International Journal of Mathematical Modelling and Numerical Optimisation (12 papers in press)
Warehousing and Analyzing Textual Data
by Sarah Attaf, Nadjia Benblidia, Omar Boussaid
Abstract: Traditional data warehousing technologies have been widely used for the analysis of simple data. Nonetheless, they are not suitable for textual data. In order to deal with this type of complex data, new systems have been proposed for text OLAP (On-Line Analytical Processing) purposes. However, they only cover partially the complexity of textual data, which might therefore affect decision-making quality. This paper proposes an efficient approach for warehousing and analyzing textual data. To tackle the main challenges facing these data, three major contributions are presented throughout our manuscript: (i) a Semantic Text Cube Model (ST-Cube), (ii) a new ETL approach (Extract Transform and Load), and (iii) an OLAP aggregation operator called Top_KRankedTopics.
For the validation of our approach, we have developed and implemented a platform for the storage and the analysis of text documents. Experimental results show that our ETL approach improves significantly the quality of information, extracted from textual document, compared to two other models while considering three different performance metrics. Moreover, the Top_KRankedTopics operator carry out effectively on-line analyses on textual data while taking different semantic factors into account.
Keywords: data warehousing; textual data analysis; semantic text cube model; ETL approach; semantic factors; On Line Analytical Processing (OLAP) Operators; top_KRankedTopics.
Optimal Design and Analysis of Hybrid Photovoltaic-Fuel Cell Power Generation System for an Advanced Converter Technologies
by Rajanand Patnaik Narasipuram
Abstract: Nowadays entire world is concentrated on Alternative Energy Sources (AES) or Renewable Energy Sources (RES) for developing the power in economical cost and the sources like tidal power, solar energy, geothermal energy, wind energy, biomass, fuel cells etc. Among all those sources solar energy and fuel cells are chosen for developing the Hybrid Power Generation (HPG) system. The Photovoltaic (PV) module is designed with an efficient Maximum Power Point Tracking (MPPT) technique of Neuro-Fuzzy (NF) tracking controller is developed to extract the maximum power and fed to boost DC-DC converter. In the mean while, Air Breathe Fuel Cell (ABFC) is designed and fed to the high step-up DC-DC converter with lesser duty cycle. The main concentration of this paper is to design the efficient Hybrid Power Generation (HPG) system for a competitive Multilevel Inverter (MLI) topology with less device count is the merit of this topology which is called Packed U Cell (PUC). In addition, this paper describes the mathematical analysis, design and operation of PV module, Neuro-Fuzzy (NF) MPPT controller based boost converter, ABFC, high step-up converter and PUC inverter. The P-V, I-V characteristics of PV module and ABFC stack effects on hydrogen pressure changes and temperature is examined. And also, the performance of HPG based PV-FC fed multilevel inverter is sifted for different load conditions. The overall performance is checked in terms of Total Harmonic Distortion (THD) for phase voltages (Vph) and phase currents (Iph) which are accomplished through FFT analysis for each load case. The whole simulations are carried out in MATLAB/Simulink environment.
Keywords: air breathe fuel cell; ABFC; alternative energy sources; AES; DC-DC converters; fuel cell; FC; hybrid power generation; HPG; maximum power point tracking; MPPT; multilevel inverter; MLI; Neuro-Fuzzy; NF; packed u cell inverter topology; PUC; photovoltaic; PV; renewable energy sources; RES; total harmonic distortion; THD;.
Tuning Runge-Kutta parameters on a family of ordinary differential equations
by Charles Audet
Abstract: The Runge-Kutta class of iterative methods is designed to approximate solutions of a system of ordinary differential equations (ODE). The second-order class of Runge-Kutta methods is determined by a system of 3 nonlinear equations and 4 unknowns, and includes the modified-Euler and mid-point methods. The fourth-order class is determined by a system of 8 nonlinear equations and 10 unknowns. This work formulates the question of identifying good values of these 8 parameters for a given family of ODE as a blackbox optimization problem.rnThe objective is to determine the parameter values that minimize the overall error produced by a Runge-Kutta method on a training set of ODE. Numerical experiments are conducted using the Nomad direct-search optimization solver.
Keywords: Runge-Kutta; Parameter tuning; Blackbox optimization; Direct-search.
