Exploiting planarity in separation routines for the symmetric traveling salesman problem

At present, the most successful approach for solving large-scale instances of the Symmetric Traveling Salesman Problem to optimality is branch-and-cut. The success of branch-and-cut is due in large part to the availability of effective separation procedures; that is, routines for identifying violated linear constraints.

For two particular classes of constraints, known as comb and domino-parity constraints, it has been shown that separation becomes easier when the underlying graph is planar. We continue this line of research by showing how to exploit planarity in the separation of three other classes of constraints: subtour elimination, 2-matching and simple domino-parity constraints.     

A quadrature finite element Galerkin scheme for a biharmonic problem on a rectangular polygon

A quadrature Galerkin scheme with the Bogner–Fox–Schmit element for a biharmonic problem on a rectangular polygon is analyzed for existence, uniqueness, and convergence of the discrete solution. It is known that a product Gaussian quadrature with at least three‐points is required to guarantee optimal order convergence in Sobolev norms. In this article, optimal order error estimates are proved for a scheme based on the product two‐point Gaussian quadrature by establishing a relation with an underdetermined orthogonal spline collocation scheme. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008     

Comparing different metaheuristic approaches for the median path problem with bounded length

In this paper we consider the Bounded Length Median Path Problem which can be defined as the problem of locating a path-shaped facility that departures from a given origin and arrives at a given destination in a network. The length of the path is assumed to be bounded by a given maximum length. At each vertex of the network (customer-point) the demand for the service is given and the cost to reach the closest service-point is computed. The objective is to minimize the sum of these costs over all the customer-points in the network.     

一种新的两道工序柔性流水车间排序问题

本文针对F_2(p),h11.1|m_1=1,m_2=μ≥2|C_(max)这一问题给出了几种近似算法,并对每种近似算法进行了最坏情形分析,给出了最坏情形界.     

A general model of parameterized OWA aggregation with given orness level

The paper proposes a general optimization model with separable strictly convex objective function to obtain the consistent OWA (ordered weighted averaging) operator family. The consistency means that the aggregation value of the operator monotonically changes with the given orness level. Some properties of the problem are discussed with its analytical solution. The model includes the two most commonly used maximum entropy OWA operator and minimum variance OWA operator determination methods as its special cases. The solution equivalence to the general minimax problem is proved. Then, with the conclusion that the RIM (regular increasing monotone quantifier) can be seen as the continuous case of OWA operator with infinite dimension, the paper further proposes a general RIM quantifier determination model, and analytically solves it with the optimal control technique. Some properties of the optimal solution and the solution equivalence to the minimax problem for RIM quantifier are also proved. Comparing with that of the OWA operator problem, the RIM quantifier solutions are usually more simple, intuitive, dimension free and can be connected to the linguistic terms in natural language. With the solutions of these general problems, we not only can use the OWA operator or RIM quantifier to obtain aggregation value that monotonically changes with the orness level for any aggregated set, but also can obtain the parameterized OWA or RIM quantifier families in some specific function forms, which can incorporate the background knowledge or the required characteristic of the aggregation problems.     

Determining optimal lot size for a two-warehouse system with deterioration and shortages using net present value

In this paper, we develop a deterministic inventory model for deteriorating items with two warehouses by minimizing the net present value of the total cost. Deterioration rates of items in the two warehouses may be different. In addition, we allow for shortages and complete backlogging. We then prove that the optimal replenishment policy not only exists but also is unique under some condition. Further, the result reveals that the reorder interval based on the average total cost, if it exists, must be longer than that derived using net present value. Finally, we use Yang’s [H.L. Yang, European Journal of Operational Research 157 (2004) 344–356] numerical example to illustrate the model and conclude the paper with suggestions for possible future research.     

车辆路径问题的改进遗传算法

提出一种基于遗传算法的求解车辆路径问题的新算法,避免传统遗传算法处理不可行约束条件中惩罚项系数选取不当所出现的问题.同时,通过现实例子分析该算法的优劣性,实验结果表明该算法是一种有效的算法.     

On non-Newtonian p-fluids. The pseudo-plastic case

In the following we study a class of stationary Navier-Stokes equations with shear dependent viscosity, under the non-slip (Dirichlet) boundary condition. We consider pseudo-plastic fluids. A fluid is said pseudo-plastic, or shear thinning, if in Eq. (1.1) below one has p<2. We are interested in global (i.e., up to the boundary) regularity results, in dimension n=3, for the second order derivatives of the velocity and the first order derivatives of the pressure. We consider a cubic domain Ω and impose the non-slip boundary condition only on two opposite faces. On the other faces we assume periodicity, as a device to avoid effective boundary conditions. This choice is made so that we work in a bounded domain Ω and simultaneously with a flat boundary.     

二阶线性微分方程的乘子可积性

在偏微分方程Riemann解法和微分方程裂变思想的启发下,引入了微分方程乘子函数(解)和乘子解法的概念,系统地讨论了二阶线性微分方程的乘子可积性.得到了二阶线性微分方程乘子可积的条件以及Riceati方程可积的充分必要条件,并分别给出了二阶线性微分方程和Riccati方程在乘子解下的通积分.     

Korn's inequality and Donati's theorem for the conformal Killing operator on pseudo-Euclidean space

We prove the Korn's inequality for the conformal Killing operator on pseudo-Euclidean space Rp,q, and an existence theorem for solutions to the non-homogeneous conformal Killing equation, which is a pseudo-Euclidean conformal generalization of Donati's theorem for Euclidean Killing operator.