Friday, June 17. 2016
Eva Volna and Martin Kotyrba1
Faculty of Science Department of Informatics and Computers, University of Ostrava, 30 dubna 22, 70103 Ostrava, Czech Republic
1Corresponding author. E-mail: martin.kotyrba@osu.cz
Abstract: The Vehicle Routing Problem (VRP) is one of the most challenging combinatorial optimization tasks. This problem consists in designing an optimal set of routes for a fleet of vehicles in order to serve a given set of customers. Vehicle routing problem forms an integral part of the supply chain management, which plays a significant role in productivity improvement in organizations through an efficient and effective delivery of goods/services to customers. This problem is known to be NP-hard; hence many heuristic procedures for its solution have been suggested. For such problems, it is often desirable to obtain approximate solutions, so they can be found fast enough and are sufficiently accurate for the purpose. In this paper, we have performed an experimental study that indicates a suitable use of genetic algorithms for the vehicle routing problem. We tested instances from Capacitated Vehicle Routing Problem Library (CVRPLIB) series A, B, E, M and X. The obtained experimental outputs were compared with the following heuristics: the Clarke and Wright heuristic, sweep algorithm, and Taillard's algorithm.
Keywords VRP - Vehicle Routing Problem, combinatorics, Clarke and Wright heuristic, Sweep algorithm,Taillard's algorithm, Genetic algorithm. Mathematics Subject Classification: 97K20, 90C59
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Monday, February 1. 2016
A. Alaimo, V. Artale, G. Barbaraci, C.L.R. Milazzo, C. Orlando and A. Ricciardello
Kore University of Enna,Faculty of Engineering and Architecture, Cittadella Universitaria - 94100 - Enna
andrea.alaimo@unikore.it, valeria.artale@unikore.it, calogero.orlando@unikore.it, cristina.milazzo@unikore.it, angela.ricciardello@unikore.it
Abstract: In this paper the mathematical model representing the dynamic of a Unmanned Aerial Vehicle (UAV) is studied in order to analyse its behaviour. In order to stabilize the entire system, linear Quadratic Regulator (LQR) control is used in such a way to set both PD and PID controls in position variables. A set simulation is performed to carry out the results for linear and non linear models. The LQR-PD and LQR-PID allow to move the plant's poles of UAV in the left half plane since without controller the systems is unstable. Simulations, LQR-PD and LQR-PID controllers are designed by using Matlab/Simulink. The simulations are performed to show how LQR tuned PD and PID controllers lead to zero the error of the position along Z earth direction, stop the rotation of Unmanned Aerial Vehicle (UAV) around body axes and stabilize the hexarotor.
Keywords: Hexarotor; LQR, PID and PD controller.
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Tuesday, January 19. 2016
S. Iqbala, A. R. Ansarib1, A. Javedc and A. M. Siddiquid
aDepartment of Computer Science, COMSATS Institute of Information Technology, Sahiwal Campus, Pakistan. bCentre for Advance Studies in Engineering (CASE), 19-Attaturk Avenue, G-5/1, Islamabad, Pakistan. cDepartment of Mathematics & Natural Sciences, Gulf University for Science & Technology, P.O. Box 7207, Hawally 32093, Kuwait dDepartment of Mathematics, York Campus, Pennsylvania State University, York,PA 17403, USA
Abstract: A weighted-residual based a posteriori error estimation formulation in Galerkin's finite element fashion using quadratic Lagrange polynomials has been formulated to find numerical solutions of obstacle, unilateral and contact second-order boundary-value problems. The approach having piecewise quadratic shape functions has been utilized for checking ">the approximate solutions for spatially adaptive finite element grids. The local element balance based on the residual has been considered as an error assessment criterion. Numerical testing indicates that local errors are large at the interface regions where the gradients are large. A comparison of an adaptive refined grid with that of a uniform mesh for second order obstacle boundary value problems, confirms the superiority of the adaptive scheme without increasing the number of unknown coefficients.
Keywords: Adaptive grid renement scheme, Quadratic Lagrange polynomials, Galerkin's method, Finite element method, Boundary-value problems
Mathematics Subject Classication: 65M60
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Thursday, July 16. 2015
Yu.E. Gorbachev 1 , E.G. Kolesnichenko 2 1Research Department, Coddan Technologies LLC, 197342 St. Petersburg, Russia 2Gas Kinetics Lab, Moscow State University, Institute for Mechanics, 117192 Moscow, Russia
Abstract: One of the main problems of the non-equilibrium physical-chemical gas-dynamics is considered: derivation of gas-dynamics equations for reactive gas mixtures. By non- equilibrium effects we mean all kinds of effects caused by deviation of the distribution function from its quasi-equilibrium value. The method which is used to obtain the normal solution for the generalized Boltzmann equation is discussed. As opposed to the tradi- tional approach, it permits a description of experimentally observed pressure dependence of the reaction rates (low- and high-pressure limits) and to generalize the theory of ther- mal dissociation for the arbitrary reaction case and for spatially inhomogeneous systems. Conclusions concerning the necessity of revising the traditional approach to the chemical reaction description and of developing the non-equilibrium chemistry are argued. In the framework of the non-equilibrium chemistry, chemical reactions are no longer independent of each other (Guldberg and Waage law is not applicable under the non-equilibrium condi- tions) and corresponding reaction rates are functions of the reacting mixture composition. Exact expressions for reaction and relaxation rates for the cut-off harmonic oscillator model are obtained. Only the case of hard potentials in Grad’s meaning is considered, while soft potentials remain an issue.
Keywords: Physical-chemical gas-dynamics, kinetic theory, Boltzmann equation, reactive mixture, transport equations, non-equilibrium effects, reaction rates Mathematics Subject Classification: 76A99, 82B40 PACS: 05.20.Dd, 05.60 +w, 51.10+y, 82.20. Mj
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Thursday, July 16. 2015
V.V. Aristov, A.A. Frolova, S.A. Zabelok
Dorodnicyn Computing Centre of Russian Academy of Sciences Vavilova str., 40, 119333, Moscow, Russia
Abstract: Simulations of flows on the basis of kinetic equations for mixtures with chemical reactions are performed. The Nonuniform Relaxation Problems (NRP) are formulated and solved. Unified Flow Solver (UFS) is used for 1D and 2D NRP. The nonequilibrium kinetics provides results outside the traditional theory of macroscopic phenomena based on the Navier-Stokes equations. Nonequilibrium flows with different properties in relaxation zones are described. Complex processes including model anabolic and catabolic chemical reactions are also considered.
Keywords: Boltzmann equation, kinetic chemical reactions, the nonuniform relaxation problem Mathematics Subject Classification: 76P05, 82C40 PACS: 05.20.Dd, 47.45.Ab, 51.10.+y
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Thursday, July 16. 2015
Lokendra K. Balyana,1, Subir Singh Lambab
a,bDepartment of Mathematics, IIIT-DM Jabalpur, India 1Corresponding author: E-mail: lokendra.balyan@gmail.com
Abstract: In this paper, we present rate of convergence estimates for eigenvalues and eigenvectors of elliptic differential operators on non-smooth domains using non-conforming spectral element methods. We define a class of compact operators on Banach space which is used to obtain the results. If coefficients of the differential operator are sufficiently smooth and the boundaries of the polygonal domain are piecewise analytic then exponential convergence to approximate solution is obtained.
Keywords: Rate of convergence; eigenvalues and eigenvectors; non-smooth domains; singularities; $h$-$p$ spectral element method.
MSC: 35Jxx; 35Pxx
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