Browsing by Author "Nahayo, Fulgence"
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Item An Efficient Non-Linear Application Algorithm Predictive Model for a Multi Aircraft Landing Dynamic System AIRLADYS R2019A+(Open Journal of Optimization, 2020) Nahayo, Fulgence; Khardi, SalahThe aim of this paper is to set up an efficient nonlinear application algorithm predictive model for a multi aircraft landing dynamic system called “Aircraft Landing Dynamic System, Release 2019A+ version “AIRLADYS R2019A+”. This programming software combines dynamic programming technic for mathematical computing and optimisation run under AMPL and KNITRO Solver. It uses also a descriptive programming technic for software design. The user interfaces designed in Glade are saved as XML, and by using the GtkBuilder GTK+ object these can be loaded by applications dynamically as needed. By using GtkBuilder, Glade XML files can be used in numerous programming languages including C, C++, C#, Java, Perl, Python, AMPL, etc. Glade is Free Software released under the GNU GPL License. By these tools, the solved problem is a mathematical modelization problem as a non-convex optimal control governed by ordinary non-linear differential equations. The dynamic programming technic is applied because it is a sufficiently high order and it does not require computation of the partial derivatives of the aircraft dynamic. This application will be coded with Linux system on 64 bit operating system, but it can also be run on the windows system. High running performances are obtained with results giving feasible trajectories with a robust optimizing of the objective function.Item iITLMA, an Intelligent Traffic Light Management Algorithm based on Wireless Sensor Networks(Wireless Personal Communications, 2023) Epela, Bernard; Manirabona, Audace; Nahayo, FulgenceThe rapid increase of vehicle population in many world cities implies the increase of road and accidents. Fortunately, intelligent transport systems (ITS) with traffic signals come to solve or at lease minimize the road problems by guaranteeing for instance safe driving at road intersections. However, they can disturb and reduce the traffic fluency due to the queue delay at each traffic flow if environmental information is not taken into account. This paper aims to overcome the above concern by studying the use of distributed systems to implement intelligent transport systems through a wireless sensor network. The proposed solution is a combination of a detection unit and two communicating sensors deployed on the tracks that can react to the passage of a vehicle. This work focuses on a four-lane intersection and an algorithm allowing sensors to cooperate and manage traffic in real time according to traffic conditions is developed. The experiment area where data have been collected is Bujumbura city, the capital of Burundi. The results of data computation show that our algorithm allows a reduction of 10% in waiting time in the case of rush hours and 32% in the case of normal hours. It leads also to the maximization of the number of vehicles passing through each intersection, which allows an improvement of road safety by reducing road accidents.Item Mathematical Modeling and Stability Analysis of Systemic Risk in the Banking Ecosystem(Hindawi Journal of Applied Mathematics, 2023) Irakoze,Irène; Nahayo, Fulgence; Ikpe, Dennis; Et al.This paper investigates the dynamics of systemic risk in banking networks by analyzing equilibrium points and stability conditions. The focus is on a model that incorporates interactions among distressed and undistressed banks. The equilibrium points are determined by solving a reduced system of equations, considering both homogeneous and heterogeneous scenarios. Local and global stability analyses reveal conditions under which equilibrium points are stable or unstable. Numerical simulations further illustrate the dynamics of systemic risk, while the theoretical findings offer insights into the behavior of distressed banks under varying conditions. Overall, the model enhances our understanding of systemic financial risk and offers valuable insights for risk management and policymaking in the banking sectorItem Modèle mathématique d'optimisation non-linéaire du bruit des avions commerciaux en approche sous contrainte energetique(Université de Lyon, 2012) Nahayo, FulgenceLa progréssion de l’aviation commerciale induit une détérioration de la qualité de l’environnement autour des aéroports à cause du bruit et des émissions de polluants. L’ACARE (Ad- visory Council For Aeronautics Research in Europe) et le Grenelle de l’Environnement recommandent d’atteindre, à l’horizon 2020, des objectifs quantitatifs permettant d’améliorer l’environnement aux environs des plateformes aéroportuaires. Cette thèse s’inscrit dans ce cadre et a pour objectif le développement d’un modèle mathématique d’optimisation acoustique des trajectoires de vol de deux avions commerciaux en approche sous contrainte énergétique, aérodynamique et opérationnelle. Il s’agit d’un modèle analytique de contrôle optimal non-linéaire et non-convexe régi par un système d’équations différentielles ordinaires issues de la dynamique de vol et des contraintes associées. Dans ce travail, notre contribution porte sur la modélisation mathématique des équations, l’optimisation et la programmation algorithmique et enfin la mise en pratique. Plus explicitement, nous mettons tout en oeuvre pour obtenir des solutions d’un modèle d’optimisation acoustique de deux avions en approche simultanée. Les points abordés sont les suivants : 1. Développement mathématique du modèle 3D « exact » de la dynamique de vol de deux avions en approche. 