Pub Date : 2019-01-01DOI: 10.1504/IJMMNO.2019.096911
Zineb Tabbakh, R. Ellaia, A. Habbal
: In this paper, we introduce a new hybrid method called Nonmonotone Spectral Gradient and Simultaneous Perturbation (NSGSP). It combines the advantages of nonmonotone spectral gradient (NSG), and simultaneous perturbation (SP) methods. The main idea of our approach is to use the simultaneous perturbation (SP) method in order to get a non expensive estimate of the gradient, and exploit the good properties of the nonmonotone spectral gradient (NSG) method in order to compute an efficient line search. Several numerical experiments are provided. The results indicate that the new method is effective and outperforms most of other popular methods. Habbal concern analysis and control of systems governed by partial differential equations (PDEs), optimization theory and algorithms and PDE-constrained games. Application fields are related to (nonlinear) mechanics, image processing, data recovering and cell dynamics.
{"title":"New hybrid algorithm based on nonmonotone spectral gradient and simultaneous perturbation","authors":"Zineb Tabbakh, R. Ellaia, A. Habbal","doi":"10.1504/IJMMNO.2019.096911","DOIUrl":"https://doi.org/10.1504/IJMMNO.2019.096911","url":null,"abstract":": In this paper, we introduce a new hybrid method called Nonmonotone Spectral Gradient and Simultaneous Perturbation (NSGSP). It combines the advantages of nonmonotone spectral gradient (NSG), and simultaneous perturbation (SP) methods. The main idea of our approach is to use the simultaneous perturbation (SP) method in order to get a non expensive estimate of the gradient, and exploit the good properties of the nonmonotone spectral gradient (NSG) method in order to compute an efficient line search. Several numerical experiments are provided. The results indicate that the new method is effective and outperforms most of other popular methods. Habbal concern analysis and control of systems governed by partial differential equations (PDEs), optimization theory and algorithms and PDE-constrained games. Application fields are related to (nonlinear) mechanics, image processing, data recovering and cell dynamics.","PeriodicalId":13553,"journal":{"name":"Int. J. Math. Model. Numer. Optimisation","volume":"78 1","pages":"32-55"},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80863388","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-01-01DOI: 10.1504/IJMMNO.2019.096919
B. Pattanayak, S. S. Mohapatra, H. Das
Rice is considered as the major staple food throughout India. Drying is one of the major alternatives available for proper storage of rice. The drying process can be suitably represented by many mathematical models. In this study 10 different mathematical models are chosen for describing the mathematical behaviour of drying. The experimental data obtained from the drying of raw rice at different temperatures, drying air velocity and relative humidity are fitted with the chosen mathematical models. The best suitable model to describe the drying behaviour of raw rice is determined by non-linear regression analysis. The statistical indicators Correlation coefficient (R2), root mean square error (RMSE) and sum of squares due to error (SSE) showed that Midilli et al. (2002) model is suitable model for all operating conditions. The coefficients of Midilli et al. 2002 model is also expressed as a function of drying air temperature, velocity and inventory of paddy.
在印度，大米被认为是主要的主食。干燥是大米适当储存的主要替代方法之一。干燥过程可以用许多数学模型来恰当地表示。在这项研究中，选择了10种不同的数学模型来描述干燥的数学行为。对不同温度、干燥风速和相对湿度条件下的原料米干燥实验数据进行了拟合。通过非线性回归分析确定了最适合描述原料米干燥特性的模型。统计指标相关系数(R2)、均方根误差(RMSE)和误差平方和(SSE)表明，Midilli et al.(2002)模型是适用于所有工况的模型。Midilli et al. 2002模型的系数也表示为干燥空气温度、速度和水稻库存的函数。
{"title":"Mathematical modelling for low temperature batch drying of paddy using fluidised bed technology","authors":"B. Pattanayak, S. S. Mohapatra, H. Das","doi":"10.1504/IJMMNO.2019.096919","DOIUrl":"https://doi.org/10.1504/IJMMNO.2019.096919","url":null,"abstract":"Rice is considered as the major staple food throughout India. Drying is one of the major alternatives available for proper storage of rice. The drying process can be suitably represented by many mathematical models. In this study 10 different mathematical models are chosen for describing the mathematical behaviour of drying. The experimental data obtained from the drying of raw rice at different temperatures, drying air velocity and relative humidity are fitted with the chosen mathematical models. The best suitable model to describe the drying behaviour of raw rice is determined by non-linear regression analysis. The statistical indicators Correlation coefficient (R2), root mean square error (RMSE) and sum of squares due to error (SSE) showed that Midilli et al. (2002) model is suitable model for all operating conditions. The coefficients of Midilli et al. 2002 model is also expressed as a function of drying air temperature, velocity and inventory of paddy.","PeriodicalId":13553,"journal":{"name":"Int. J. Math. Model. Numer. Optimisation","volume":"29 1","pages":"89-103"},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76443339","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-01-01DOI: 10.1504/IJMMNO.2019.096906
A. Jameel, N. Anakira, A. Alomari, D. M. Alsharo, A. Saaban
In this paper, a semi analytical algorithm, namely homotopy analysis method (HAM) is presented for the first time to obtain approximate analytical solutions of nth order two point fuzzy boundary value problems (TPFBVP) involving ordinary differential equations. This method allows for the solution of the TPFBVP to be calculated in the form of an infinite series with the components that can be easily calculated. The HAM utilises a convergence control parameter to control the convergence region of the infinite series solution. Numerical experiment is tested to highlight the important features of the HAM algorithm. Comparison of the HAM results and available exact solution reveal that this algorithm is effective and simple and for solving TPFBVP.
