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.
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.
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.