On lexicographic optimal solutions in transportation problems

Lexicographic versions of the cost minimizing transportation problem (CMTP) and the time minimizing transportation problem (TMTP) are presented in this paper. In addition to minimizing the quantity sent on the costliest routes in a cost minimizing transportation problem. an attempt is made to minimize the quantity transported on the second-costliest routes. if the shipment on the costliest routes is as small as possible and the quantity shipped on the third-costliest routes, if the shipments on the costliest and the second- costliest routes are as small as possible. and so on. In a lexicographic time minimizing transportation problem one is not only interested in minimizing the transportation cost on the routes of the longest duration but also on the routes of second longest, third-longest duration and so on. For finding lexicographic optimal solutions (LOS) of lexicographic cost minimizing and time minimizing transportation problems a standard cost minimizing transportation problem is formulated whose optimal solution is shown to provide the answer. Some extensions are also discussed     

Convergence analysis of finite volume scheme for nonlinear aggregation population balance equation

In this work, we introduce the convergence analysis of the recently developed finite volume scheme to solve a pure aggregation population balance equation that is of substantial interest in many areas such as chemical engineering, aerosol physics, astrophysics, polymer science, pharmaceutical sciences, and mathematical biology. The notion of the finite volume scheme is to conserve total mass of the particles in the system by introducing weight in the formulation. The consistency of the finite volume scheme is also analyzed thoroughly as it is an influential factor. The convergence study of the numerical scheme shows second order convergence on uniform, nonuniform smooth (geometric) as well as on locally uniform meshes independent of the aggregation kernel. Moreover, the first‐order convergence is shown when the finite volume scheme is implemented on oscillatory and random meshes. In order to check the accuracy, the numerical experimental order of convergence is also computed for the physically relevant as well as analytically tractable kernels and validated against its analytical results.     

Application in Aerohydrodynamics of the Solution of an Inverse Boundary Value Problem for Analytic Functions

We consider a modified inverse boundary value problem of aerohydrodynamics in which it is required to find the shape of an airfoil streamlined by a potential flow of an incompressible nonviscous fluid, when the distribution of the velocity potential on one section of the airfoil is given as a function of the abscissa, while, on other sections of the airfoil, as a function of the ordinate of the point. The velocity of the undisturbed flow streamlining the sought-for airfoil is determined in the process of solving the problem. It is shown that, under rather general conditions on the initially set functions, the sought-for contour is closed unlike the inverse problem in the case when, on the unknown contour, the velocity distribution is given as a function of the arc abscissa of the contour point. We also consider the case when, on the entire desired contour, the distribution of the velocity potential is given as a function of one and the same Cartesian coordinate of the contour point.     

Laminar magnetohydrodynamic duct flow in the presence of a magnetic dipole

We study magnetohydrodynamic flow of a liquid metal in a straight duct. The magnetic field is produced by an exterior magnetic dipole. This basic configuration is of fundamental interest for Lorentz force velocimetry (LFV), where the Lorentz force opposing the relative motion of conducting medium and magnetic field is measured to determine the flow velocity. The Lorentz force acts in equal strength but opposite direction on the flow as well as on the dipole. We are interested in the dependence of the velocity on the flow rate and on strength of the magnetic field as well as on geometric parameters such as distance and position of the dipole relative to the duct. To this end, we perform numerical simulations with an accurate finite-difference method in the limit of small magnetic Reynolds number, whereby the induced magnetic field is assumed to be small compared with the external applied field. The hydrodynamic Reynolds number is also assumed to be small so that the flow remains laminar. The simulations allow us to quantify the magnetic obstacle effect as a potential complication for local flow measurement with LFV. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Adaptive Reservoir Evolutionary Algorithm: An Evolutionary On-Line Adaptation Scheme for Global Function Optimization

This paper introduces a novel global optimization heuristic algorithm based on the basic paradigms of Evolutionary Algorithms (EA). The algorithm greatly extends a previous strategy proposed by the authors in Munteanu and Lazarescu (1998). In the newly designed algorithm the exploration/exploitation of the search space is adapted on-line based on the current features of the landscape that is being searched. The on-line adaptation mechanism involves a decision process as to whether more exploitation or exploration is needed depending on the current progress of the algorithm and on the current estimated potential of discovering better solutions. The convergence with probability 1 in finite time and discrete space is analyzed, as well as an extensive comparison with other evolutionary optimization heuristics is performed on a set of test functions.     