{"title":"New semi-analytical method for solving two point nth order fuzzy boundary value problem","authors":"A. Jameel, N. Anakira, A. Alomari, D. M. Alsharo, A. Saaban","doi":"10.1504/IJMMNO.2019.096906","DOIUrl":"https://doi.org/10.1504/IJMMNO.2019.096906","url":null,"abstract":"In this paper, a semi analytical algorithm, namely homotopy analysis method (HAM) is presented for the first time to obtain approximate analytical solutions of nth order two point fuzzy boundary value problems (TPFBVP) involving ordinary differential equations. This method allows for the solution of the TPFBVP to be calculated in the form of an infinite series with the components that can be easily calculated. The HAM utilises a convergence control parameter to control the convergence region of the infinite series solution. Numerical experiment is tested to highlight the important features of the HAM algorithm. Comparison of the HAM results and available exact solution reveal that this algorithm is effective and simple and for solving TPFBVP.","PeriodicalId":13553,"journal":{"name":"Int. J. Math. Model. Numer. Optimisation","volume":"79 1","pages":"12-31"},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78435747","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-01-01DOI: 10.1504/IJMMNO.2019.096918
A. Raghib, B. A. E. Majd
Radio frequency identification (RFID) systems have received increased attention from academia and practitioners. RFID facilitates data acquisition and storage; it can provide accurate and real-time data without human intervention. This work proposes a new approach based on multi-level strategy with the aim to solve the deployment of RFID readers problem by focusing on the coverage, the interference and the number of deployed readers as the main objectives to optimise. In this way, speed constrained multi-objective particle swarm optimisation algorithm (SMPSO) is adopted in order to minimise the total number of readers required to identify all tags in a given area. The proposed multilevel approach based on SMPSO Algorithm is more efficient and converge rapidly which makes it ideal for our research involving optimal deployment of RFID readers. The simulation results show the effectiveness of the proposed approach.
{"title":"Hierarchical multiobjective approach for optimising RFID reader deployment","authors":"A. Raghib, B. A. E. Majd","doi":"10.1504/IJMMNO.2019.096918","DOIUrl":"https://doi.org/10.1504/IJMMNO.2019.096918","url":null,"abstract":"Radio frequency identification (RFID) systems have received increased attention from academia and practitioners. RFID facilitates data acquisition and storage; it can provide accurate and real-time data without human intervention. This work proposes a new approach based on multi-level strategy with the aim to solve the deployment of RFID readers problem by focusing on the coverage, the interference and the number of deployed readers as the main objectives to optimise. In this way, speed constrained multi-objective particle swarm optimisation algorithm (SMPSO) is adopted in order to minimise the total number of readers required to identify all tags in a given area. The proposed multilevel approach based on SMPSO Algorithm is more efficient and converge rapidly which makes it ideal for our research involving optimal deployment of RFID readers. The simulation results show the effectiveness of the proposed approach.","PeriodicalId":13553,"journal":{"name":"Int. J. Math. Model. Numer. Optimisation","volume":"149 1","pages":"70-88"},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76792199","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-01-01DOI: 10.1504/ijmmno.2019.102601
Ryoichi Chiba
{"title":"Natural convection analysis of water near its density extremum between finite vertical plates: a differential transform approach","authors":"Ryoichi Chiba","doi":"10.1504/ijmmno.2019.102601","DOIUrl":"https://doi.org/10.1504/ijmmno.2019.102601","url":null,"abstract":"","PeriodicalId":13553,"journal":{"name":"Int. J. Math. Model. Numer. Optimisation","volume":"6 1","pages":"429-448"},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74350158","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-01-01DOI: 10.1504/IJMMNO.2019.096907
S. Banerjea, R. Chakraborty, A. Samanta
A simple numerical technique namely boundary element method (BEM) is employed here to solve Fredholm and Volterra integral equations of the second kind. In this method, the integral equation is converted into a system of linear algebraic equations by discretising the range of the integration and interval of definition into a finite number of line elements. By solving the system of linear equations by standard technique the solution of the integral equation is obtained for points in each line element. The method is computationally very simple and gives quite accurate results.