2. Modélisation mathématique de la commande optimale de ce système. 3. Introduction de la consommation du carburant par les avions comme une équation différentielle avec une fonction consommation spécifique variable en fonction de l’évolution de la dynamique des avions. 4. Modélisation mathématique instantanée de la fonction objectif représentant le bruit global des deux avions en approche. 5. Au niveau de la résolution du problème de contrôle optimal obtenu, nous avons utilisé le langage de modélisation AMPL et le solveur de programmation non linéaire KNITRO pour calculer des solutions locales. 6. D’une part, ces solutions sont trouvées de manière globale par la méthode de programmation séquentielle quadratique avec régions de confiance. Cette méthode directe résout le problème discrétisé, en transformant un problème de commande optimale à contraintes instantanées en un problème de programmation non linéaire en dimension finie. Cette transformation permet d’appliquer la technique de programmation séquentielle quadratique en considérant les conditions d’optimalités de Karush-Kuhn-Tucker. 7. D’une autre part, nous avons aussi utilisé une méthode indirecte en appliquant le principe de maximun de Pontryaguine suivie d’une discrétisation de type Runge Kutta partitionnée symplectique d’ordre 8. Démonstration de la commutation entre l’approche directe et l’approche indirecte en utilisant l’algorithme de Runge Kutta partitionnée symplectique et le principe de maximum de Pontryaguine pour la résolution du problème de contrôle optimal dans le cas de deux avions en approche en minimisant le bruit. Les résultats obtenus sont en accord avec les résultats obtenus en utilisant des coefficients de Runge Kutta classique comme cela est indiqué dans la commutation. 9. La comparaison entre les résultats obtenus avec les deux approches montrent que la solution optimale reste la même quelque soit la démarche adoptée. 10. Au niveau physique, des trajectoires optimales en descente continue, réduisant le bruit au sol ainsi que la consommation de carburant sont obtenues. Les résultats obtenus permettent de construire des trajectoires réduisant les niveaux de bruit perçus au sol et la consommation de kérosène pendant la phase d’approche simultanée des deux avions. Les gains en bruit se situent entre 5% et 8% pour les valeurs maximales en fonction des positions d’observation lorsque l’optimisation est considérée ou non. Une analyse de leur séparation a été menée. Cette recherche pourrait être étendue ultérieurement à la gestion du trafic aérien en considérant la résolution des conflits pour plusieurs types d’avions soit en approche ou en décollage.Item Optimal Predictive Algorithm for the Pickup and Delivery Problem with Time Windows and Scheduled Lines: Innovative Routing Transport Systems(Applied Mathematical Sciences, Vol. 14, 2020) Nahayo, Fulgence; Bigirimana , M.This paper concerns the Pickup and Delivery Problem with Time Windows and Scheduled Lines "PDPTW-SL" by modeling it mathematically on the one hand with the help of dynamic programming, on the other hand, it presents two optimal predictive methods of combinatorial optimization intended to solve it and which must provide stable and high accuracy solutions. The Pickup and Delivery Problem with Time Windows and Scheduled lines aims at routing a given set of vehicles to transport freight requests from their origins to their corresponding destinations, where the requests can use scheduled passenger transportation services during a stump of their journeys. We describe the PDPTW-SL as a mixed-integer program. Computational results on a set of small-size instances provide a clear understanding of the bene ts of preprocessing step and valid inequalities using scheduled line services as a part of freights journey.Item Pontryagin Principle Applied to Commercial Aircrafts Optimal Control Problem under Physical and Energetic Constraints(ICSRS Publication, 2017) Nahayo, FulgenceThe objective of this work is the development of a control and optimization flight paths model minimizing fuel consuption and noise perceived on the ground for two aircraft when flight constraints are considered. Flight dynamics, combined with the criterion to minimize noise levels generates an optimal control problem governed by nonlinear di erential equations . This problem is solved using an indirect method applying the minimum principle of Pontryagin and a dynamic programming method. Obtained optimal results showed signi cant reductions of fuel consumption and noise levels. This model shows and con rm environmental Approach impact around airport by reduction of the gene for neighbors due to noise. Reduction of Economic cost to airlines and for builders are also con rmed. An optimal approach path when compared to standard flight path is con rmed.This model can be generalized for any type of aircraft when considering real case for airport traffic and air traffic.Item Predictive Mathematical and Statistical Modeling of the Dynamic Poverty Problem in Burundi: Case of an Innovative Economic Optimization System(Open Journal of Optimization, 2021) Nahayo, Fulgence; Bagorizamba, Ancille; Bigirimana, Marc; Et al.The mathematical and statistical modeling of the problem of poverty is a major challenge given Burundi’s economic development. Innovative economic optimization systems are widely needed to face the problem of the dynamic of the poverty in Burundi. The Burundian economy shows an inflation rate of −1.5% in 2018 for the Gross Domestic Product growth real rate of 2.8% in 2016. In this research, the aim is to find a model that contributes to