An Iterative Solution Approach for General Network Problems with Routing

In this paper, a straightforward approach is developed to solve the nonlinear position equations for a linkage when a closed-form solution to some of the equations can be obtained. This is done with the aid of dependency checking concepts that organizes a system 2n equations and 2n unknowns (variables) into smaller sets of equations. When a set of two equations and two unknowns is obtained, the variables are analyzed using a closed-form (non-iterative) solution approach. Otherwise, an iterative approach such as the Newton-Raphson method is used for the analysis.

Download Full-text

An iterative solution approach to a multi-objective facility location problem

Applied Soft Computing ◽

10.1016/j.asoc.2017.10.035 ◽

2018 ◽

Vol 62 ◽

pp. 272-287 ◽

Cited By ~ 26

Author(s):

Mumtaz Karatas ◽

Ertan Yakıcı

Keyword(s):

Facility Location ◽

Location Problem ◽

Facility Location Problem ◽

Iterative Solution ◽

Solution Approach ◽

Multi Objective

Download Full-text

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

Geophysics ◽

10.1190/1.3427538 ◽

2010 ◽

Vol 75 (3) ◽

pp. C25-C35 ◽

Cited By ~ 45

Author(s):

Ulrich Theune ◽

Ingrid Østgård Jensås ◽

Jo Eidsvik

Keyword(s):

Synthetic Data ◽

Iterative Solution ◽

Seismic Inversion ◽

Inversion Method ◽

Optimization Approach ◽

Additional Parameter ◽

Inversion Algorithm ◽

Borehole Data ◽

Solution Approach ◽

Exploration And Production

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.

Download Full-text