reproduction number R02, and the strain-3 reproduction number R03. Numerical simulations are given to confirm our theoretical results. It is shown that in order to eradicate the infection, the basic reproduction numbers of all the strains must be less than unity. Full article
(This article belongs to the Special Issue Ghana Numerical Analysis Day)
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18 pages, 2006 KiB  
Article
Temperature Patterns in TSA for Different Frequencies and Material Properties: A FEM Approach
by Guilherme Duarte, Ana Neves and António Ramos Silva
Math. Comput. Appl. 2023, 28(1), 8; https://doi.org/10.3390/mca28010008 - 06 Jan 2023
Viewed by 1643
Abstract
Thermography techniques are gaining popularity in structural integrity monitoring and analysis of mechanical systems’ behavior because they are contactless, non-intrusive, rapidly deployable, applicable to structures under harsh environments, and can be performed on-site. More so, the use of image optical techniques has grown [...] Read more.
Thermography techniques are gaining popularity in structural integrity monitoring and analysis of mechanical systems’ behavior because they are contactless, non-intrusive, rapidly deployable, applicable to structures under harsh environments, and can be performed on-site. More so, the use of image optical techniques has grown quickly over the past several decades due to the progress in the digital camera, infrared camera, and computational power. This work focuses on thermoelastic stress analysis (TSA), and its main goal was to create a computational model based on the finite element method that simulates this technique, to evaluate and quantify how the changes in material properties, including orthotropic, affect the results of the stresses obtained with TSA. The numeric simulations were performed for two samples, compact and single lap joints. when comparing the numeric model developed with previous laboratory tests, the results showed a good representation of the stress test for both samples. The created model is applicable to various materials, including fiber-reinforced composites. This work also highlights the need to perform laboratory tests using anisotropic materials to better understand the TSA potential and improve the developed models. Full article
(This article belongs to the Special Issue Mathematical and Computational Modelling in Mechanics of Materials and Structures)
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21 pages, 4106 KiB  
Article
An Adaptive in Space, Stabilized Finite Element Method via Residual Minimization for Linear and Nonlinear Unsteady Advection–Diffusion–Reaction Equations
by Juan F. Giraldo and Victor M. Calo
Math. Comput. Appl. 2023, 28(1), 7; https://doi.org/10.3390/mca28010007 - 06 Jan 2023
Cited by 3 | Viewed by 1279
Abstract
We construct a stabilized finite element method for linear and nonlinear unsteady advection–diffusion–reaction equations using the method of lines. We propose a residual minimization strategy that uses an ad-hoc modified discrete system that couples a time-marching schema and a semi-discrete discontinuous Galerkin formulation [...] Read more.
We construct a stabilized finite element method for linear and nonlinear unsteady advection–diffusion–reaction equations using the method of lines. We propose a residual minimization strategy that uses an ad-hoc modified discrete system that couples a time-marching schema and a semi-discrete discontinuous Galerkin formulation in space. This combination delivers a stable continuous solution and an on-the-fly error estimate that robustly guides adaptivity at every discrete time. We show the performance of advection-dominated problems to demonstrate stability in the solution and efficiency in the adaptivity strategy. We also present the method’s robustness in the nonlinear Bratu equation in two dimensions. Full article
(This article belongs to the Special Issue Discontinuous Galerkin Methods)
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29 pages, 1019 KiB  
Article
An Experimental Study of Grouping Mutation Operators for the Unrelated Parallel-Machine Scheduling Problem
by Octavio Ramos-Figueroa, Marcela Quiroz-Castellanos, Efrén Mezura-Montes and Nicandro Cruz-Ramírez
Math. Comput. Appl. 2023, 28(1), 6; https://doi.org/10.3390/mca28010006 - 05 Jan 2023
Cited by 2 | Viewed by 1588
Abstract
The Grouping Genetic Algorithm (GGA) is an extension to the standard Genetic Algorithm that uses a group-based representation scheme and variation operators that work at the group-level. This metaheuristic is one of the most used to solve combinatorial optimization grouping problems. Its optimization [...] Read more.
