Forthcoming articles

International Journal of Mathematical Modelling and Numerical Optimisation

International Journal of Mathematical Modelling and Numerical Optimisation (IJMMNO)

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International Journal of Mathematical Modelling and Numerical Optimisation (16 papers in press)

Regular Issues

  • A new fuzzy transportation algorithm for finding fuzzy optimal solution   Order a copy of this article
    by Farikhin Farikhin, Muhammad Sam'an 
    Abstract: Based on the literature, many algorithms have been proposed to solve fuzzy transportation problems in real life. Among the existing algorithms, some do not use the ranking method to convert fuzzy numbers into crisp numbers, whereas some use ranking methods that fail to rank non-normal fuzzy numbers correctly and compensate with the use of areas. Therefore, in this paper, a new fuzzy transportation algorithm, i.e., the NNWC, NLC and NVA, is used to solve a fuzzy transportation problem. The ranking methods involving non-normal trapezoidal fuzzy numbers and triangular fuzzy numbers as well as a new ranking method using total integral value are used to solve case studies 1 and 2, and the results are compared with the results from existing methods. Because of the proposed method is a direct extension of a classical method, it is reasonable to apply it to real-life transportation problems.
    Keywords: fuzzy transportation problem; new fuzzy transportation algorithm;new total integral value; non-normal trapezoidal fuzzy numbers.

  • Marine reserve and its consequences in a predator-prey system for ecotourism and fishing   Order a copy of this article
    by Debabrata Das, T.K. Kar 
    Abstract: This article investigates the effects of introducing density regulation in terms of theta logistic, over a fishery with the implementation of marine reserve. For various density regulations, we discuss the inter-relationship between fishing effort and marine reserve with fish biomass, catches and total rent. It also depicts the impacts of exploitation up to maximum sustainable yield (MSY) and maximum economic yield (MEY) both for single species and predator prey system. We also illustrate some economic consequences of introducing marine reserve both on fishery and ecotourism including the effect of density dependence on these issues. It is interpreted that introducing reserve area, extinction due to over exploitation could be prevented but when there is a predator prey interaction, the benefit of reserve is diminished to some extent. It is found that the safe minimum biomass level (SMBL) also increases with increasing reserve size. With the increase of density regulation, fish biomass increases both in single species and predator-prey model, though in the absence of reserve catches vanishes as effort exceeds a certain level, irrespective of given importance to density regulation. Finally, it is observed that the optimal reserve size corresponding to fisheries management is less than the reserve size when both the fishery rent and ecotourism rent are considered jointly.
    Keywords: Predator-prey; theta logistic; marine reserve; MSY; ecotourism.

  • Modelling Biological Control Dynamics of the Banana Weevil Cosmopolites sordidus (Germar) by Generalist Predators in a Banana Agroecosystem   Order a copy of this article
    by Eliab Horub Kweyunga, Julius Tumwiine, Eldad B. Karamura 
    Abstract: The biological control dynamics of the banana weevil Cosmopolites sordidus (Germar) by the generalist predator, P. javanus are studied by adopting a logistic model incorporating ratiodependent functional response. The steady states are obtained and their stability established. The expression for the banana weevil intrinsic growth rate, a key threshold that governs the control or persistence of the banana weevil is derived and its implications studied. Analysis of the model reveals that the model can have at least one and at most two equilibria depending on the relative sizes of the intrinsic growth rate vis-vis the carrying capacity and the predation rate. The banana weevil intrinsic growth rate and the predation rate are identified as the target parameters in managing infestation of the banana weevil. Numerical simulations are carried out to validate the theoretical findings. The study highlights the need for implementation of a complete integrated pest management (IPM) package against the banana weevil.
    Keywords: banana weevil; biological control; logistic growth; integrated pest management; ratio-dependent functional response; transcritical bifurcation.

