An effective solution for a real cutting stock problem in manufacturing plastic rolls

We confront a practical cutting stock problem from a production plant of plastic rolls. The problem is a variant of the well-known one dimensional cutting stock, with particular constraints and optimization criteria defined by the experts of the company. We start by giving a problem formulation in which optimization criteria have been considered in linear hierarchy according to expert preferences, and then propose a heuristic solution based on a GRASP algorithm. The generation phase of this algorithm solves a simplified version which is rather similar to the conventional one dimensional cutting stock. To do that, we propose a Sequential Heuristic Randomized Procedure (SHRP). Then in the repairing phase, the solution of the simplified problem is transformed into a solution to the real problem. For experimental study we have chosen a set of problem instances of com-mon use to compare SHRP with another recent approach. Also, we show by means of examples, how our approach works over instances taken from the real production process. All authors are supported by MEC-FEDER Grant TIN2007-67466-C02-01 and by contract CN-05-127 of the University of Oviedo and the company ERVISA, and by FICYT under grant BP04-021.     

THREE-DIMENSIONAL NUMERICAL LOCALIZATION OF IMPERFECTIONS BASED ON A LIMIT MODEL IN ELECTRIC FIELD AND A LIMIT PERTURBATION MODEL

From a limit model in electric field obtained by letting the frequency vanish in the time-harmonic Maxwell equations, we consider a limit perturbation model in the tangential boundary trace of the curl of the electric field for localizing numerically certain small electromagnetic inhomogeneities, in a three-dimensional bounded domain. We introduce here two localization procedures resulting from the combination of this limit perturbation model with each of the following inversion processes： the Current Projection method and an Inverse Fourier method. Each localization procedure uses, as data, a finite number of boundary measurements, and is employed in the single inhomogeneity case; only the one based on an Inverse Fourier method is required in the multiple inhomogeneities case. Our localization approach is numerically suitable for the context of inhomogeneities that are not purely electric. We compare the numerical results obtained from the two localization procedures in the single inhomogeneity configuration, and describe, in various settings of multiple inhomogeneities, the results provided by the procedure based on an Inverse Fourier method.     

A NUMERICAL STUDY OF UNIFORM SUPERCONVERGENCE OF LDG METHOD FOR SOLVING SINGULARLY PERTURBED PROBLEMS

In this paper, we consider the local discontinuous Galerkin method （LDG） for solving singularly perturbed convection-diffusion problems in one- and two-dimensional settings. The existence and uniqueness of the LDG solutions are verified. Numerical experiments demonstrate that it seems impossible to obtain uniform superconvergence for numerical fluxes under uniform meshes. Thanks to the implementation of two-type different anisotropic meshes, i.e., the Shishkin and an improved grade meshes, the uniform 2p ＋ i-order superconvergence is observed numerically for both one-dimensional and twodimensional cases.     

Permutation-induced acyclic networks for the job shop scheduling problem

In the literature of the combinatorial optimization problems, it is a commonplace to find more than one mathematical model for the same problem. The significance of a model may be measured in terms of the efficiency of the solution algorithms that can be built upon it. The purpose of this article is to present a new network model for the well known combinatorial optimization problem – the job shop scheduling problem. The new network model has similar structure as the disjunctive graph model except that it uses permutations of jobs as decision variables instead of the binary decision variables associated with the disjunctive arcs. To assess the significance of the new model, the performances of exact branch-and-bound algorithmic implementations that are based on both the new model and the disjunctive graph model are compared.     

Travelling wave solutions to Stokes’ problem for a fourth grade fluid

A non-linear partial differential equation modelling the flow of a fourth-grade fluid is derived. Both analytical and numerical travelling wave solutions admitted by the model equation are obtained.     

Numerical simulation and analysis of generalized difference method on triangular networks for electrical impedance tomography

Electrical impedance tomography is an inverse problem of elliptic differential equations. Numerical methods based on combining generalized difference method and Levenberg–Marquardt iteration on a planar domain are proposed. Positive semi-definiteness and existence of solution of the generalized difference scheme are proved. Element geometry matrix is introduced to shortcut calculation and standardize computer program. A series of numerical experiments verify the reliability of its mathematical model and the feasibility of the algorithm. A class of electrical current patterns is proposed to minimize the number of direct problems to be solved in each iteration. These methods have been applied successfully in practical simulation of electrical impedance tomography.     

Application of the Sinc method to a dynamic elasto-plastic problem

This paper presents the application of Sinc bases to simulate numerically the dynamic behavior of a one-dimensional elastoplastic problem. The numerical methods that are traditionally employed to solve elastoplastic problems include finite difference, finite element and spectral methods. However, more recently, biorthogonal wavelet bases have been used to study the dynamic response of a uniaxial elasto-plastic rod [Giovanni F. Naldi, Karsten Urban, Paolo Venini, A wavelet-Galerkin method for elastoplasticity problems, Report 181, RWTH Aachen IGPM, and Math. Modelling and Scient. Computing, vol. 10, 2000]. In this paper the Sinc–Galerkin method is used to solve the straight elasto-plastic rod problem. Due to their exponential convergence rates and their need for a relatively fewer nodal points, Sinc based methods can significantly outperform traditional numerical methods [J. Lund, K.L. Bowers, Sinc Methods for Quadrature and Differential Equations, SIAM, Philadelphia, 1992]. However, the potential of Sinc-based methods for solving elastoplasticity problems has not yet been explored. The aim of this paper is to demonstrate the possible application of Sinc methods through the numerical investigation of the unsteady one dimensional elastic-plastic rod problem.     

Representation for the Lagrangian numerical differentiation formula involving elementary symmetric functions

By using elementary symmetric functions, this paper presents an explicit representation for the Lagrangian numerical differentiation formula as well as the error estimate for local approximation. And we also point out that the numerical differentiation formula constructed by Li [J.P. Li, General explicit difference formulas for numerical differentiation, J. Comput. Appl. Math. 183 (2005) 29-52] is actually a special case of the Lagrangian numerical differentiation formula to approximate the values of the derivatives at the nodes.     

On dependence of dynamical structure of numerical solutions of fluid simulations on forcibly added randomness

In the present paper, the dependencies of the numerical results of fluid simulations on forcibly added randomness are discussed. The incompressible Navier-Stokes equations and the continuity equation are solved numerically by using the MAC (Maker-And-Cell) method and implicit temporal scheme. The model adopted in the present study is a flow around a two-dimensional circular cylinder and the Reynolds number is 1500. The randomness which is given by using the pseudo-random number is forcibly added in the time marching step of the discretized Navier-Stokes equations. Dependencies of the averaged structure of asymptotic numerical solutions on the randomness are discussed. Furthermore, the dependence of the qualitative structure of the asymptotic solution of each sample calculation on the amplitude of randomness is also studied. It is clarified that forcibly added random errors may cover the nonlinear errors which make the system unstable.     

Non-negatively constrained image deblurring with an inexact interior point method

Nonlinear image deblurring procedures based on probabilistic considerations have been widely investigated in the literature. This approach leads to model the deblurring problem as a large scale optimization problem, with a nonlinear, convex objective function and non-negativity constraints on the sign of the variables. The interior point methods have shown in the last years to be very reliable in nonlinear programs. In this paper we propose an inexact Newton interior point (IP) algorithm designed for the solution of the deblurring problem. The numerical experience compares the IP method with another state-of-the-art method, the Lucy Richardson algorithm, and shows a significant improvement of the processing time.