{"title":"Boundary element approach of solving Fredholm and Volterra integral equations","authors":"S. Banerjea, R. Chakraborty, A. Samanta","doi":"10.1504/IJMMNO.2019.096907","DOIUrl":"https://doi.org/10.1504/IJMMNO.2019.096907","url":null,"abstract":"A simple numerical technique namely boundary element method (BEM) is employed here to solve Fredholm and Volterra integral equations of the second kind. In this method, the integral equation is converted into a system of linear algebraic equations by discretising the range of the integration and interval of definition into a finite number of line elements. By solving the system of linear equations by standard technique the solution of the integral equation is obtained for points in each line element. The method is computationally very simple and gives quite accurate results.","PeriodicalId":13553,"journal":{"name":"Int. J. Math. Model. Numer. Optimisation","volume":"14 1","pages":"1-11"},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89041543","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-09-11DOI: 10.1504/IJMMNO.2018.10015799
A. Das, S. Natesan
In this paper, we consider a class of singularly perturbed 2D delay parabolic convection-diffusion initial-boundary-value problems. To solve this problem numerically, we use a modified Shishkin mesh (Bakhvalov-Shishkin mesh) for the discretisation of the domain in the spatial directions and uniform mesh in the temporal direction. The time derivative is discretised by the implicit-Euler scheme and the spatial derivatives are discretised by the upwind finite difference scheme. We derive some conditions on the mesh-generating functions which are useful for the convergence of the method, uniformly with respect to the perturbation parameter. We prove that the proposed scheme on the Bakhvalov-Shishkin mesh is first-order convergent in the discrete supremum norm, which is optimal and does not require any extra computational effort compared to the standard Shishkin mesh. Numerical experiments verify the theoretical results.
{"title":"Uniformly convergent numerical method for singularly perturbed 2D delay parabolic convection-diffusion problems on Bakhvalov-Shishkin mesh","authors":"A. Das, S. Natesan","doi":"10.1504/IJMMNO.2018.10015799","DOIUrl":"https://doi.org/10.1504/IJMMNO.2018.10015799","url":null,"abstract":"In this paper, we consider a class of singularly perturbed 2D delay parabolic convection-diffusion initial-boundary-value problems. To solve this problem numerically, we use a modified Shishkin mesh (Bakhvalov-Shishkin mesh) for the discretisation of the domain in the spatial directions and uniform mesh in the temporal direction. The time derivative is discretised by the implicit-Euler scheme and the spatial derivatives are discretised by the upwind finite difference scheme. We derive some conditions on the mesh-generating functions which are useful for the convergence of the method, uniformly with respect to the perturbation parameter. We prove that the proposed scheme on the Bakhvalov-Shishkin mesh is first-order convergent in the discrete supremum norm, which is optimal and does not require any extra computational effort compared to the standard Shishkin mesh. Numerical experiments verify the theoretical results.","PeriodicalId":13553,"journal":{"name":"Int. J. Math. Model. Numer. Optimisation","volume":"91 1","pages":"305-330"},"PeriodicalIF":0.0,"publicationDate":"2018-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76121042","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-09-11DOI: 10.1504/IJMMNO.2018.10015806
P. Rajadurai
This paper deals with a single server retrial queueing system with working vacations and vacation interruption. There are three different types of customers are considered, which are priority customers, ordinary customers and negative customers. The priority customers do not form any queue and have an exclusive preemptive priority to receive their services over ordinary customers. The negative customer is arriving during the service time of any positive customer, will remove the positive customer from the service. If the interrupted customer is an ordinary customer, he will leave the system. As soon as the orbit becomes empty at the time of service completion, the server goes for a working vacation. The server works at a lower speed during a working vacation period. Using the supplementary variable technique, the steady-state probability generating a function of the system and its orbit are found. Some numerical examples are presented.