solving the problem of poverty in Burundi. The results of this research fill the knowledge gap in the modeling and optimization of the Burundian economic system. The aim of this model is to solve an optimization problem combining the variables of production, consumption, budget, human resources and available raw materials. Scientific modeling and optimal solving of the poverty problem show the tools for measuring poverty rate and determining various countries’ poverty levels when considering advanced knowledge. In addition, investigating the aspects of poverty will properly orient development aid to developing countries and thus, achieve their objectives of growth and the fight against poverty. This paper provides a new and innovative framework for global scientific research regarding the multiple facets of this problem. An estimate of the poverty rate allows good progress with the theory and optimization methods in measuring the poverty rate and achieving sustainable development goals. By comparing the annual food production and the required annual consumption, there is an imbalance between different types of food. Proteins, minerals and vitamins produced in Burundi are sufficient when considering their consumption as required by the entire Burundian population. This positive contribution mains in deficit. The lipids, acids, calcium, fibers and carbohydrates produced in Burundi are insufficient for consumption. This negative contribution proves a Burundian food deficit. It is a decision-making indicator for the design and updating of agricultural policy and implementation programs as well as projects. Investment and economic growth are only possible when food security is mastered. The capital allocated to food investment must be revised upwards. Demographic control is also a relevant indicator to push forward Burundi among the emerging countries in 2040. Meanwhile, better understanding of the determinants of poverty by taking cultural and organizational aspects into account guides managers for poverty reduction projects and programs.Item Réduction du bruit de deux avions commerciaux en approche par une technique de commande optimale(Researchgate, 2010) Nahayo, Fulgence; Khardi, Salah; Hamadiche, Mahmoud; Et al.L’objectif de ce travail est le d´eveloppement d’un mod`ele d’optimisation acoustique de trajectoires de vol minimisant les bruits per¸cus au sol pour deux avions. Il s’agit de minimiser le bruit tenant compte des contraintes de vol. La dynamique de vol, associ´ee au crit`ere `a minimiser g´en`ere un probl`eme de commande optimale r´egi par des ´equations diff´erentielles ordiniaires non-lin´eaires. Le probl`eme est resolu `a l’aide d’une m´ethode newtonienne consid´erant les conditions d’optimalit´e de Karush-Kuhn-Tucker et une m´ethode SQP. Les r´esultats obtenus montrent des r´eductions significatives des niveaux de bruit. En fonction de la distance s´eparant les deux avions en vol, la trajectoire optimale d’approche est obtenue.Item Statistic Modeling for Understanding the Origin of the Random Effects in the Tax Revenues Panel Data System in DR-Congo : Case of North-Kivu Province(Mathematical and Statistical Economics, 2021) Byamungu, Wanguwabo David; Nahayo, Fulgence; Fono, Louis Aimé; Et al.Forecasting tax revenues, particularly in Democratic Republic of the Congo economy, is an uphill task. Recent past of the country has been dominated by economic uncertainty, precisely in mining and in agriculture sectors. This factor, alone, has greatly contributed to high volatility of tax revenues collected by customs officers. The fuzzy characteristic of tax revenues has made it quite impossible for researchers to detect or distinguish from randomness the three well known components of a classical time series, precisely trends, seasonality, and cyclical phenomena .What are the factors which explain the random effects in the tax revenues panel in DRC? Our purpose is to detect and understand the origin of the random effects in the tax revenues panel data in DR-Congo through statistics about citizen’s perceptions around tax operation. A quantitative questionnaire with scaled values, open and closed questions, consisting in collecting various perceptions of different economic operators in the import-export sector has been administered to 170 taxpayers randomly selected. Through Analysis of variance, t-test analysis and Pearson Chi-square results show that dissatisfaction of taxpayers, lack of legitimacy in political institutions and government policies, highest tax rate, non-compliance with tax rate for all taxpayers, low level of knowledge in tax matters and corruption, fraud and tax evasion perpetuated by customs officers are the most factors which explain the random effects in DRC’s tax revenues panel data. Marital status is not a source influencing taxation. Mind of counterpart of the taxes in terms of achievements for improving social conditions which is not visible involves broken contract between taxpayers and tax authorities for several reasons sources of random effects above developed.Item Statistics Analysis Towards Capturing Comparison Between Taxation Systems of Neighboring Economies Versus DRC Taxation System(Applied Mathematical Sciences, 2021) Byamungu, Wanguwabo David; Nahayo, Fulgence; Fono, Louis AiméTax determinants are factors with tax system including collection machinery, penal system and tax rate and this differs from a country to another because of the strength of political institutions, efficient tax collection systems, tax rate. We deal with comparison of tax treatment of DRC to what applied to Rwanda, Tanzania, Uganda and Burundi as transit countries