The Grouping Genetic Algorithm (GGA) is an extension to the standard Genetic Algorithm that uses a group-based representation scheme and variation operators that work at the group-level. This metaheuristic is one of the most used to solve combinatorial optimization grouping problems. Its optimization process consists of different components, although the crossover and mutation operators are the most recurrent. This article aims to highlight the impact that a well-designed operator can have on the final performance of a GGA. We present a comparative experimental study of different mutation operators for a GGA designed to solve the Parallel-Machine scheduling problem with unrelated machines and makespan minimization, which comprises scheduling a collection of jobs in a set of machines. The proposed approach is focused on identifying the strategies involved in the mutation operations and adapting them to the characteristics of the studied problem. As a result of this experimental study, knowledge of the problem-domain was gained and used to design a new mutation operator called 2-Items Reinsertion. Experimental results indicate that the state-of-the-art GGA performance considerably improves by replacing the original mutation operator with the new one, achieving better results, with an improvement rate of 52%. 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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22 pages, 1027 KiB  
Article
Stability Results for a Weakly Dissipative Viscoelastic Equation with Variable-Exponent Nonlinearity: Theory and Numerics
by Adel M. Al-Mahdi, Mohammad M. Al-Gharabli, Maher Noor and Johnson D. Audu
Math. Comput. Appl. 2023, 28(1), 5; https://doi.org/10.3390/mca28010005 - 04 Jan 2023
Viewed by 888
Abstract
In this paper, we study the long-time behavior of a weakly dissipative viscoelastic equation with variable exponent nonlinearity of the form [...] Read more.
In this paper, we study the long-time behavior of a weakly dissipative viscoelastic equation with variable exponent nonlinearity of the form utt+Δ2u−∫0tg(t−s)Δu(s)ds+a|ut|n(·)−2ut−Δut=0, where n(.) is a continuous function satisfying some assumptions and g is a general relaxation function such that g′(t)≤−ξ(t)G(g(t)), where ξ and G are functions satisfying some specific properties that will be mentioned in the paper. Depending on the nature of the decay rate of g and the variable exponent n(.), we establish explicit and general decay results of the energy functional. We give some numerical illustrations to support our theoretical results. Our results improve some earlier works in the literature. Full article
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21 pages, 6550 KiB  
Article
Analysis of Multi-Stacked Dielectric Resonator Antenna with Its Equivalent R-L-C Circuit Modeling for Wireless Communication Systems
by Ram Krishna, Agbotiname Lucky Imoize, Rajveer Singh Yaduvanshi, Harendra Singh, Arun Kumar Rana and Subhendu Kumar Pani
Math. Comput. Appl. 2023, 28(1), 4; https://doi.org/10.3390/mca28010004 - 29 Dec 2022
Cited by 2 | Viewed by 1699
Abstract
The dielectric resonator antenna (DRA) can be modeled as a series and parallel combination of electrical networks consisting of a resistor (R), inductor (L), and capacitor (C) to address peculiar challenges in antennas suitable for application in emerging wireless communication systems for higher [...] Read more.
The dielectric resonator antenna (DRA) can be modeled as a series and parallel combination of electrical networks consisting of a resistor (R), inductor (L), and capacitor (C) to address peculiar challenges in antennas suitable for application in emerging wireless communication systems for higher frequency range. In this paper, a multi-stacked DRA has been proposed. The performance and characteristic features of the DRA have been analyzed by deriving the mathematical formulations for dynamic impedance, input impedance, admittance, bandwidth, and quality factor for fundamental and high-order resonant modes. Specifically, the performance of the projected multi-stacked DRA was analyzed in MATLAB and a high-frequency structure simulator (HFSS). Generally, results indicate that variation in the permittivity of substrates, such as high and low, can potentially increase and decrease the quality factor, respectively. In particular, the impedance, radiation fields and power flow have been demonstrated using the proposed multi-stacked electrical network of R, L, and C components coupled with a suitable transformer. Overall, the proposed multi-stacked DRA network shows an improved quality factor and selectivity, and bandwidth is reduced reasonably. The multi-stacked DRA network would find useful applications in radio frequency wireless communication systems. Additionally, for enhancing the impedance, BW of DRA a multi-stacked DRA is proposed by the use of ground-plane techniques with slots, dual-segment, and stacked DRA. The performance of multi-stacked DRA is improved by a factor of 10% as compared to existing models in terms of better flexibility, moderate gain, compact size, bandwidth, quality factor, resonant frequency, frequency impedance at the resonance frequency, and the radiation pattern with Terahertz frequency range. Full article
(This article belongs to the Special Issue Setting the Future of Smart Industry 4.0 with Metaheuristic Algorithms)
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15 pages, 590 KiB  
Article
A Model for the Generalised Dispersion of Synovial Fluids on Nutritional Transport with Joint Impacts of Electric and Magnetic Field
by B. Rushi Kumar, R. Vijayakumar and A. Jancy Rani
Math. Comput. Appl. 2023, 28(1), 3; https://doi.org/10.3390/mca28010003 - 27 Dec 2022
Cited by 1 | Viewed by 1338
Abstract
This work analyses the effect of electromagnetic fields on cartilaginous cells in human joints and the nutrients that flow from the synovial fluid to the cartilage. The perturbation approach and the generalised dispersion model is used to solve the governing equation of momentum [...] Read more.
