Iterative Solution Approach Research Articles

A Heuristic Approach to the Railroad Track Maintenance Scheduling Problem

Abstract: Every year, billions of dollars are spent on rail track maintenance to keep the serviceability of the railroad network. These maintenance projects (of different types) must be performed by suitable maintenance teams within a planning horizon. This article presents a time-space network model to solve the track maintenance scheduling problem (TMSP). The objective is to minimize the total travel costs of the maintenance teams as well as the impact of maintenance projects on railroad operation, which are formulated by three types of side constraints: mutually exclusive, time window, and precedence constraints. An iterative heuristic solution approach is proposed to solve the large-scale TMSP model with a large number of side constraints. The proposed model and solution approach are applied to a large-scale real-world problem. Compared to the current industry practice the model outcome eliminated all hard side-constraint violations and reduced the total objective value (travel costs and soft side-constraint violation penalties) by 66.8%.

An Iterative Solution Approach to Partial Differential Equations with Recursive Structure

An Iterative Solution Approach to Partial Differential Equations with Recursive Structure

Formulation of the high-fidelity generalized method of cells with arbitrary cell geometry for refined micromechanics and damage in composites

A new parametric formulation for high-fidelity generalized method of cells (HFGMC) is presented for the micromechanical analysis of multiphase periodic composites. To this end, a linear parametric and geometric mapping is employed to transform arbitrary quadrilateral cell shapes from the physical space to an auxiliary uniform square shapes. A complete quadratic displacement expansion is performed in the mapped space. Thus, a new bilinear term is added to the quadratic displacement expansion; unlike the original HFGMC for regular array of rectangular cells where this term in not required. The continuity of displacements, tractions, together with the periodicity and equilibrium conditions are imposed in the average sense, similar to the original HFGMC formulation, using both the physical and mapping variables. However, the addition of bilinear terms requires the introduction of the first averaged moments of the equilibrium equations. In order to demonstrate the ability the new HFGMC formulation, spatial stress fields are compared with analytical and numerical solutions of circular and elliptical fibers in an infinite medium. Furthermore, two progressive damage methodologies are coupled with the new HFGMC formulation in order to predict the strain softening and elastic degrading behaviors. The first methodology employs a cell extinction approach, while the second uses cohesive interfaces between the cells. Due to the strain softening, both damage methodologies require an iterative solution approach of the governing system nonlinear equations. Damage applications are presented for the transverse loading of composites with square and hexagonal repeating unit-cells (RUC).

Analysis of prior models for a blocky inversion of seismic AVA data

Resolving thinner layers and focusing layer boundaries better in inverted seismic sections are important challenges in exploration and production seismology to better identify a potential drilling target. Many seismic inversion methods are based on a least-squares optimization approach that can intrinsically lead to unfocused transitions between adjacent layers. A Bayesian seismic amplitude variation with angle (AVA) inversion algorithm forms sharper boundaries between layers when enforcing sparseness in the vertical gradients of the inversion results. The underlying principle is similar to high-resolution processing algorithms and has been adapted from digital-image-sharpening algorithms. We have investigated the Cauchy and Laplace statistical distributions for their potential to improve contrasts betweenlayers. An inversion algorithm is derived statistically from Bayes’ theorem and results in a nonlinear problem that requires an iterative solution approach. Bayesian inversions require knowledge of certain statistical properties of the model we want to invert for. The blocky inversion method requires an additional parameter besides the usual properties for a multivariate covariance matrix, which we can estimate from borehole data. Tests on synthetic and field data show that the blocky inversion algorithm can detect and enhance layer boundaries in seismic inversions by effectively suppressing side lobes. The analysis of the synthetic data suggests that the Laplace constraint performs more reliably, whereas the Cauchy constraint may not find the optimum solution by converging to a local minimum of the cost function and thereby introducing some numerical artifacts.

An Integrated Outbound Logistics Model for Frito-Lay: Coordinating Aggregate-Level Production and Distribution Decisions

In this paper, we describe research to improve Frito-Lay's outbound supply chain activities by simultaneously optimizing its inventory and transportation decisions. Motivated by Frito-Lay's practice, we first develop a mixed-integer programming formulation from which we develop a large-scale, integrated multiproduct inventory lot-sizing and vehicle-routing model with explicit (1) inventory holding costs, truck loading and dispatch costs, and mileage costs; (2) production, storage, and truck capacity limitations; and (3) direct (plant-to-store) and interplant (plant-to-plant) delivery considerations. Second, we present an iterative solution approach in which we decompose the problem into inventory and routing components. The results demonstrate the impact of direct deliveries on distribution costs and show that direct deliveries and efficient inventory and routing decisions can provide significant savings opportunities over two benchmark models, one of which represents the existing Frito-Lay system. We implemented our models using an application that allows strategy evaluation, analysis of output files, and technology transfer. This application was particularly useful in evaluating potential direct-delivery locations and inventory reductions throughout the supply chain.