On p-Willmore disks with boundary energies

We consider an energy functional on surface immersions which includes contributions from both boundary and interior. Inspired by physical examples, the boundary is modeled as the center line of a generalized Kirchhoff elastic rod, while the interior term is arbitrarily dependent on the mean curvature and linearly dependent on the Gaussian curvature. We study equilibrium configurations for this energy in general among topological disks, as well as specifically for the class of examples known as p-Willmore energies.     

An A Posteriori Error Estimate for a Stabilized FEM in the Stokes Flow

We derive an a posteriori error estimate for a stabilized version of the finite element method applied to the Stokes problem on a two‐dimensional polygonal domain, as well as on a three‐dimensional polyhedral domain. We consider the Douglas‐Wang technique for stabilization. Special attention is payed to the sources of the constants in the estimate, as these play a crucial role in practical applications to adaptive refinements, as we also show. The proposed technique is based on estimating the residual components.     

长方体上均匀分布的密度函数

讨论了长方体上均匀分布密度函数问题,得到了长方体体积的估计量、估计量的点估计及估计量的密度函数.     

Infrastructure topology optimization under competition through cross-entropy

In this article, we study a two-level non-cooperative game between providers acting on the same geographic area. Each provider has the opportunity to set up a network of stations so as to capture as many consumers as possible. Its deployment being costly, the provider has to optimize both the number of settled stations as well as their locations. In the first level each provider optimizes independently his infrastructure topology while in the second level they price dynamically the access to their network of stations. The consumers’ choices depend on the perception (in terms of price, congestion and distances to the nearest stations) that they have of the service proposed by each provider. Each providers' market share is then obtained as the solution of a fixed point equation since the congestion level is supposed to depend on the market share of the provider, which increases with the number of consumers choosing the same provider. We prove that the two-stage game admits a unique equilibrium in price at any time instant. An algorithm based on the cross-entropy method is proposed to optimize the providers' infrastructure topology and it is tested on numerical examples providing economic interpretations.     

The design of branch and bound algorithms for a class of nonlinear integer programs

This paper is concerned with computational experimentation leading to the design of effective branch and bound algorithms for an important class of nonlinear integer programming problems, namely linearly constrained problems, which are used to model several real-world situations. The main contribution here is a study of the effect of node and branching variable selection and storage reduction strategies on overall computational effort for this class of problems, as well as the generation of a set of adequate test problems. Several node and branching variable strategies are compared in the context of a pure breadth-first enumeration, as well as in a special breadth and depth enumeration combination approach presented herein. Also, the effect of using updated pseudocosts is briefly addressed. Computational experience is presented on a set of eighteen suitably-sized nonlinear test problems, as well as on some random linear integer programs. Some of the new rules proposed are demonstrated to be significantly superior to previously suggested strategies; interestingly, even for linear integer programming problems.     

Guided Local Search for Final Placement in VLSI Design

The design of a VLSI circuit consists of two main parts: First, the logical functionality of the circuit is described, and then the physical layout of the modules and connections is settled. In the latter process one wishes to place the modules such that the necessary wiring becomes as small as possible in order to minimize area usage and delays on signal paths. The placement problem is the subproblem of the layout problem which considers the geometric locations of the modules. A new heuristic is presented for the general cell placement problem where the objective is to minimize total bounding box netlength. The heuristic is based on the Guided Local Search (GLS) metaheuristic. GLS modifies the objective function in a constructive way to escape local minima. Previous attempts to use local search on final (or detailed) placement problems have often failed as the neighbourhood quickly becomes too excessive for large circuits. Nevertheless, by combining GLS with Fast Local Search it is possible to focus the search on appropriate sub-neighbourhoods, thus reducing the time complexity considerably. Comprehensive computational experiments with the developed algorithm are reported on a broad range of industrial circuits. The experiments demonstrate that the developed algorithm is able to improve the estimated routing length of large-sized layouts with as much as 20 percent when compared to existing algorithms.     

