Search results for "routing"
showing 10 items of 587 documents
Large time behavior for a porous medium equation in a nonhomogeneous medium with critical density
2014
Abstract We study the large time behavior of solutions to the Cauchy problem for the porous medium equation in nonhomogeneous media with critical singular density | x | − 2 ∂ t u = Δ u m , in R N × ( 0 , ∞ ) , where m > 1 and N ≥ 3 , with nonnegative initial condition u ( x , 0 ) = u 0 ( x ) ≥ 0 . The asymptotic behavior proves to have some interesting and striking properties. We show that there are different asymptotic profiles for the solutions, depending on whether the continuous initial data u 0 vanishes at x = 0 or not. Moreover, when u 0 ( 0 ) = 0 , we show the convergence towards a peak-type profile presenting a jump discontinuity, coming from an interesting asymptotic simplification…
On Fixed Point (Trial) Methods for Free Boundary Problems
1992
In this note we consider the trial methods for solving steady state free boundary problems. For two test examples (electrochemical machining and continuous casting) we discuss the convergence of a fixed point method. Moreover, using the techniques of shape optimization we introduce a modification of the method, which gives us superlinear convergence rate. This is also confirmed numerically.
On the Extension of the DIRECT Algorithm to Multiple Objectives
2020
AbstractDeterministic global optimization algorithms like Piyavskii–Shubert, direct, ego and many more, have a recognized standing, for problems with many local optima. Although many single objective optimization algorithms have been extended to multiple objectives, completely deterministic algorithms for nonlinear problems with guarantees of convergence to global Pareto optimality are still missing. For instance, deterministic algorithms usually make use of some form of scalarization, which may lead to incomplete representations of the Pareto optimal set. Thus, all global Pareto optima may not be obtained, especially in nonconvex cases. On the other hand, algorithms attempting to produce r…
Convergence of Markovian Stochastic Approximation with discontinuous dynamics
2016
This paper is devoted to the convergence analysis of stochastic approximation algorithms of the form $\theta_{n+1} = \theta_n + \gamma_{n+1} H_{\theta_n}({X_{n+1}})$, where ${\left\{ {\theta}_n, n \in {\mathbb{N}} \right\}}$ is an ${\mathbb{R}}^d$-valued sequence, ${\left\{ {\gamma}_n, n \in {\mathbb{N}} \right\}}$ is a deterministic stepsize sequence, and ${\left\{ {X}_n, n \in {\mathbb{N}} \right\}}$ is a controlled Markov chain. We study the convergence under weak assumptions on smoothness-in-$\theta$ of the function $\theta \mapsto H_{\theta}({x})$. It is usually assumed that this function is continuous for any $x$; in this work, we relax this condition. Our results are illustrated by c…
When a convergence of filters is measure-theoretic
2022
Abstract Convergence almost everywhere cannot be induced by a topology, and if measure is finite, it coincides with almost uniform convergence and is finer than convergence in measure, which is induced by a metrizable topology. Measures are assumed to be finite. It is proved that convergence in measure is the Urysohn modification of convergence almost everywhere, which is pseudotopological. Extensions of these convergences from sequences to arbitrary filters are discussed, and a concept of measure-theoretic convergence is introduced. A natural extension of convergence almost everywhere is neither measure-theoretic, nor finer than a natural extension of convergence in measure. A straightforw…
Calculation of frequency-dependent polarizabilities using general coupled-cluster models
2006
Abstract An analytic scheme for the calculation of frequency-dependent polarizabilities within a response-theory approach has been implemented for the use within general coupled-cluster (CC) models with arbitrary excitations in the cluster operator. Calculations for CH + and CN demonstrate the fast convergence of the coupled-cluster approach when successively higher excitations are considered. Quadruple excitation effects on the frequency-dependent polarizabilities are found to be rather small except close to the poles.
Basis Set Convergence of Indirect Spin-Spin Coupling Constants in the Kohn-Sham Limit for Several Small Molecules
2012
The performance of more than 40 density functionals in predicting indirect spin-spin coupling constants (SSCCs) in the Kohn-Sham basis set limit was tested. For comparison, similar calculations were performed using the RHF, SOPPA, SOPPA(CC2), and SOPPA(CCSD) methods, and the results were estimated toward the complete basis set (CBS) limit. The SSCCs of nine small molecules (N(2), CO, CO(2), NH(3), CH(4), C(2)H(2), C(2)H(4), C(2)H(6), and C(6)H(6)) were calculated using the dedicated Jensen pcJ-n polarization-consistent basis sets and used for the CBS limit estimations within the Kohn-Sham limit. These CBS results were compared with calculations using the aug-cc-pVTZ-J basis set. Among the 4…
Explicitly correlated internally contracted multireference coupled-cluster singles and doubles theory: ic-MRCCSD(F12∗)
2013
Abstract An explicitly correlated ansatz employing Slater-type geminals and cusp conditions is developed for the internally contracted multireference coupled-cluster singles and doubles method. Only the most important geminal terms are retained in the spirit of earlier work for single-reference theory. Throughout all our test calculations, the new ic-MRCCSD(F12∗) method improves the basis set convergence of many properties, e.g., spectroscopic constants or singlet–triplet splittings, with only little extra computational cost. If a perturbative correction for connected triples is included (the ic-MRCCSD(F12∗)+(T) method), very accurate results can be obtained even with minimal active spaces.
Automatic Customization Framework for Efficient Vehicle Routing System Deployment
2017
Vehicle routing systems provide several advantages over manual transportation planning and they are attracting growing attention. However, deployment of these systems can be prohibitively costly, especially for small and medium-sized enterprises: the customization, integration, and migration is laborious and requires operations research expetise. We propose an automated configuration workflow for vehicle routing system and data flow customization, which provides the necessary basis for more experimental work on the subject. Our preliminary results with learning and adaptive algorithms support the assumption of applicability of the proposed configuration framework. The strategies presented h…
Some recent contributions to routing and location problems
2003
CORAL 2003, a Conference on Routing and Location, washeld in Puerto de la Cruz (Tenerife, Spain) from February24–26, 2003. A wonderful place, close to the black sand ofthe beach, and a nice temperature welcomed a group ofsenior and young researchers from Canada, England,France, Germany, and Spain. Social activities were alsoprovided and sponsored by the Cabildo Insular de Tenerife(the local government) and TITSA (the public bus transpor-tation company on the island). The conference corre-sponded to the third annual meeting of a research project,funded by the Spanish Ministry of Science and Technology,developing a Decision Support System for Vehicle Routingand Facility Location Problems (SAD…