Pub Date : 2020-01-01DOI: 10.1504/ijmmno.2020.10031726
P. A. Simionescu
{"title":"A collection of bivariate nonlinear optimisation test problems with graphical representations","authors":"P. A. Simionescu","doi":"10.1504/ijmmno.2020.10031726","DOIUrl":"https://doi.org/10.1504/ijmmno.2020.10031726","url":null,"abstract":"","PeriodicalId":13553,"journal":{"name":"Int. J. Math. Model. Numer. Optimisation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85307652","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 : 2020-01-01DOI: 10.1504/ijmmno.2020.10031725
Nirmalya Kumar Mohanty, R. K. Nayak
{"title":"A new efficient hybrid conjugate gradient method based on LS-DY-HS conjugate gradient parameter","authors":"Nirmalya Kumar Mohanty, R. K. Nayak","doi":"10.1504/ijmmno.2020.10031725","DOIUrl":"https://doi.org/10.1504/ijmmno.2020.10031725","url":null,"abstract":"","PeriodicalId":13553,"journal":{"name":"Int. J. Math. Model. Numer. Optimisation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74338034","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 : 2020-01-01DOI: 10.1504/ijmmno.2020.10026055
M. J. Huntul, M. S. Hussein, D. Lesnic, M. Ivanchov, N. Kinash
Raw materials are anisotropic and heterogeneous in nature, and recovering their conductivity is of utmost importance to the oil, aerospace and medical industries concerned with the identification of soils, reinforced fibre composites and organs. Due to the ill-posedness of the anisotropic inverse conductivity problem certain simplifications are required to make the model tracktable. Herein, we consider such a model reduction in which the conductivity tensor is orthotropic with the main diagonal components independent of one space variable. Then, the conductivity components can be taken outside the divergence operator and the inverse problem requires reconstructing one or two components of the orthotropic conductivity tensor of a two-dimensional rectangular conductor using initial and Dirichlet boundary conditions, as well as non-local heat flux over-specifications on two adjacent sides of the boundary. We prove the unique solvability of this inverse coefficient problem. Afterwards, numerical results indicate that accurate and stable solutions are obtained.
{"title":"Reconstruction of an orthotropic thermal conductivity from non-local heat flux measurements","authors":"M. J. Huntul, M. S. Hussein, D. Lesnic, M. Ivanchov, N. Kinash","doi":"10.1504/ijmmno.2020.10026055","DOIUrl":"https://doi.org/10.1504/ijmmno.2020.10026055","url":null,"abstract":"Raw materials are anisotropic and heterogeneous in nature, and recovering their conductivity is of utmost importance to the oil, aerospace and medical industries concerned with the identification of soils, reinforced fibre composites and organs. Due to the ill-posedness of the anisotropic inverse conductivity problem certain simplifications are required to make the model tracktable. Herein, we consider such a model reduction in which the conductivity tensor is orthotropic with the main diagonal components independent of one space variable. Then, the conductivity components can be taken outside the divergence operator and the inverse problem requires reconstructing one or two components of the orthotropic conductivity tensor of a two-dimensional rectangular conductor using initial and Dirichlet boundary conditions, as well as non-local heat flux over-specifications on two adjacent sides of the boundary. We prove the unique solvability of this inverse coefficient problem. Afterwards, numerical results indicate that accurate and stable solutions are obtained.","PeriodicalId":13553,"journal":{"name":"Int. J. Math. Model. Numer. Optimisation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81276740","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 : 2020-01-01DOI: 10.1504/ijmmno.2020.10026038
L. Tartibu
This work proposes the use of an improved version of the augmented e-constraint method (AUGMENCON2) for the analysis of the thermal performance of a micro-channel heat sink. In order to highlight the strength and the effectiveness of this new approach, a trapezoidal micro-channel heat sink has been considered. The geometrical configuration namely the micro-channel widths and depth are the main variables considered in this study. Surrogate models based on the response surface methodology have been adopted to approximate the thermal resistance and the pumping power which provide an indication of the thermal performance of the micro-channel heat sink. A two-objective nonlinear problem have been formulated and implemented within the general algebraic modelling system. Global Pareto optimal solutions have been computed using the proposed method. Despite being a relatively straightforward method, the AUGMENCON2 provides a reasonable level of accuracy and shortens the required computational time in comparison to two existing approaches.
