Scatter search for the single source capacitated facility location problem

This paper considers the Single Source Capacitated Facility Location Problem (SSCFLP). We propose a Scatter Search approach to provide upper bounds for the optimal solution of the problem. The proposed approach uses GRASP to initialize the Reference Set. Solutions of the Reference Set are combined using a procedure that consists of two phases: (1) the initialization phase and (2) the improvement phase. During the initialization phase each client is assigned to an open facility to obtain a solution that is then improved with the improvement phase. Also, a tabu search algorithm is applied. In order to evaluate the proposed approach we use different sets of test problems. According to the results obtained we observe that the method provides good quality solutions with reasonable computational effort.     

Computing Approximate Solutions of the Maximum Covering Problem with GRASP

We consider the maximum covering problem, a combinatorial optimization problem that arises in many facility location problems. In this problem, a potential facility site covers a set of demand points. With each demand point, we associate a nonnegative weight. The task is to select a subset of p > 0 sites from the set of potential facility sites, such that the sum of weights of the covered demand points is maximized. We describe a greedy randomized adaptive search procedure (GRASP) for the maximum covering problem that finds good, though not necessarily optimum, placement configurations. We describe a well-known upper bound on the maximum coverage which can be computed by solving a linear program and show that on large instances, the GRASP can produce facility placements that are nearly optimal.     

Noisy one-dimensional maps near a crisis. I. Weak Gaussian white and colored noise

We study one-dimensional single-humped maps near the boundary crisis at fully developed chaos in the presence of additive weak Gaussian white noise. By means of a new perturbation-like method the quasi-invariant density is calculated from the invariant density at the crisis in the absence of noise. In the precritical regime, where the deterministic map may show periodic windows, a necessary and sufficient condition for the validity of this method is derived. From the quasi-invariant density we determine the escape rate, which has the form of a scaling law and compares excellently with results from numerical simulations. We find that deterministic transient chaos is stabilized by weak noise whenever the maximum of the map is of orderz>1. Finally, we extend our method to more general maps near a boundary crisis and to multiplicative as well as colored weak Gaussian noise. Within this extended class of noises and for single-humped maps with any fixed orderz>0 of the maximum, in the scaling law for the escape rate both the critical exponents and the scaling function are universal.     

The Geometry of Lightlike Hypersurfaces of the de Sitter Space

It is proved that the geometry of lightlike hypersurfaces of the de Sitter space Sn+11 is directly connected with the geometry of hypersurfaces of the conformal space Cn. This connection is applied for a construction of an invariant normalization and an invariant affine connection of lightlike hypersurfaces as well as for studying singularities of lightlike hypersurfaces.     

On Spin Models,Triply Regular Association Schemes,and Duality

Motivated by the construction of invariants of links in 3-space, we study spin models on graphs for which all edge weights (considered as matrices) belong to the Bose-Mesner algebra of some association scheme. We show that for series-parallel graphs the computation of the partition function can be performed by using series-parallel reductions of the graph appropriately coupled with operations in the Bose-Mesner algebra. Then we extend this approach to all plane graphs by introducing star-triangle transformations and restricting our attention to a special class of Bose-Mesner algebras which we call exactly triply regular. We also introduce the following two properties for Bose-Mesner algebras. The planar duality property (defined in the self-dual case) expresses the partition function for any plane graph in terms of the partition function for its dual graph, and the planar reversibility property asserts that the partition function for any plane graph is equal to the partition function for the oppositely oriented graph. Both properties hold for any Bose-Mesner algebra if one considers only series-parallel graphs instead of arbitrary plane graphs. We relate these notions to spin models for link invariants, and among other results we show that the Abelian group Bose-Mesner algebras have the planar duality property and that for self-dual Bose-Mesner algebras, planar duality implies planar reversibility. We also prove that for exactly triply regular Bose-Mesner algebras, to check one of the above properties it is sufficient to check it on the complete graph on four vertices. A number of applications, examples and open problems are discussed.     

Location of Chemical Reaction of Indirect Electrochemical Synthesis in a Porous Hydrophobized Electrode

Location of chemical reaction of IES performed in a porous hydrophobized electrode is considered. Depending on the rate constant and order of the reaction, it can proceed in the electrode's porous space and in the electrolyte chamber.     

Surfaces in the lightlike cone

In this paper, we study surfaces in the lightlike cone. We first obtain fundamental formulas for surfaces in a lightlike cone of general dimensions and then characterize certain homogeneous surfaces in the three-dimensional lightlike cone and four-dimensional lightlike cone, respectively.     

Convergence of the Krylov-Bogolyubov procedure in Bowan’s example

In this paper, we study the behavior of time averages of the measure in Bowan’s example: a vector field on the plane with two saddles joined by two separatrix connections. We present an explicit criterion for the convergence of averaged measures and describe the set of their partial limits. As a consequence, we show that, for a typical initial measure, its time averages do not converge.     

基于网络优化模型的变电站选址决策研究

利用Cplex优化软件,设计C语言程序,求解有资金约束与无资金约束的变电站最小费用模型。证明在无资金约束条件下修建的变电站数量可能比有资金约束条件下修建的变电站数量要少,建议决策者在进行电网规划时比较使用上述两种模型,使总费用最低,避免主观决策失误。同时指出了Hakimi文章中的计算错误。