  • Global stability of a fractional order eco-epidemiological system with infected prey   Order a copy of this article
    by Mahmoud Moustafa, Mohd Mohd, Ahmad Ismail, Farah Abdullah 
    Abstract: A fractional order eco-epidemiological system with infected prey is proposed and studied. Threshold parameters are obtained to determine the existence and stability conditions of equilibrium points of the proposed fractional order system. In order to clarify the characteristics of the proposed fractional order system, the analysis of existence, uniqueness, non-negativity and boundedness of the solutions, as well as the stability conditions of the system are examined. The global properties of all biologically feasible equilibrium points are studied by constructing suitable Lyapunov functions. It is proved that all equilibrium points of the proposed fractional order system are globally stable whenever they are locally stable. Some numerical simulations are conducted to verify the theoretical results.
    Keywords: Eco-epidemiological system; Predator-prey; Fractional order system; Global stability.

  • Guiding iterative optimisation methods to a predefined kind of optima for unconstrained optimisation problems   Order a copy of this article
    by Christina Nikolakakou, Athanasia Papanikolaou, Eirine Nikolopoulou, Theodoula Grapsa, George Androulakis 
    Abstract: One of the most fundamental issues in the field of mathematical optimisation is the convergence of an iterative optimization method and by this we are referring to two things. First, will the method find an optimum and second, will this optimum be a local one or a global one? A recently proposed technique [NGNA15] that is used in order to lessen the dependance a locally convergent iterative optimization method has on the initial guess, is exploited in this paper. A way so that such a method may be guided to a predefined kind of minimum (local or global) is presented. Well known test functions were used for experimentation. Statistical analysis was conducted by applying a logistic regression classification model on data arisen from the numerical results which confirmed that iterative optimisation methods can be guided to a predefined kind of optimum.
    Keywords: Unconstrained Optimisation; Priorities; Global minimum; Local minimum; Prediction; Classification; Hypothesis Testing; Logistic Regression.

  • A bioeconomic model applied to a small pelagic species along the Moroccan coast   Order a copy of this article
    by Imane AGMOUR, Meriem BENTOUNSI, Naceur ACHTAICH, Youssef EL FOUTAYENI 
    Abstract: This paper proposes a case study of five small pelagic species: sardina pilchrdus, sardinella, engraulis encrasicolus, scomber scombrus and trachurus exploited by seiners in the maritime zones of Morocco. A comparison is made between the fishing effort calculated using the generalized Nash equilibrium problem and the actual fishing effort given by the National Institute of Fisheries Research. In this work, fishing effort represents the number of fishing trips that must be made by seiners and that allows them to maximize their gain taking into account the preservation of marine species. As a result, we find that master data of the National Institute of Fisheries Research support the outcomes shown in the end of this paper.
    Keywords: Bio-economic model; Small pelagic species dynamics;\r\nFishing effort; Linear Complementarity Problems; Nash equilibrium.

  • Numerical investigation for solutions and derivatives of singularly perturbed initial value problems   Order a copy of this article
    by Subal Ranjan Sahu, Jugal Mohapatra 
    Abstract: This article proposes a hybrid scheme on layer-adapted meshes for solving singularly perturbed initialrnvalue problem depending on a parameter. Layer-adapted meshes namely standard Shishkin mesh and modified Shishkin mesh (Bakhvalov-Shishkinrnmesh and Vulanovi'{c} mesh) are considered. The hybrid scheme is a combinationrnof second order central difference scheme on the fine mesh and a modified midpoint upwindrnscheme on the coarse mesh. The error analysis is carried out. We establish a second order parameter uniformrnconvergence rate for the numerical solution and also for the scaled numerical derivative.rnIt is also shown that the modified Shishkin mesh and graded mesh likernGartland Shishkin mesh and Duran Shishkin mesh give better results than the standardrnShishkin mesh. In order to illustrate the efficiency of thernproposed method, some numerical experiments are shown which support the theoretical findings.
    Keywords: Singular perturbation; Initial value problem; Hybrid scheme; Layer adapted meshes; Uniform convergence.

  • A Hybrid Backtracking Search Algorithm for Energy Management in a Microgrid   Order a copy of this article
    by Zineb Garroussi, Rachid Ellaia, El-Ghazali Talbi, Jean-yves Lucas 
    Abstract: Recently, due to the high penetration of distributed generators and storages, and the rapid growth of environmental concerns, energy optimization plays a vital role in the operation of microgrids. In this paper, we propose a hybrid backtracking search matheuristic algorithm with a multiobjective indirect encoding (H-MOBSA) for the multiobjective mixed-integer non-linear formulation of economic-emission dispatch in a grid-connected microgrid. In this approach, each partial discrete solution represented by the backtracking search algorithm is associated with a set of Pareto solutions of the related continuous subproblem where the fitness and diversity assignments are adapted to take into account all associated decoded solutions. The proposed algorithm aims to provide generation planning and the battery size that satisfy the trade-off between the total operating cost and pollutant emissions under equality and inequality constraints. To show the effectiveness of our approach, the proposed H-MOBSA is tested on typical MG and compared to other algorithms.
    Keywords: Backtracking Search Algorithm; battery storage sizing; distributed generation; matheuristics; microgrid.