An adaptive guidance approach for the heuristic solution of a minimum multiple trip vehicle routing problem

One of the most important problems in combinatorial optimization is the well-known vehicle routing problem (VRP), which calls for the determination of the optimal routes to be performed by a fleet of vehicles to serve a given set of customers. Recently, there has been an increasing interest towards extensions of VRP arising from real-world applications. In this paper we consider a variant in which time windows for service at the customers are given, and vehicles may perform more than one route within a working shift. We call the resulting problem the minimum multiple trip VRP (MMTVRP), where a “multiple trip” is a sequence of routes corresponding to a working shift for a vehicle. The problem objective is to minimize the overall number of the multiple trips (hence the size of the required fleet), breaking ties in favor of the minimum routing cost. We propose an iterative solution approach based on the decomposition of the problem into simpler ones, each solved by specific heuristics that are suitably combined to produce feasible MMTVRP solutions. An adaptive guidance mechanism is used to guide the heuristics to possibly improve the current solution. Computational experiments have been performed on a set of real-world instances arising from a multi-regional scale distribution problem. The obtained results show that the proposed adaptive guidance mechanism is considerably effective, being able to reduce the overall number of required vehicles within a limited computing time.

The oncological safety of axillary node clearance in the lateral decubitus position in patients with immediate ALD reconstructions

Optical flow fields are useful to describe the motion of objects relative to the observer of a scene. Smoothness requirements facilitate the estimation of optical flow fields even for areas with constant or only linearly sloping gray value distributions. Horn and Schunck (Artif. Intell. 17, 1981, 185–203) formulated the estimation of optical flow fields as a minimization problem. In order to avoid problems with the general smoothness constraint of Horn and Schunck (op. cit.), Nagel (in Proceedings, IJCAI, Karlsruhe, Aug. 1983, pp. 945–951) developed the “oriented smoothness constraint.” Here, a modified formulation of this “oriented smoothness constraint” will be compared to an earlier one. The differences between these formulations will be discussed analytically. Starting with an iterative solution approach for the system of nonlinear partial differential equations resulting from the “oriented smoothness constraint,” the iterative solution approach could be improved significantly using multigrid methods. Results obtained from experiments with real world image sequences will be presented.

Numerical method of slope failure probability based on Bishop model

Based on Bishop’s model and by applying the first and second order mean deviations method, an approximative solution method for the first and second order partial derivatives of functional function was deduced according to numerical analysis theory. After complicated multi-independent variables implicit functional function was simplified to be a single independent variable implicit function and rule of calculating derivative for composite function was combined with principle of the mean deviations method, an approximative solution format of implicit functional function was established through Taylor expansion series and iterative solution approach of reliability degree index was given synchronously. An engineering example was analyzed by the method. The result shows its absolute error is only 0.78% as compared with accurate solution.

A microslip friction model with normal load variation induced by normal motion

A two-dimensional microslip friction model with normal load variation induced by normal motion is presented in this paper. The model is a distributed parameter model, which characterizes the stick-slip-separation of the contact interface and determines the resulting friction force, including its time variance and spatial distribution, between two elastic structures. When the relative motion is simple harmonic motion, the stick-slip-separation transition angles associated with any point in the contact area can be analytically determined within a cycle of motion. In addition, if the relative motion is given, stick-slip-separation transition boundaries inside the contact area and their time variances can be determined. Along with an iterative multi-mode solution approach utilizing harmonic balance method (HBM), the developed model can be employed to determine the forced response of frictionally constrained structures. In the approach, the forced response is constructed in terms of the free mode shapes of the structure; consequently, it can be determined at any excitation frequency and for any type of normal load distribution. Two examples, a one-dimensional beam like damper and a more realistic blade to ground damper, are employed to illustrate the predictive abilities of the developed model. It is shown that while employing a single mode model, transition boundaries for the beam like damper agrees with the results given in the literature, the developed method identifies the phase difference along the slip to stick transition boundary when a multi-mode model is employed. Moreover, while partial slip is illustrated in the two examples, typical softening and hardening effects, due to separation of the contact surface, are also predicted for the blade to ground damper.

