Search results for "Mathematical optimization"
showing 10 items of 1300 documents
ε-Regularized two-level optimization problems: Approximation and existence results
2006
The purpose of this work is to improve some results given in [12], relating to approximate solutions for two-level optimization problems. By considering an e-regularized problem, we get new properties, under convexity assumptions in the lower level problems. In particular, we prove existence results for the solutions to the e-regularized problem, whereas the initial two-level optimization problem may fail to have a solution. Finally, as an example, we consider an approximation method with interior penalty functions.
Bayesian model averaging and weighted-average least squares: Equivariance, stability, and numerical issues
2011
In this article, we describe the estimation of linear regression models with uncertainty about the choice of the explanatory variables. We introduce the Stata commands bma and wals, which implement, respectively, the exact Bayesian model-averaging estimator and the weighted-average least-squares estimator developed by Magnus, Powell, and Prüfer (2010, Journal of Econometrics 154: 139–153). Unlike standard pretest estimators that are based on some preliminary diagnostic test, these model-averaging estimators provide a coherent way of making inference on the regression parameters of interest by taking into account the uncertainty due to both the estimation and the model selection steps. Spec…
Wideband impedance matrix representation of passive waveguide components based on cascaded planar junctions
2009
[1] A very efficient technique for the full-wave analysis of passive waveguide components, composed of the cascade connection of planar junctions, is presented. This novel technique provides the wideband generalized impedance matrix representation of the whole structure in the form of pole expansions, thus extracting the most expensive computations from the frequency loop. For this purpose, the structure is segmented into planar junctions and uniform waveguide sections, which are characterized in terms of wideband impedance matrices. Then, an efficient iterative algorithm for combining such matrices, and finally providing the wideband generalized impedance matrix of the complete structure, …
An alternative and easy approach to fixed point results via simulation functions
2017
Abstract We discuss, extend, improve and enrich results on simulation functions established by several authors. Furthermore, by using Lemma 2.1 of Radenovic et al. [Bull. Iran. Math. Soc., 2012, 38, 625],we get much shorter and nicer proofs than the corresponding ones in the existing literature.
Decision-aid for discrete multiple criteria decision making problems with imprecise data
1999
Abstract We describe ways of aiding decision making with a discrete set of alternatives. In many decision situations, it is not possible to obtain explicit preference information from the decision makers. Instead, useful decision-aid can be provided to the decision makers by describing what kind of weighting of the criteria result in certain choices of the alternatives. The suggested treatment is based on the basic ideas of the ELECTRE III method. The modelling of the preferences by pseudo-criteria is especially helpful in case the data, that is, the criterion values are imprecise. Unlike ELECTRE III, no ranking of the alternatives is produced. Based on a minimum-procedure in the exploitati…
Assessing energy forecasting inaccuracy by simultaneously considering temporal and absolute errors
2017
Abstract Recent years have seen a growing trend in wind and solar energy generation globally and it is expected that an important percentage of total energy production comes from these energy sources. However, they present inherent variability that implies fluctuations in energy generation that are difficult to forecast. Thus, forecasting errors have a considerable role in the impacts and costs of renewable energy integration, management, and commercialization. This study presents an important advance in the task of analyzing prediction models, in particular, in the timing component of prediction error, which improves previous pioneering results. A new method to match time series is defined…
Integer Preemption Problems
2014
A fundamental assumption in the basic RCPSP is that activities in progress are non-preemptable. Some papers reveal the potential benefits of allowing activity interruptions in the schedule when the objective is the makespan minimization. In this chapter we consider the Maxnint_PRCPSP in which it is assumed that activities can be interrupted at any integer time instant with no cost incurred, that each activity can be split into a maximum number of parts, and that each part has a minimum duration established. We show how some procedures developed for the RCPSP can be adapted to work with the Maxnint_PRCPSP and we introduce some procedures specifically designed for this problem. Furthermore, p…
Selecting Genetic Operators to Maximise Preference Satisfaction in a Workforce Scheduling and Routing Problem
2017
The Workforce Scheduling and Routing Problem (WSRP) is a combinatorial optimisation problem that involves scheduling and routing of workforce. Tackling this type of problem often requires handling a considerable number of requirements, including customers and workers preferences while minimising both operational costs and travelling distance. This study seeks to determine effective combinations of genetic operators combined with heuristics that help to find good solutions for this constrained combinatorial optimisation problem. In particular, it aims to identify the best set of operators that help to maximise customers and workers preferences satisfaction. This paper advances the understand…
Solving the pentahedron problem
2015
Nowadays, all geometric modelers provide some tools for specifying geometric constraints. The 3D pentahedron problem is an example of a 3D Geometric Constraint Solving Problem (GCSP), composed of six vertices, nine edges, five faces (two triangles and three quadrilaterals), and defined by the lengths of its edges and the planarity of its quadrilateral faces. This problem seems to be the simplest non-trivial problem, as the methods used to solve the Stewart platform or octahedron problem fail to solve it. The naive algebraic formulation of the pentahedron yields an under-constrained system of twelve equations in eighteen unknowns. Even if the use of placement rules transforms the pentahedron…
Using the witness method to detect rigid subsystems of geometric constraints in CAD
2010
International audience; This paper deals with the resolution of geometric constraint systems encountered in CAD-CAM. The main results are that the witness method can be used to detect that a constraint system is over-constrained and that the computation of the maximal rigid subsystems of a system leads to a powerful decomposition method. In a first step, we recall the theoretical framework of the witness method in geometric constraint solving and extend this method to generate a witness. We show then that it can be used to incrementally detect over-constrainedness. We give an algorithm to efficiently identify all maximal rigid parts of a geometric constraint system. We introduce the algorit…