  • Exploring the Linkages between HIV/AIDS and Poverty: Insights through a Mathematical Model   Order a copy of this article
    by Symon Bilesi Chibaya, Farai Nyabadza 
    Abstract: Poverty continues to impact people living with HIV/AIDS negatively and it drives HIV/AIDS epidemics mostly in poor resource countries such as Malawi. In this paper, a mathematical model for HIV/AIDS that provides linkages between HIV/AIDS and poverty is formulated and analysed using non-linear ordinary differential equations. The theoretical evaluations identified four equilibria namely; an equilibrium in which there is no disease and per capita income is zero, disease-free, an equilibrium in which per capita income is zero and endemic. An epidemic threshold value, $R_M$, called the reproduction number is determined using the next-generation matrix method. The analysis of the model shows that the disease-free and endemic equilibria are globally stable for $R_M<1$ and $R_M>1$ respectively. Sensitivity analysis of $R_M$ is performed in order to determine how the parameters affect the dynamics of HIV/AIDS epidemics. Numerical simulations are done to show the role of some key model parameters on HIV/AIDS as well as to verify some analytical results. The results of the model suggest that income has the propensity to control the spread of HIV/AIDS because it has the capacity of decreasing unemployed people's vulnerability to sexually transmitted diseases such as HIV/AIDS.
    Keywords: Reproduction number; Equilibria; HIV/AIDS; Poverty; Simulation.

  • Bifurcation analysis of a diffusive predator-prey model with schooling behaviour and cannibalism in prey   Order a copy of this article
    by Salih Djilali, Abdelheq Mezouaghi, Omar Belhamiti 
    Abstract: In this paper, we study a predator-prey diffusion model, where we consider two very important factors, herd behavior and cannibalism in prey. These strange behaviors may exist is some aquatic carnivorous living being such as tuna. Our main objective in this work is to highlight the effect of prey cannibalism on the interaction between predator and prey. In a first step, we make an analysis of the system in the absence of diffusion, where the stability of the equilibrium states and the Hopf bifurcation are treated. Then, the effect of the presence of spatial diffusion is investigated by studying the global stability of the free equilibrium of cannibalism, the Hopf bifurcation and the stability of the periodic solution. The results of the proposed model are then raised, analyzed and discussed.
    Keywords: Predator-Prey Model; Cannibalism; Herd Behavior; Spatial Diffusion; Hopf Bifurcation.

  • A deeper Newton descent direction with generalized Hessian matrix for SVMs: an application to Face Detection   Order a copy of this article
    by Amir Abdessamad, Korichi Mokhtar El Amine 
    Abstract: By formulating the generalized Newton descent direction according to the parameter resulting from the calculation of the subgradient of the max function, a new version ofNSVM(Fung and Mangasarian, (2004)) is presented in this paper. This descent direction ensures even more the precision of the solution in a fast time. Associated with a good feautures extraction technique like Gabors wavelets, the application of the proposed method in the context of facial detection, shows that either the direction is calculated as an optimal solution of a onedimensional problem or by an heuristic approach, manages to detect faces not detected by advanced methods.
    Keywords: SupportVector Machines; Quadratic Programming; Newton Method; Face detection.

  • Explicit error estimates in a method of moments for recovering boundary data   Order a copy of this article
    by Abdeljalil Sakat, Boujema Achchab, Ali Souissi 
    Abstract: We consider a data completion method for the Cauchy problem of Laplace equation, that is known as a highly ill-posed problem. For an approximate solution given by any one of algorithms of the data completion methods, we give the moment of the error between the true solution and the approximate one, which allows us to find an a posteriori explicit error estimation.rnThis error indicator is used to improve the approximate solution, to give a knowledge of stability and can be used as a stopping criterion. Eventually, numerical experiments are provided.
    Keywords: Cauchy problem; Laplace equation; data completion problem; explicit a posteriori error estimate; moment problem; stopping criterion.