{"title":"A study on M/G/1 retrial queueing system with three different types of customers under working vacation policy","authors":"P. Rajadurai","doi":"10.1504/IJMMNO.2018.10015806","DOIUrl":"https://doi.org/10.1504/IJMMNO.2018.10015806","url":null,"abstract":"This paper deals with a single server retrial queueing system with working vacations and vacation interruption. There are three different types of customers are considered, which are priority customers, ordinary customers and negative customers. The priority customers do not form any queue and have an exclusive preemptive priority to receive their services over ordinary customers. The negative customer is arriving during the service time of any positive customer, will remove the positive customer from the service. If the interrupted customer is an ordinary customer, he will leave the system. As soon as the orbit becomes empty at the time of service completion, the server goes for a working vacation. The server works at a lower speed during a working vacation period. Using the supplementary variable technique, the steady-state probability generating a function of the system and its orbit are found. Some numerical examples are presented.","PeriodicalId":13553,"journal":{"name":"Int. J. Math. Model. Numer. Optimisation","volume":"19 1","pages":"393-417"},"PeriodicalIF":0.0,"publicationDate":"2018-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91204893","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-09-11DOI: 10.1504/IJMMNO.2018.10015800
L. Abdurrahman, Suhardi, A. Langi, T. Simatupang
This paper proposes the developed business performance based on the IT value model, which offers superior performance with profit maximisation due to increased revenue and reduced costs. The model stands on the resource-based view (RBV) theory, the partial adjustment valuation (PAV) theory, and the systems engineering approach. The model consists of firm performance, firm core competence, firm capability, and information technology resource subsystems. Each subsystem has inputs, namely the regular capital (K), the regular labour expense (L), and IT capital (I) where the output is the gross revenue (y). The data was collected from Telkom, Indosat, and XL, which are telco firms in Indonesia. The IT value model optimisation testing displays that the model is able to provide superior performance with increased revenue at a lower cost.
{"title":"Information technology value model and its optimal application in IT-based firms","authors":"L. Abdurrahman, Suhardi, A. Langi, T. Simatupang","doi":"10.1504/IJMMNO.2018.10015800","DOIUrl":"https://doi.org/10.1504/IJMMNO.2018.10015800","url":null,"abstract":"This paper proposes the developed business performance based on the IT value model, which offers superior performance with profit maximisation due to increased revenue and reduced costs. The model stands on the resource-based view (RBV) theory, the partial adjustment valuation (PAV) theory, and the systems engineering approach. The model consists of firm performance, firm core competence, firm capability, and information technology resource subsystems. Each subsystem has inputs, namely the regular capital (K), the regular labour expense (L), and IT capital (I) where the output is the gross revenue (y). The data was collected from Telkom, Indosat, and XL, which are telco firms in Indonesia. The IT value model optimisation testing displays that the model is able to provide superior performance with increased revenue at a lower cost.","PeriodicalId":13553,"journal":{"name":"Int. J. Math. Model. Numer. Optimisation","volume":"101 1","pages":"331-350"},"PeriodicalIF":0.0,"publicationDate":"2018-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78080700","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-09-11DOI: 10.1504/IJMMNO.2018.10015804
R. Viriyapong, Gunyarat Koompawan
Rotavirus infection is one of the significant causes of death in infants and children under five years of age in Thailand and worldwide. In this paper, a deterministic model for rotavirus transmission in children under five years old in Thailand incorporating with hygiene care control and maternal immunity is developed. The basic reproduction number (Rv) is derived and becomes a threshold indicating the stability of both disease-free and endemic equilibrium points. Through the analysis, the results show that the disease-free equilibrium point is locally asymptotically stable when Rv 1 and satisfies the Routh-Hurwitz criteria. Further, numerical simulation demonstrates that both hygiene care and maternal immunity to the infection due to breastfeeding should be encouraged as a strategy to control rotavirus infection.
{"title":"The impact of hygiene care and maternal immunity on stability behaviour of rotavirus infection model for children under the age of five in Thailand","authors":"R. Viriyapong, Gunyarat Koompawan","doi":"10.1504/IJMMNO.2018.10015804","DOIUrl":"https://doi.org/10.1504/IJMMNO.2018.10015804","url":null,"abstract":"Rotavirus infection is one of the significant causes of death in infants and children under five years of age in Thailand and worldwide. In this paper, a deterministic model for rotavirus transmission in children under five years old in Thailand incorporating with hygiene care control and maternal immunity is developed. The basic reproduction number (Rv) is derived and becomes a threshold indicating the stability of both disease-free and endemic equilibrium points. Through the analysis, the results show that the disease-free equilibrium point is locally asymptotically stable when Rv 1 and satisfies the Routh-Hurwitz criteria. Further, numerical simulation demonstrates that both hygiene care and maternal immunity to the infection due to breastfeeding should be encouraged as a strategy to control rotavirus infection.","PeriodicalId":13553,"journal":{"name":"Int. J. Math. Model. Numer. Optimisation","volume":"9 1","pages":"378-392"},"PeriodicalIF":0.0,"publicationDate":"2018-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82240117","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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