{"title":"Numerical analysis on thermal performance of a trapezoidal micro-channel heat sink using an improved version of the augmented ε-constraint method","authors":"L. Tartibu","doi":"10.1504/ijmmno.2020.10026038","DOIUrl":"https://doi.org/10.1504/ijmmno.2020.10026038","url":null,"abstract":"This work proposes the use of an improved version of the augmented e-constraint method (AUGMENCON2) for the analysis of the thermal performance of a micro-channel heat sink. In order to highlight the strength and the effectiveness of this new approach, a trapezoidal micro-channel heat sink has been considered. The geometrical configuration namely the micro-channel widths and depth are the main variables considered in this study. Surrogate models based on the response surface methodology have been adopted to approximate the thermal resistance and the pumping power which provide an indication of the thermal performance of the micro-channel heat sink. A two-objective nonlinear problem have been formulated and implemented within the general algebraic modelling system. Global Pareto optimal solutions have been computed using the proposed method. Despite being a relatively straightforward method, the AUGMENCON2 provides a reasonable level of accuracy and shortens the required computational time in comparison to two existing approaches.","PeriodicalId":13553,"journal":{"name":"Int. J. Math. Model. Numer. Optimisation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75114389","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 : 2020-01-01DOI: 10.1504/ijmmno.2020.10026042
A. Q. E. Idrissi, B. Achchab, A. C. Maloum
In this paper, we propose a numerical method to solve the European and the American options by using the SPH method. Because its robustness and efficacy, this numerical method has been widely applied in the computation of partial differential equations particularly in fluid dynamic. To model these financial options, we use the Black Scholes equation. It is a mathematical model consisting of a set of partial differential equation supplemented by some boundary conditions. We evaluate the accuracy of our numerical method by giving some comparisons between the analytic solution and the numerical simulation.
{"title":"Numerical analysis of the European and American options with the SPH method","authors":"A. Q. E. Idrissi, B. Achchab, A. C. Maloum","doi":"10.1504/ijmmno.2020.10026042","DOIUrl":"https://doi.org/10.1504/ijmmno.2020.10026042","url":null,"abstract":"In this paper, we propose a numerical method to solve the European and the American options by using the SPH method. Because its robustness and efficacy, this numerical method has been widely applied in the computation of partial differential equations particularly in fluid dynamic. To model these financial options, we use the Black Scholes equation. It is a mathematical model consisting of a set of partial differential equation supplemented by some boundary conditions. We evaluate the accuracy of our numerical method by giving some comparisons between the analytic solution and the numerical simulation.","PeriodicalId":13553,"journal":{"name":"Int. J. Math. Model. Numer. Optimisation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80659699","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 : 2020-01-01DOI: 10.1504/ijmmno.2020.10031724
Mengta Chung
{"title":"A Metropolis within Gibbs algorithm for knowledge discovery in language assessments","authors":"Mengta Chung","doi":"10.1504/ijmmno.2020.10031724","DOIUrl":"https://doi.org/10.1504/ijmmno.2020.10031724","url":null,"abstract":"","PeriodicalId":13553,"journal":{"name":"Int. J. Math. Model. Numer. Optimisation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85376306","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 : 2020-01-01DOI: 10.1504/ijmmno.2020.10031728
A. Carboni, L. O. Seman, E. Camponogara
{"title":"MINLP models for dimensional synthesis of planar four-bar linkages","authors":"A. Carboni, L. O. Seman, E. Camponogara","doi":"10.1504/ijmmno.2020.10031728","DOIUrl":"https://doi.org/10.1504/ijmmno.2020.10031728","url":null,"abstract":"","PeriodicalId":13553,"journal":{"name":"Int. J. Math. Model. Numer. Optimisation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89150780","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 : 2019-05-24DOI: 10.1504/ijmmno.2019.102571
Narender Kumar, M. I. Faizan, S. Parveen, Ravins Dohare
We formulated a susceptible-exposed-infected-recovered (SEIR) mathematical model for transmission of ZIKV. The model was used to estimate different parameters using the outbreak data obtained from Puerto Rico during 2015-2016 in this region. The inclusion of climatic factors in the model assisted in more realistic predictions of the transmission dynamics of ZIKV. The value basic reproduction number R0= 3.2869 calculated at estimated parameters suggested outbreak of infection in this region. The sensitivity analysis revealed that R0 was highly influenced by death rate, mosquito biting rate and maturation rate of immature mosquitoes. The R0 further implied that around 70% of the individuals should be immunised to develop herd immunity to prevent propagation of the disease. The simulation of controlled reproduction number revealed the values of different isolation coefficients (e1 > 0.4, e2 > 0.14, τ1 < 0.1). These coefficients might be utilised by policy makers in the control strategies against the infection.