  • Analysis of a multi server queueing inventory model with self-service   Order a copy of this article
    by Rasmi K, Jacob M.J 
    Abstract: This paper considers a Markovian queueing inventory system with c servers and optional self-service facility, driven by an inventory under the (s, S) protocol. When an arrival occurs, if both an idle server and free inventory are available, then service by a server is initiated. If a customer on arrival finds all servers active but free inventory available, then he can either wait for the server (join the waiting line) or go for a self-service. If an arriving customer finds all servers busy and there is no free inventory, then he either joins the waiting line or leaves the system. We analyze the system as a 3-dimensional quasi-birth-and-death(QBD) process and numerically evaluate steady-state probabilities and express several important performance measures and a cost function in terms of them. A modified case of the framework has been considered by changing the presumption that in the event that an arriving customer finds all the servers active, but a few inventories free will choose to have self-service. Here also we obtain steady-state probabilities and express a cost function in terms of some important performance measures. We made a point to point investigation on recycle time. A cost optimization problem has been stated and numerically solved. Also, the impacts of certain parameters on a few performance measures are moreover outlined numerically.
    Keywords: Multiserver queue; self-service; (s; S) inventory; Matrix analytic method.

  • Upgraded Family of Estimators of Population Mean using Known Parameters of Auxiliary and Study Variables   Order a copy of this article
    by S.K. Yadav, Dinesh Sharma, Shanya Baghel 
    Abstract: This paper proposes an elevatedfamily of estimators for the population mean of a primary variable using the known auxiliary information combined with the known median of the study variable under the Simple Random Sampling Scheme. Various existing estimators of population mean are the members of the proposed class. The Bias and MSE of the proposed class are derived up to the first order of approximation. The minimum values of Bias and MSE are obtained by optimizing the characterizing scalar. The Bias and MSE of the suggested family have also been compared with that of existing estimators. Finally, we have suggested some new members of the proposed class, which are more efficient than the existing ones both theoretically and numerically.The empirical study has been done using R software for computing biases and the MSEs of the suggested and the competing estimators under the said sampling scheme.
    Keywords: Main Variable; Auxiliary Variable; Simple Random Sampling; Bias; MSE. rn.

  • A survey on update parameters of nonlinear conjugate gradient methods   Order a copy of this article
    by Nirmalya Kumar Mohanty, Rupaj Nayak 
    Abstract: Nonlinear Conjugate gradient methods are a class of techniques that are used for solving nonlinear optimization problems frequently arise in many engineering applications such as machine learning, computer vision, least-square optimizations to name a few. With so many surveys on the nonlinear conjugate gradient method (NLCG) available around, this paper addresses the current updates and sheds a new light on the evolution of hybrid conjugate gradient parameters with their global convergence properties.
    Keywords: Unconstrained Optimization; conjugate gradient method; nonlinearrnconjugate gradient method; Hybrid conjugate parameter.

  • Workload control with shifting bottlenecks: norms optimisation through Design of Experiments   Order a copy of this article
    by Francesco Zammori, Piero Ganugi, Camilla Ferretti, Davide Mezzogori 
    Abstract: Abstract\r\nWorkload Control is a production planning and control system designed to overcome the tradeoff between high Throughput Rates and short and Lead Times. Specifically, Work-In-Process is continuously monitored, and new jobs are not admitted in the shop floor until WIP drops below predefined threshold values or norms. To exploit performance, norms should be fine-tuned to minimize queues, without generating starvation at the bottleneck machines. The optimization process is straightforward for a perfectly balanced system, but much harder in case of shifting bottlenecks. The paper focuses on this issue and presents an innovative procedure, based on the Response Surfaces Method, which allows one to optimize the norms in a precise way, keeping unaltered the desired Throughput Rate. A comprehensive simulation analysis demonstrated the quality of the proposed approach and showed the importance of using different norms to boost the overall performance of the manufacturing system.\r\n
    Keywords: Bottleneck Shiftiness; Design of Experiments; Flow-Shop; Response Surfaces; Simulation; Workload Control.