Modelling and Predicting the Bitcoin Volatility Using GARCH Models
by Viviane Naimy, Marianne Hayek
Abstract: This paper is the first to model and forecast the volatility of the Bitcoin/USD exchange rate. It assesses and compares the predictive ability of the Generalized AutoRegressive Conditional Heteroskedasticity GARCH (1,1), the Exponentially Weighted Moving Average EWMA, and the Exponential Generalized AutoRegressive Conditional Heteroskedasticity EGARCH (1,1) in forecasting the volatility of the Bitcoin/USD exchange rate. Models parameters are first estimated from the in sample Bitcoin/USD exchange rate returns and in sample volatility is calculated. Out of sample volatility is forecasted afterward. Estimated volatilities are then compared to realized volatilities relying on error statistics, after which the models are ranked. The EGARCH (1,1) model outperforms the GARCH (1,1) and EWMA models in both in sample and out of sample contexts with increased accuracy in the out of sample period. Results show an original reflection concern with regard to the nature of the Bitcoin, which behaves differently than traditional currencies. Given the early-stage behavior of the Bitcoin, results might change in the future.
Keywords: Bitcoin; Modelling Volatility; Realized Volatility; Predictive Ability; GARCH(1,1); EWMA; EGARCH; in sample; out of sample; Optimization; Errors Test Statistics; MAE; RMSE; MAPE.
Stellar Population Analysis of Galaxies Based on Improved Flower Pollination Algorithm
by Mohamed Abdo., Yongquan Zhou, Ibrahim M. Hezam
Abstract: When numerical simulations are used for determining the age and contribution of different stellar populations in the integrated color of a galaxy some problems were encountered. In this paper, a modified flower pollination algorithm (MFPA) is proposed for determining the age and relative contribution of different stellar populations of galaxies. The results show that the proposed algorithm can search efficiently through the very large space of the possible ages for different integrated color of galaxies. The proposed algorithm will be applied to integrated color of galaxy NGC 3384. The numerical results and statistical analysis show that the proposed algorithm perform significantly better than previously used genetic algorithm, . The study revealed that the proposed algorithm can successfully be applied to a wide range of stellar population and space optimization problems.
Keywords: flower pollination algorithm; Meta-heuristics; Optimization; Stellar Population; Galaxies.
Uniformly convergent numerical method for singularly perturbed 2D delay parabolic convection-diffusion problems on Bakhvalov-Shishkin mesh
by Srinivasan Natesan, Abhishek Das
Abstract: In this article, we consider a class of singularly perturbed 2D delay parabolic convection-diffusion initial-boundary-value problems. To solve the problem numerically, we consider upwind finite difference scheme on a modified Shishkin mesh (Bakhvalov-Shishkin mesh) to discretize the domain in spatial directions and we apply implicit-Euler scheme for the time derivative on uniform mesh in the temporal direction. 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 applied 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 compare to the standard Shishkin mesh. Numerical experiments verify the theoretical results.
Keywords: Singularly perturbed 2D delay parabolic convection-diffusion problems; boundary layers; finite difference scheme; Bakhvalov-Shishkin mesh; uniform convergence.
Information technology value model and its optimal application in IT-based firms
by Lukman Abdurrahman, Suhardi Suhardi, Armein Z.R. Langi, Togar M. Simatupang
Abstract: This paper proposes the developed business performance based on the IT value model, which offers superior performance with profit maximization due to increased revenue and reduced costs. The model stands on the resource-based view theory, the partial adjustment valuation theory, and the systems engineering approach. Therefore, the model consists of firm performance, firm core competence, firm capability, and information technology resource subsystems. Each subsystem has inputs, i.e. the regular capital (K), the regular labour expense (L), and IT capital (I) where the output is y (the gross revenue). In addition, the synthesis result states that the model with the structure of the composition of each subsystem with the addition operation is more acceptable. The data used came from Telkom, Indosat, and XL, which are telco firms in Indonesia. Similarly, the IT value model optimization testing displays that the model is able to provide superior performance with increased revenue, but at a lower cost. Thus, the proposed model can address the mentioned main problems. However, it needs further studies to enhance this model.
Keywords: capital;systems engineering;information technology;model;partial adjustment;performance;revenue;cost;value.
Backtracking search algorithm for multi-objective design optimisation
by Ahmed Tchvagha Zeine, Abdelkhalak El Hami, Rachid Ellaia, Emmanuel Pagnacco
Abstract: In engineering, design problems are generally multi-objective with complex non-linear constraints. Therefore, the computing effort can often rise significantly with the number of objectives and constraints' evaluation. The metaheuristics algorithms are nowadays considered as powerful algorithms to deal with multi-objective optimisation problems. In this article, we develop a new backtracking search algorithm for multi-objective optimisation, called BSAMO, to solve this kind of problems. It is evaluated here through a set of benchmarks problems and two structural design applications. BSAMO's numerical results are compared with those of NSGA-II by two performance measures. They show that the proposed algorithm is able to produce a better convergence towards the Pareto front and to preserve the diversity of the solutions.