for goods of Congolese traders to determine whether the fluctuation underlying the problem of our study is due to the difference in tax collection model or the tax rate or if it is linked to another variable. Dealing with this, a quantitative questionnaire with open and closed questions, scaled values consisting in collecting various assessments of Congolese traders in import-export sector has been submitted to 340 taxpayers randomly selected. Through t-test analysis, Analysis of Variance and Chi-square results reveal that: tax rate is low in neighboring countries versus the highest tax rate in DRC applied to the same traders ‘goods. The statistically significant difference between different import products based on cross-border trade in the assessment of tax rate, on the one hand, and the relationship observed between the type of imported goods and the tax rate, on the other hand, proves the fact that in neighboring countries the tax administration sets the tax according to the types of goods and its weight while tax rate does depend on goods’ nomenclature declared in DRC.The degree of governance in tax administration is on of important factors to improve in tax revenues matters. Neighboring countries, as DRC, taxpayers with higher education level have civism development and higher attitudes towards more compliance. Finally, statistics reveal out that there is no statistically difference in attitudes towards tax compliance between male and female in DRC as in transit countries.Item The AppliedMathematical SimulationModeling Algorithm for a Multi Aircraft Landing Dynamic System at Bujumbura International Airport Mathematics and Innovative Technologies in Africa(European Scientific Journal, 2019) Nahayo, Fulgence; Ndimubandi, J.; Manirabona, A.; Niyongere, A.The aim of this paper is to set up an efficient nonlinear application algorithm simulation model for a multi aircraft landing dynamic system in one Runway when considering Bujumbura International Airport. The mathematical modelization of the solved problem is a non-convex optimal control governed by ordinary non-linear differential equations.The dynamic programming technic is applied because it is a sufficiently high order and it does-not require computation of the partial derivatives of the aircraft dynamic. This application is be coded with Linux operating system, but it can also be run on the windows system. High runing performance are obtained with results giving feasible trajectories with a robust optimizing of the objective function. The user interfaces designed in Glade are saved as XML, and by using the GtkBuilder GTK+ object these can be loaded by applications dynamically as needed. By using GtkBuilder, Glade XML files can be used in numerous programming languages including C, C++, C#, Java, Perl, Python,AMPL,etc.. Glade is Free Software released under the GNU GPL License. The algorithm is implemented when considering discrete mathematics while using Bujumbura International Airport Geographic Information System.Item The Trust Region Sequential Quadratic Programming method applied to twoaircraft acoustic optimal control problem(Researchage, 2011) Khardi, Salah; Nahayo, Fulgence; Haddou, MounirThis paper aims to reduce noise levels of two-aircraft landing simultaneously on approach. Constraints related to stability, performance and ight safety are taken into account. The problem of optimal control is described and solved by a Sequential Quadratic Programming numerical method 'SQP' when globalized by the trust region method. By using a merit function, a sequential quadratic programming method associated with global trust regions bypasses the non-convex problem. This method used a nonlinear interior point trust region optimization solver under AMPL. Among several possible solutions, it is shown that there is an optimal trajectory leading to a reduction of noise levels on approach.Item Two-Aircraft Dynamic System on Approach. Flight Path and noise Optimization(ResearchGate, 2012) Nahayo, Fulgence; Khardi, Salah; Haddou, MounirThe aim of this paper is to present and to solve a mathematical model of two-aircraft optimal control problem reducing noise during the approach. This is a non-convex optimal control problem governed by ordinary non-linear differential equations. A Symplectic Partitioned Runge-Kutta discretization and the Pontryaguin maximum principle are used. Discretization scheme provides a sufficiently high order requiring a computation of the partial derivatives of the aircraft dynamic parameters. The nonlinear interior point trust region optimization solver is applied. Numerical experiments and results are presented. They confirm the feasible optimized trajectories contributing to a significant noise reduction.Item Two-Aircraft optimal control problem. The in-flight noise reduction(ResearchGate, 2012) Nahayo, Fulgence; Khardi, Salah; Haddou,Mounir; Et al.The aim of this paper is to present and solve a mathematical model of a two-aircraft optimal control problem reducing the noise on the ground during the approach. The mathematical modelization of this problem is a non-convex optimal control governed by ordinary non-linear differential equations. To solve this problem, A direct method and a Runge-Kutta RK4 discretization schema are used. This discretization schema is chosed because it is a sufficiently high order and it does-not require computation of the partial derivatives of the aircraft dynamic. The Nonlinear Interior point Trust Region Optimization solver KNITRO is applied. A large set of numerical experiments is presented. The obtained results give feasible trajectories with a significant noise reduction.