Matrix Adjustment Problem Research Articles

Hybrid gradient-swarm intelligence to improve quality of solutions for origin–destination matrix adjustment problem

Hybrid gradient-swarm intelligence to improve quality of solutions for origin–destination matrix adjustment problem

Entropy-Based Solutions for Ecological Inference Problems: A Composite Estimator

Information-based estimation techniques are becoming more popular in the field of Ecological Inference. Within this branch of estimation techniques, two alternative approaches can be pointed out. The first one is the Generalized Maximum Entropy (GME) approach based on a matrix adjustment problem where the only observable information is given by the margins of the target matrix. An alternative approach is based on a distributionally weighted regression (DWR) equation. These two approaches have been studied so far as completely different streams, even when there are clear connections between them. In this paper we present these connections explicitly. More specifically, we show that under certain conditions the generalized cross-entropy (GCE) solution for a matrix adjustment problem and the GME estimator of a DWR equation differ only in terms of the a priori information considered. Then, we move a step forward and propose a composite estimator that combines the two priors considered in both approaches. Finally, we present a numerical experiment and an empirical application based on Spanish data for the 2010 year.

基于层次分析法的通信指挥效能评估方法

本文提出了一种基于层次分析法的通信指挥效能评估方法，针对问题评估过程中判断矩阵的一致性调整问题，提出了一种两阶段调整方法。第一阶段构造一致性矩阵，计算原判断矩阵中与一致性矩阵相比偏差最大的元素；第二阶段定义调整规则，迭代修改与一致性矩阵偏差最大的原矩阵元素。最后，利用通信指挥效能评估问题算例对本文方法进行验证，结果证明本文方法方便高效，且求解结果能够最大程度保留原专家意见。 An evaluation method of communication command effectiveness based on the Analytical Hierarchy Process (AHP) is proposed in this paper. To solve the issue of consistency of judgment matrix adjustment problem, a two-stage adjustment method is proposed. Firstly, construct the consistency matrix, and calculate the maximum deviation elements of the original judgment matrix comparing to the consistency matrix. Secondly, define the adjustment rules, and iteratively adjust the maximum deviation elements according to the rules. Finally, a communication and command effectiveness assessment instance is calculated to validate our method. The calculation results prove that our effectiveness evaluation method can solve the problem conveniently and efficiently, and can maximum retain the original expert opinion.

A heuristic for the OD matrix adjustment problem in a congested transport network

Abstract We study the Demand Adjustment Problem (DAP) associated to the urban traffic planning. The framework for the formulation of the DAP is mathematical programming with equilibrium constraints. In particular, if we consider the optimization problem equivalent to the equilibrium problem, the DAP becomes a bilevel optimization problem. In this work we present a descent scheme based on the approximation of the gradient of the objective function of DAP.

GPCEMA.GMS: A General Purpose Cross-Entropy Matrix Adjustment Program (Quick User Guide)

This note briefly presents the GAMS matrix adjustment program GPCEMA.gms (GPCEMA stands for General Purpose Cross-Entropy Matrix Adjustment). The matrix adjustment problem tackled in GPCEMA.gms is to adjust an existing matrix (called the prior matrix) so that the adjusted matrix (the posterior matrix) has row and column sums that conform to known marginal totals. GPCEMA.gms is based on the minimum information-gain principle (also known as minimum cross-entropy), as it has been extended to deal with negative entries by Junius and Oosterhaven (2003). The program automatically deals with situations where row sums, column sums, or both are constrained to zero.

New algorithmic alternatives for the O–D matrix adjustment problem on traffic networks

In the last years the O–D matrix adjustment problem using link counts on a traffic network modelled by means of a static user equilibrium approach has been formulated advantageously by means of bilevel programs. The algorithms developed to solve the problem present heuristic components in a lesser or greater degree. In this paper two new algorithmic alternatives are presented for this problem. The first alternative is an hybrid scheme proximal point-steepest descent that is based on a development of Codina for the approximation of the steepest descent direction of the upper level function and the second alternative is developed by García and Marín and consists of solving a sequence of simplified bilevel programs. In order to highlight the characteristics of the two methods a set of test problems have been solved in conjunction with other well known methods, such as the method of Spiess, the method of Chan, the method of Yang as well as with an adaptation of the Wolfe’s conjugate directions method for non-differentiable optimization, in order to provide a better perspective of their advantages and tradeoffs.

Approximation of the steepest descent direction for the O-D matrix adjustment problem

In this paper, a method to approximate the directions of Clarke's generalized gradient of the upper level function for the demand adjustment problem on traffic networks is presented. Its consistency is analyzed in detail. The theoretical background on which this method relies is the known property of proximal subgradients of approximating subgradients of proximal bounded and lower semicountinuous functions using the Moreau envelopes. A double penalty approach is employed to approximate the proximal subgradients provided by these envelopes. An algorithm based on partial linearization is used to solve the resulting nonconvex problem that approximates the Moreau envelopes, and a method to verify the accuracy of the approximation to the steepest descent direction at points of differentiability is developed, so it may be used as a suitable stopping criterion. Finally, a set of experiments with test problems are presented, illustrating the approximation of the solutions to a steepest descent direction evaluated numerically.

Adjustment of O–D trip matrices from observed volumes: An algorithmic approach based on conjugate directions

This paper presents a new algorithmic alternative to the O–D matrix adjustment problem from observed link volumes when it is formulated as a mathematical programming problem with a bilevel structure. The algorithmic approach presented is based on a method for nondifferentiable optimization due to Wolfe that can be interpreted as a conjugate directions method with better convergence properties as shown with a set of computational tests. Closely related to the algorithm presented, the problem of approximating gradients of the upper level function is discussed and a new and consistent approach is presented and analyzed with a detailed description of the algorithmic aspects involved.

A coordinate descent method for the bi-level O-D matrix adjustment problem

Abstract We present a Gauss-Seidel type algorithm for the problem of adjusting an O-D matrix by using observed flows in congested networks. The problem is formulated as a bi-level optimization problem. Necessary conditions for some properties of the solution of the O-D matrix adjusting problem are derived and a coordinate descent method is developed. The algorithm takes full advantage of the network structure of the lower level problem and does not require many objective function evaluations. Computational results for some numerical examples are reported.

A Coordinate Descent Method for the Bi‐level O–D Matrix Adjustment Problem

We present a Gauss–Seidel type algorithm for the problem of adjusting an O–D matrix by using observed flows in congested networks. The problem is formulated as a bi‐level optimization problem. Necessary conditions for some properties of the solution of the O–D matrix adjusting problem are derived and a coordinate descent method is developed. The algorithm takes full advantage of the network structure of the lower level problem and does not require many objective function evaluations. Computational results for some numerical examples are reported.