一个电力分配的数学模型与算法

用电分配涉及整个社会的各行各业和千家万户,评价分配方案优劣既要考虑经济效益又要考虑社会效益,因此属于多目标决策分析问题。本文运用目标规划原理建立了用电分配数学模型,其中包括利润、产值、电业局收入及各种电量限制等96个目标,按5个优先级进行优化。文中所用算法的基础是单纯形方法,为给出有实用价值的优化分配方案,本文提出以上一年同期实际用电指标为基础研究现行分配方案的基本思想,并采取若干相应措施。     

Mould calculus,polyhedral cones,and characters of combinatorial Hopf algebras

We describe a method for constructing characters of combinatorial Hopf algebras by means of integrals over certain polyhedral cones. This is based on ideas from resurgence theory, in particular on the construction of well-behaved averages induced by diffusion processes on the real line. We give several interpretations and proofs of the main result in terms of noncommutative symmetric and quasi-symmetric functions, as well as generalizations involving matrix quasi-symmetric functions. The interpretation of noncommutative symmetric functions as alien operators in resurgence theory is also discussed, and a new family of Lie idempotents of descent algebras is derived from this interpretation.     

Random Dynamics of the Boussinesq System with Dynamical Boundary Conditions

Abstract

A coupled system of the two-dimensional Navier–Stokes equations and the salinity transport equation with spatially correlated white noise on the boundary as well as in fluid is investigated. The noise affects the system through a dynamical boundary condition. This system may be considered as a model for gravity currents in oceanic fluids. The noise is due to uncertainty in salinity flux on fluid boundary. After transforming this system into a random dynamical system, we first obtain asymptotic estimates on system evolution, and then show that the long time dynamics is captured by a random attractor.     

The center of an effect algebra

An effect algebra is a partial algebra modeled on the standard effect algebra of positive self-adjoint operators dominated by the identity on a Hilbert space. Every effect algebra is partially ordered in a natural way, as suggested by the partial order on the standard effect algebra. An effect algebra is said to be distributive if, as a poset, it forms a distributive lattice. We define and study the center of an effect algebra, relate it to cartesian-product factorizations, determine the center of the standard effect algebra, and characterize all finite distributive effect algebras as products of chains and diamonds.     

Use of VNS heuristics for scheduling of patients in hospital

One of the important problems in hospital management is how to schedule the treatments of resident patients in hospital for a given day due to the restrictions imposed by their medical condition as well as restrictions on medical machines and qualified medical personnel availability. Patients are to be subjected to different kinds of treatments, each requiring a medical machine of a certain type as well as a physician being qualified to operate it. This is a highly complex problem not yet adequately addressed in the literature. At present in most hospitals the problem is being solved manually by specialized personnel. However, the resulting schedules are very often inaccurate and inefficient with patients waiting for a long time to be treated and medical personnel often working overtime. In this paper we formulate the model for this problem and develop a simple and efficient method based on Variable Neighbourhood Search for solving it. The heuristics has been tested on real-life as well as on generated instances. Numerical results show that the heuristics proposed outperform commercial software for optimization as well as manual solutions both in quality of solution and in computational time.     

An algorithm for the removal of noise and jitter in signals and its application to picosecond electrical measurement

The accuracy of data recorded by many measurement systems is limited both by uncertainty in the measured value as well as by uncertainty in the trigger input to the system which controls when a measurement is taken. The former effect, which appears as noise on the underlying signal, is due, in part, to the sampling process and can often be reduced to an acceptable level by averaging many measurements. Noise on the trigger input gives rise to uncertainty in time between the trigger and the measurement points. The effect, known as jitter, causes a distortion of the signal which cannot be removed by averaging.We describe and analyse the effects of noise and jitter on a waveform, and an algorithm for removing, or reducing, these effects is presented. The work is motivated by an application in picosecond electrical and optoelectronic metrology where a laser pulse is measured by a system consisting of a photodiode and sampling oscilloscope. Here, since the length of the pulse is so short, perhaps only tens of picoseconds in duration, the effect of jitter is as pronounced as that of measurement noise. Results obtained by applying the algorithm to simulated data obtained from this application are presented.     

GPU implementation of a Helmholtz Krylov solver preconditioned by a shifted Laplace multigrid method

A Helmholtz equation in two dimensions discretized by a second order finite difference scheme is considered. Krylov methods such as Bi-CGSTAB and IDR(s) have been chosen as solvers. Since the convergence of the Krylov solvers deteriorates with increasing wave number, a shifted Laplace multigrid preconditioner is used to improve the convergence. The implementation of the preconditioned solver on CPU (Central Processing Unit) is compared to an implementation on GPU (Graphics Processing Units or graphics card) using CUDA (Compute Unified Device Architecture). The results show that preconditioned Bi-CGSTAB on GPU as well as preconditioned IDR(s) on GPU is about 30 times faster than on CPU for the same stopping criterion.