Noniterative analytical formula for inverse scattering of multiply scattering point targets

This paper derives, in the exact framework of multiple scattering theory for point targets, a noniterative analytical formula for the nonlinear inversion of the target scattering strengths from the scattering or response matrix that can be applied after the target positions have been estimated in a previous step via, e.g., time-reversal multiple signal classification or another approach. The new formula provides a noniterative analytical alternative to the iterative numerical solution approach for the same problem presented in a recent paper [A. J. Devaney, E. A. Marengo, and F. K. Gruber, "Time-reversal-based imaging and inverse scattering of multiply scattering point targets," J. Acoust. Soc. Am. 118, 3129-3138 (2005)]. The two methods (noniterative versus iterative) are comparatively investigated with two numerical examples.

Modeling of Diode in Fdtd Simulation of Printed Circuit Board

Finite-Difference Time-Domain (FDTD) method has evolved into a powerful tool to model electromagnetic wave propagation in a printed circuit board environment [1-7]. A simple, efficient and systematic approximate method to incorporate nonlinear diode is presented in this paper. This method applies Taylor expansion on the nonlinear diode equation, which result in one step explicit finite difference scheme for the electromagnetic fields in the vicinity of the diode. Simulation examples are performed. The result compares well with FDTD diode model using iterative solution approach and SPICE simulation.

Financial Asset-Pricing Theory and Stochastic Programming Models for Asset/Liability Management: A Synthesis

Practical portfolio investment problems under uncertainty can be modeled well as multiperiod stochastic programs. However, the numerical optimization methods that need to be used to solve such models seriously limit the level of detail in the uncertainty about future asset prices and returns that can be incorporated. Somewhat surprisingly, the question how this necessarily approximate description of the uncertainty should be constructed has received relatively little attention in the stochastic programming literature. Moreover, many of the descriptions that have been used are not arbitrage-free, and therefore inconsistent with modern financial asset-pricing theory. In this paper we will present aggregation methods that can be used in combination with financial asset-pricing models to obtain a description of the uncertainty that is arbitrage-free, consistent with observed market prices as well as concise enough for a stochastic programming model. Furthermore, we will discuss how these aggregation methods can form the basis of an iterative solution approach.

Using a simplified gradient method to solve a system or linear equations

The general gradient method of iterative solution to the system Ax == b is complicated. This paper presents a simplified iterative solution approach to the system. It utilizes the general gradient method; however, the method is simpler than the conjugate gradient method in concept as well as in its algorithm. Also, this proposed method is efficient in finding a solution.

Investigations of multigrid algorithms for the estimation of optical flow fields in image sequences

Optical flow fields are useful to describe the motion of objects relative to the observer of a scene. Smoothness requirements facilitate the estimation of optical flow fields even for areas with constant or only linearly sloping gray value distributions. Horn and Schunck ( Artif. Intell. 17, 1981, 185–203) formulated the estimation of optical flow fields as a minimization problem. In order to avoid problems with the general smoothness constraint of Horn and Schunck (op. cit.), Nagel (in Proceedings, IJCAI, Karlsruhe, Aug. 1983, pp. 945–951) developed the “oriented smoothness constraint.” Here, a modified formulation of this “oriented smoothness constraint” will be compared to an earlier one. The differences between these formulations will be discussed analytically. Starting with an iterative solution approach for the system of nonlinear partial differential equations resulting from the “oriented smoothness constraint,” the iterative solution approach could be improved significantly using multigrid methods. Results obtained from experiments with real world image sequences will be presented.

Concurrent iterative solution of large finite element systems

AbstractA general iterative algorithm for the solution of large finite element systems of arbitrary domain geometry is designed to operate efficiently on modern computers with concurrent processors. The domain is recursively and automatically subdivided into the same number of subdomains as available processors. Convergence is ensured because of the Gauss–Seidel type of iterations operated on each subdomain and corresponding interface. This subdomain iterative solution approach is compatible with the other phases of a complete concurrent finite element analysis (concurrent stiffness formation and assembly and concurrent element post‐processing), from both the data structure and computation points of view. Implementation of the resulting stratagem on MIMD computers is presented. Several examples are run on a hypercube multiprocessor to validate the proposed algorithm and assess its performance. An efficiency of 91 per cent is achieved for a problem with 16,000 degrees‐of‐freedom.

On the estimation of dense displacement vector fields from image sequences (abstract only)

Based on recent experimental as well as theoretical investigations, a generalization of previously published approaches towards the estimation of displacement vector fields is formulated. The calculus of variation allows to transform this approach into a set of two partial differential equations for the two components of the displacement vector field. Some simplifying assumptions facilitate the derivation of an iterative solution approach which can be studied in closed form.