This work analyses the effect of electromagnetic fields on cartilaginous cells in human joints and the nutrients that flow from the synovial fluid to the cartilage. The perturbation approach and the generalised dispersion model is used to solve the governing equation of momentum and mass transfer. The dispersion coefficient increases with dimensionless time. It aids in grasping the level of nutritional transport to the synovial joint. Low-molecular-weight solutes have a lower concentration distribution at the same depth in articular cartilage than high-molecular-weight solutes. Thus, diffusion dominates nutrition transport for low-molecular-weight solutes, whereas a mechanical pumping action dominates nutrition transport for high-molecular-weight solutes. The report says that the cells in the centre of the cartilage surface receive more nutrients during imbibition and exudation than the cells on the periphery, and the earliest indications of cartilage degradation emerge in the uninflected regions. As a result, cartilage nutrition is considered necessary to joint mobility. It also predicts that, as the viscoelastic parameter increases, the concentration in the articular cartilage diminishes, resulting in the cartilage cells receiving less nutrition, which might lead to harmful effects. The dispersion coefficient and mean concentration for distinct factors, such as the Hartmann number, porous parameter, and viscoelastic parameters of gel formation, have been computed and illustrated through graphics. Full article
(This article belongs to the Special Issue Mathematical and Computational Modeling on Fluid Flow and Heat Transfer)
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12 pages, 2664 KiB  
Article
Impacts of Casson Model on Hybrid Nanofluid Flow over a Moving Thin Needle with Dufour and Soret and Thermal Radiation Effects
by Vinodh Srinivasa Reddy, Jagan Kandasamy and Sivasankaran Sivanandam
Math. Comput. Appl. 2023, 28(1), 2; https://doi.org/10.3390/mca28010002 - 27 Dec 2022
Cited by 7 | Viewed by 1394
Abstract
The current study used a novel Casson model to investigate hybrid Al2O3-Cu/Ethylene glycol nanofluid flow over a moving thin needle under MHD, Dufour–Soret effects, and thermal radiation. By utilizing the appropriate transformations, the governing partial differential equations are transformed [...] Read more.
The current study used a novel Casson model to investigate hybrid Al2O3-Cu/Ethylene glycol nanofluid flow over a moving thin needle under MHD, Dufour–Soret effects, and thermal radiation. By utilizing the appropriate transformations, the governing partial differential equations are transformed into ordinary differential equations. The transformed ordinary differential equations are solved analytically using HAM. Furthermore, we discuss velocity profiles, temperature profiles, and concentration profiles for various values of governing parameters. Skin friction coefficient increases by upto 45% as the Casson parameter raised upto 20%, and the heat transfer rate also increases with the inclusion of nanoparticles. Additionally, local skin friction, a local Nusselt number, and a local Sherwood number for many parameters are entangled in this article. Full article
(This article belongs to the Special Issue Mathematical and Computational Modeling on Fluid Flow and Heat Transfer)
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16 pages, 323 KiB  
Article
Finite-Time Static Output-Feedback H∞ Control for Discrete-Time Singular Markov Jump Systems Based on Event-Triggered Scheme
by Xiaofu Ji and Xueqing Yan
Math. Comput. Appl. 2023, 28(1), 1; https://doi.org/10.3390/mca28010001 - 20 Dec 2022
Viewed by 1342
Abstract
The problem of finite-time static output feedback H∞ control for a class of discrete-time singular Markov jump systems is studied in this paper. With the consideration of network transmission delay and event-triggered schemes, a closed-loop model of a discrete-time singular Markov jump [...] Read more.
The problem of finite-time static output feedback H∞ control for a class of discrete-time singular Markov jump systems is studied in this paper. With the consideration of network transmission delay and event-triggered schemes, a closed-loop model of a discrete-time singular Markov jump system is established under the static output feedback control law, and the corresponding sufficient condition is given to guarantee this system will be regular, causal, finite-time bounded and satisfy the given H∞ performance. Based on the matrix decomposition algorithm, the output feedback controller can be reduced to a feasible solution of a set of strict matrix inequalities. A numerical example is presented to show the effectiveness of the presented method. Full article
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