{"title":"Temperature and rainfall dependent mathematical modelling for progression of Zika virus infection","authors":"Narender Kumar, M. I. Faizan, S. Parveen, Ravins Dohare","doi":"10.1504/ijmmno.2019.102571","DOIUrl":"https://doi.org/10.1504/ijmmno.2019.102571","url":null,"abstract":"We formulated a susceptible-exposed-infected-recovered (SEIR) mathematical model for transmission of ZIKV. The model was used to estimate different parameters using the outbreak data obtained from Puerto Rico during 2015-2016 in this region. The inclusion of climatic factors in the model assisted in more realistic predictions of the transmission dynamics of ZIKV. The value basic reproduction number R0= 3.2869 calculated at estimated parameters suggested outbreak of infection in this region. The sensitivity analysis revealed that R0 was highly influenced by death rate, mosquito biting rate and maturation rate of immature mosquitoes. The R0 further implied that around 70% of the individuals should be immunised to develop herd immunity to prevent propagation of the disease. The simulation of controlled reproduction number revealed the values of different isolation coefficients (e1 > 0.4, e2 > 0.14, τ1 < 0.1). These coefficients might be utilised by policy makers in the control strategies against the infection.","PeriodicalId":13553,"journal":{"name":"Int. J. Math. Model. Numer. Optimisation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81311217","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 : 2019-05-23DOI: 10.1504/ijmmno.2019.102576
Raja Chandrasekaran, R. Saravanan, D. Kumar, N. Gangatharan
Particle swarm optimisation is a trendy optimisation technique that is inhaled from the space navigational intelligence of birds. The optimisation technique is popular among the researchers for several decades because of the fact that it is inspired by the zonal and universal best members in all the generations. The optimisation by PSO is found better than few other optimisation techniques, in several trials with the optimisation of the mathematical benchmarks and real-time applications. But the more-than-modest orientation style of the algorithm often leads the population to premature convergence. Inertia weight parameter is used to tune the explorability of the population. In this paper, a zonal monitor (based on success in the recent iterations)-based inertia weight tuning is redressed by including universal monitors (based on the success with a universal fitness perspective). The proposed algorithm excels the conventional PSO, the PSO with zonal monitors alone. The inertia weight of the PSO with zonal monitor is also not dynamic whereas the proposed PSO's inertia weight are found to be more dynamic with tuning the explore ability with regard to zonal and universal context of fitness.
{"title":"A novel particle swarm optimisation with search space tuning parameter to avoid premature convergence","authors":"Raja Chandrasekaran, R. Saravanan, D. Kumar, N. Gangatharan","doi":"10.1504/ijmmno.2019.102576","DOIUrl":"https://doi.org/10.1504/ijmmno.2019.102576","url":null,"abstract":"Particle swarm optimisation is a trendy optimisation technique that is inhaled from the space navigational intelligence of birds. The optimisation technique is popular among the researchers for several decades because of the fact that it is inspired by the zonal and universal best members in all the generations. The optimisation by PSO is found better than few other optimisation techniques, in several trials with the optimisation of the mathematical benchmarks and real-time applications. But the more-than-modest orientation style of the algorithm often leads the population to premature convergence. Inertia weight parameter is used to tune the explorability of the population. In this paper, a zonal monitor (based on success in the recent iterations)-based inertia weight tuning is redressed by including universal monitors (based on the success with a universal fitness perspective). The proposed algorithm excels the conventional PSO, the PSO with zonal monitors alone. The inertia weight of the PSO with zonal monitor is also not dynamic whereas the proposed PSO's inertia weight are found to be more dynamic with tuning the explore ability with regard to zonal and universal context of fitness.","PeriodicalId":13553,"journal":{"name":"Int. J. Math. Model. Numer. Optimisation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78625205","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 : 2019-05-23DOI: 10.1504/ijmmno.2019.102582
Anu Sayal, A. Singh, Deepak Aggarwal
Deterioration is an unavoidable condition prevalent in all spheres of the inventory system involving perishable goods. Though other factors are also responsible for the depletion of the level of the inventory but the effect of deterioration in this regards is quite high. In the present paper, we have considered the deterioration rate of the form of Weibull distribution and the demand rate is taken as a ramp type function of time, when the inventory system starts without any kind of shortage. We have developed a mechanism for the optimisation of the total cost of the EOQ inventory system in both crisp and fuzzy environment. An appropriate numerical example has been proposed in order to validate the model in both crisp and fuzzy system.
{"title":"Optimisation of EOQ model with Weibull deterioration under crisp and fuzzy environment","authors":"Anu Sayal, A. Singh, Deepak Aggarwal","doi":"10.1504/ijmmno.2019.102582","DOIUrl":"https://doi.org/10.1504/ijmmno.2019.102582","url":null,"abstract":"Deterioration is an unavoidable condition prevalent in all spheres of the inventory system involving perishable goods. Though other factors are also responsible for the depletion of the level of the inventory but the effect of deterioration in this regards is quite high. In the present paper, we have considered the deterioration rate of the form of Weibull distribution and the demand rate is taken as a ramp type function of time, when the inventory system starts without any kind of shortage. We have developed a mechanism for the optimisation of the total cost of the EOQ inventory system in both crisp and fuzzy environment. An appropriate numerical example has been proposed in order to validate the model in both crisp and fuzzy system.","PeriodicalId":13553,"journal":{"name":"Int. J. Math. Model. Numer. Optimisation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75907929","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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