Local search intensified: Very large-scale variable neighborhood search for the multi-resource generalized assignment problem

We introduce a heuristic for the Multi-Resource Generalized Assignment Problem (MRGAP) based on the concepts of Very Large-Scale Neighborhood Search and Variable Neighborhood Search. The heuristic is a simplified version of the Very Large-Scale Variable Neighborhood Search for the Generalized Assignment Problem. Our algorithm can be viewed as a k-exchange heuristic; but unlike traditional k-exchange algorithms, we choose larger values of k resulting in neighborhoods of very large size with high probability. Searching this large neighborhood (approximately) amounts to solving a sequence of smaller MRGAPs either by exact algorithms or by heuristics. Computational results on benchmark test problems are presented. We obtained improved solutions for many instances compared to some of the best known heuristics for the MRGAP within reasonable running time. The central idea of our heuristic can be used to develop efficient heuristics for other hard combinatorial optimization problems as well.     

随机环境中的受控分枝过程

本文建立了随机环境中受控分枝过程模型．它是更一般意义下的随机环境中的分枝过程，在平稳遍历环境下，研究了其灭绝概率问题，通过对控制函数作适当的假设，利用平稳遗历过程的性质及概率母函数的迭代关系式，得到了判断过程灭绝的一个判定准则．     

两两PQD序列的完全收敛性和强大数定律

本文给出两两PQD序列部分和的几个不等式，并研究了两两PQD序列的完全收敛性和强大数定律．     

关于指数型超椭圆方程x^2=p^2m-p^m＋n＋1

证明了指数型超椭圆方程x^2=p^2m-p^m＋n＋1无解（x,p,m,n）,其中x,m,n∈N^＋,m〉n〉1,p∈P．上述结果部分解决了组合论中关于可逆Abel差集的Ma猜想．     

相对φ强伪压缩算子不动点的迭代逼近

在没有任何有界以及迭代参数列不必收敛于零等条件下,使用新的分析方法建立了相对φ强伪压缩算子不动点与相对φ强增生算子方程解具误差Ishikawa迭代序列的强收敛定理,推广和改进了有关文献中的相应结果,而且还给出了收敛率的估计式.     

A new discrete filled function algorithm for discrete global optimization

A definition of the discrete filled function is given in this paper. Based on the definition, a discrete filled function is proposed. Theoretical properties of the proposed discrete filled function are investigated, and an algorithm for discrete global optimization is developed from the new discrete filled function. The implementation of the algorithms on several test problems is reported with satisfactory numerical results.     

Minimization of the Ratio of Functions Defined as Sums of the Absolute Values

This paper addresses a new class of linearly constrained fractional programming problems where the objective function is defined as the ratio of two functions which are the sums of the absolute values of affine functions. This problem has an important application in financial optimization. This problem is a convex-convex type of fractional program which cannot be solved by standard algorithms. We propose a branch-and-bound algorithm and an integer programming algorithm. We demonstrate that a fairly large scale problem can be solved within a practical amount of time. The research of the first author was supported in part by the Grant-in-Aid for Scientific Research of the Ministry of Education, Science, Culture and Sports of the Government of Japan, B(2) 15310122 and 15656025.     

关于二次域理论求解一类Diophantus方程的整数解

本文研究了两个典型Diophantus方程在实二次域中整数解的问题.利用二次域中的理论和二次代数整数环中算术基本定理,得到了该类方程的一般解法和在实二次域中的所有整数解的相关结论,推广了文献[1]和[2]的结果.