An Explicit Integer Programming Model of the Minimal Spanning Tree Problem for Digraphs with Asymmetric Weights

As far as the minimal spanning tree problem for the digraph with asymmetric weightsis concerned, an explicit integer programming model is proposed, which could be solved successfullyusing the integer programming packages such as LINDO, and furthermore this model is extendedinto the stochastic version, that is, the minimal spanning tree problem for the digraph with theweights is not constant but random variables. Several algorithms are also developed to solve themodels. Finally, a numerical demonstration is given.

The minimal spanning tree method for calculating seismic multi-fractal

There are many methods to calculate seismic fractal at present. However, there are still more or less questions to every method. In this paper, we introduce a new way to calculate seismic fractal-the minimal spanning tree. We make an important improvement for this method. By studying some seismic events of four regions including Wushi, Wusu, Tangshan and Haicheng, we obtain that before the strong earthquake occurrence, the multi-fractal spectrum of the space-time distribution of earthquakes changes from centralized to loose. The result shows that the complexity of fractal structure and the inhomogeneity of the space-time distribution of earthquakes are both increasing. By studying the numerical simulation of point sets, we draw the conclusion that the physical essence of multi-fractal spectrums before and after a strong earthquake occurrence is a changing process from homogeneous to inhomogeneous, from simple to complex.

A Gene-Pool Based Genetic Algorithm for TSP

Based on the analysis of previous genetic algorithms (GAs) for TSP, a novel method called Ge- GA is proposed. It combines gene pool and GA so as to direct the evolution of the whole population. The core of Ge- GA is the construction of gene pool and how to apply it to GA. Different from standard GAs, Ge- GA aims to enhance the ability of exploration and exploitation by incorporating global search with local search. On one hand a local search called Ge- Lo-calSearch operator is proposed to improve the solution quality, on the other hand the modified Inver-Over operator called Ge InverOver is considered as a global search mechanism to expand solution space of local minimal. Both of these operators are based on the gene pool. Our algorithm is applied to 11 well-known traveling salesman problems whose numbers of cities are from 70 to 1577 cities. The experiments results indicate that Ge- GA has great robustness for TSP. For each test instance, the average value of solution quality, found in accepted time, stays within 0. 001% from the optimum.

Research on a toolpath generation method of NC milling based on space-filling curve

Tool path generated by space-filling curve always turns frequently causing trembling to machine,reducing toollife and affecting workpiece quality. Length and generation time of tool paths are both relatively long. In order to solve these problems,a toolpath generation method of NC milling based on space-filling curve is proposed. First,T-spline surface is regarded as the modeling surface,the grid,which is based on the limited scallop-height,can be got in the parameter space,and the influence value of grid node is determined. Second,a box is defined and planned,and the tool paths are got preliminarily,which is based on minimal spanning tree; Finally,based on an improved chamfering algorithm,the whole tool paths are got. A simulation system is developed for computer simulation,and an experiment is carried out to verify the method. The results of simulation and experiment show that the method is effective and feasible,and length and time of the tool paths are reduced.

Symmetrical Independence Tests for Two Random Vectors with Arbitrary Dimensional Graphs

Test of independence between random vectors X and Y is an essential task in statistical inference.One type of testing methods is based on the minimal spanning tree of variables X and Y.The main idea is to generate the minimal spanning tree for one random vector X,and for each edges in minimal spanning tree,the corresponding rank number can be calculated based on another random vector Y.The resulting test statistics are constructed by these rank numbers.However,the existed statistics are not symmetrical tests about the random vectors X and Y such that the power performance from minimal spanning tree of X is not the same as that from minimal spanning tree of Y.In addition,the conclusion from minimal spanning tree of X might conflict with that from minimal spanning tree of Y.In order to solve these problems,we propose several symmetrical independence tests for X and Y.The exact distributions of test statistics are investigated when the sample size is small.Also,we study the asymptotic properties of the statistics.A permutation method is introduced for getting critical values of the statistics.Compared with the existing methods,our proposed methods are more efficient demonstrated by numerical analysis.