Keywords: backtracking search; design optimisation; evolutionary algorithms; multi-objective optimisation; structural optimisation.
A complex encoding flower pollination algorithm for constrained engineering optimisation problems
by Mohamed Abdel-Baset, Haizhou Wu, Yongquan Zhou
Abstract: In this paper, we apply a complex encoding flower pollination algorithm (CEFPA) to solve constrained engineering optimisation problems. The performance of the proposed algorithm is tested using five standard benchmark functions and four engineering problems. A comparative study of the results with those obtained well-known algorithms is used to validate and verify the efficiency of CEFPA. The CEFPA performs expressively better in terms of the speed and stability for the optimal solution.
Keywords: complex-valued encoding; constrained problems; flower pollination algorithm; optimisation.
The nonlinear dynamics of the dengue mosquito reproduction with respect to climate in urban Colombo: a discrete time density dependent fuzzy model
by W.P.T.M. Wickramaarachchi, S.S.N. Perera
Abstract: Dengue has been a major public health concern in most parts of the tropical world and the dynamics of dengue disease transmission is complex due to several external factors. Various mathematical models have been developed to understand the transmission dynamic of the dengue disease. However, the fixed parameter values have been used in those models so the real dynamics of the transmission is not explained completely. Mosquito density is responsible for the transmission of dengue locally, whilst human mobility causes transmission of the disease globally. Thus mosquito density is a vital parameter for study the dengue transmission which depends heavily on climate, geography and human behaviour. In this study, the density dependent Gompertz model with climate variation factor is used to model the mosquito density. Various levels of climate factor combinations act differently on the dynamics of mosquito density. Thus modelling the climate effect to grow mosquito populations should be done under uncertainty. The fuzzy membership functions are constructed for each factor rainfall and temperature where the membership value in [0, 1] explains the degree of favorability to mosquitoes from each factor in different levels. The Modified Einstein Sum operator is used to compute the overall measure of unfavorability from these two climate factors. The standardised mosquito density and real risk of dengue are compared using urban Colombo data and defining a mapping function. It is noted that 94.77% of data points are able to determine the real dengue risk 90% accurately.
Keywords: climate; dengue; fuzzy logic; mosquito density; SIR models.
An integer linear programming approach for optimising energy consumption in mobile wireless sensor networks under realistic constraints
by Khadidja Fellah, Bouabdellah Kechar
Abstract: Recent advances in miniature mobile robotics have fostered the emergence of mobile wireless sensor networks (MWSN). As sensor nodes are battery-powered devices, the first important constraint is how to reduce the energy consumption to extend the lifetime of the network. In this paper, we propose an optimisation approach based on integer linear programming (0-1 ILP) to significantly reduce energy consumption in MWSN. To do so, we formulate the problem as an objective function aiming to minimise the overall energy consumption related to communication operations and the mobility of the sensor nodes and/or sink. The developed formulation is performed under some realistic and relevant constraints of MWSN, such as sensing coverage, connectivity, adjustable transmission range and the case of adjustable sensing range. The proposed approach is evaluated using flat and cluster-based topologies by doing intensive experiments using the CPLEX solver. The obtained results reveal that the mobility factor in MWSN coupled with the considered additional constraints makes it possible to extend significantly the network lifetime.
Keywords: adjustable sensing range; adjustable transmission range; coverage and connectivity; energy saving; integer linear programming; mobility; MWSN; optimisation.
Special Issue on: Data Analytics and Modelling
A weighted model confidence set: applications to local and mixture model confidence sets
by Amir T. Payandeh Najafabadi, Ghobad Barmalzan, Shahla Aghaei
Abstract: Using the Kullback-Leibler (KL) divergence along with Vuong's test, this article constructs a set of appropriate weighted models, say weighted model confidence set, for unknown true density h(·) which is a subset of a class of non-nested models. A weighted confidence set provides an appropriate model for random variable X which some part of its support conveys some important information about the underlying true model. Application of such a weighted model confidence set for local and mixture model confidence sets have been given. Two simulation studies have been conducted to show practical application of our findings.
Keywords: inference under constraints; Kullback-Leibler divergence; local goodness of fitness; mixture models; model confidence set.