Graph Coloring with Adaptive Evolutionary Algorithms

This paper presents the results of an experimental investigation on solving graph coloring problems with Evolutionary Algorithms (EAs). After testing different algorithm variants we conclude that the best option is an asexual EA using order-based representation and an adaptation mechanism that periodically changes the fitness function during the evolution. This adaptive EA is general, using no domain specific knowledge, except, of course, from the decoder (fitness function). We compare this adaptive EA to a powerful traditional graph coloring technique DSatur and the Grouping Genetic Algorithm (GGA) on a wide range of problem instances with different size, topology and edge density. The results show that the adaptive EA is superior to the Grouping (GA) and outperforms DSatur on the hardest problem instances. Furthermore, it scales up better with the problem size than the other two algorithms and indicates a linear computational complexity.     

一类多维0-1背包问题的约束归并方法

提出一种新的关于多维背包(Multi-dimensions Knapsack Problem,MKP)的约束替代问题,MKP是NP-完全问题,称这种约束替代方法为不等式单约束平面生成法.叙述了单约束不等平面生成算法的基本思想,证明了此方法的一些性质及化简问题后所得到的新问题MKPS与原问题MKP的等价性.最后用实例证实了这种化简方法及其有效性。     

Boundary-value problems and the validity of the Post constraint in modern electromagnetism

When a (frequency-domain) boundary-value problem involving a homogeneous linear material is solved to assess the validity of the Post constraint, a conflict arises between the fundamental differential equations of electromagnetism in the chosen material and a naïve application of the usual boundary conditions. It is shown here that the conflict vanishes when the boundary conditions are properly derived from the fundamental equations, and the validity of the Post constraint in modern macroscopic electromagnetism is thereby reaffirmed.     

Existences theorems of systems of vector quasi-equillibrium problems and mathematical programs with equilibrium constraint

In this paper, we introduce systems of vector quasi-equilibrium problems and prove the existence of their solutions. As applications of our results, we derive the existence theorems for solution of system of vector quasi-saddle point problem, the existences theorems of a solution of system of generalized quasi-minimax inequalities, the mathematical program with equilibrium constraint, semi-infinite and bilevel problems.     

New Relaxation Method for Mathematical Programs with Complementarity Constraints

In this paper, we present a new relaxation method for mathematical programs with complementarity constraints. Based on the fact that a variational inequality problem defined on a simplex can be represented by a finite number of inequalities, we use an expansive simplex instead of the nonnegative orthant involved in the complementarity constraints. We then remove some inequalities and obtain a standard nonlinear program. We show that the linear independence constraint qualification or the Mangasarian–Fromovitz constraint qualification holds for the relaxed problem under some mild conditions. We consider also a limiting behavior of the relaxed problem. We prove that any accumulation point of stationary points of the relaxed problems is a weakly stationary point of the original problem and that, if the function involved in the complementarity constraints does not vanish at this point, it is C-stationary. We obtain also some sufficient conditions of B-stationarity for a feasible point of the original problem. In particular, some conditions described by the eigenvalues of the Hessian matrices of the Lagrangian functions of the relaxed problems are new and can be verified easily. Our limited numerical experience indicates that the proposed approach is promising.     

二硫化钼表面氧化行为的研究（Ⅱ）─—二硫化钼摩擦表面氧化与电子转移的研究

利用电子自旋共振谱和Ｘ射线光电子能谱研究了二硫化钼ＭｏＳ＿２摩擦表面的氧化和电子转移，发现ＭｏＳ＿２在摩擦过程中是以Ｍｏ￣（４＋）经由Ｍｏ￣（５＋）过渡态继而与氧作用生成稳定的Ｍｏ￣（６＋），并且是以ＭｏＯ＿３的形式存在，证明ＭｏＳ＿２的摩擦表面除有一般认为的Ｍｏ￣（４＋）和Ｍｏ￣（６＋）这两种化学状态以外，还有Ｍｏ￣（５＋）自由基离子这种从未发现的的中间态。Ｍｏ￣（５＋）是４ｄ￣１电子构型，其在室温下于空气或氧气中是稳定的，然而在摩擦环境或添加剂的作用下，Ｍｏ￣（５＋）所含不成对电子很容易发生转移而生成Ｍｏ￣（６＋），这种研究结果更加深入地揭示了ＭｏＳ＿２摩擦表面氧化过程的复杂性，因此，应当从摩擦化学角度重新认识ＭｏＳ＿２摩擦氧化产物及其形成机制，这于研究摩擦环境和添加剂对润滑剂的抗氧化协同效应具有重要意义。     

奇异系统Hamilton正则方程的Mei对称性、Noether对称性和Lie对称性

研究奇异系统Hamilton正则方程的形式不变性即Mei对称性，给出其定义、确定方程、限制方程和附加限制方程.研究奇异系统Hamilton正则方程的Mei对称性与Noether对称性、Lie对称性之间的关系，寻求系统的守恒量.给出一个例子说明结果的应用. 关键词： 奇异系统 Hamilton正则方程 约束 对称性 守恒量     

Smooth positive extensions and nonlinear programming

We establish a smooth positive extension theorem: Given any closed subset of a finite-dimensional real Euclidean space, a function zero on the closed set can be extended to a function smooth on the whole space and positive on the complement of the closed set. This result was stimulated by nonlinear programming. We give several applications of this result to nonlinear programming.This paper is dedicated to the memory of Emily Sue Merkle Waite, Ph.D.The author wishes to thank W. Cunningham for suggesting the question about constraint qualifications, A. Karr for noticing the example of a Brownian motion sample path, R. Byrd and P. Hartman for discussions, and E. Waite for support and encouragement.     

DEVELOPMENT OF AN OPTIMAL WATER ALLOCATION DECISION TOOL FOR THE MAJOR CROPS DURING THE WATER DEFICIT PERIOD IN THE SOUTHEAST UNITED STATES

ABSTRACT. We developed a dynamic economic model to optimize irrigation water allocations during water deficit periods for three major crops grown in the humid southeastern United States. Analysis involved the use of crop simulation models to capture (a) the yield water relationship and (b) soil moisture dynamics from one week to another week. A hy‐drological model was used to find the water supply; combinations of hydrological and simulation models were used to find the optimal water allocation during each week in corn, cotton and peanuts. Results indicated that farmers should irrigate the most valuable crop first (peanuts) before applying water to other crops (corn and cotton). Results also showed that, because of restriction on total water supply, an increase in crop acreage did not increase the net revenue of the farm in a proportionate amount. Results should provide guidelines to water managers, engineers, policy makers, and farmers regarding an optimal amount of water allocation that will maximize net returns when water shortage is a serious concern.     

韧性断裂的微观模型及其在约束断裂中的应用

详细分析了不同形状断裂试件及小范围屈服模型裂纹端部的损伤演化，提出了韧性断裂的宏观起裂相当于裂尖前方一特征位置处的损伤达到一临界值。利用此模型获得了与实验相一致的宏观断裂韧性及与约束无关的理论断裂韧性。