人力资本存量计算方法的改进与试算

在Jorgenson和Fraumeni的理论框架下提出了一种计算人力资本存量的新方法,并且具体计算了我国2000年人力资本存量以及城乡人力资本存量.分析得出结论:我国人力资本总量巨大,而人均极少;城乡人均人力资本差距很大,且有进一步加大的趋势.     

基于存档策略的多目标优化的遗传算法及其收敛性分析

设计了一种用遗传算法求解多目标优化问题的有效方法——基于存档策略的多目标优化的遗传算法,并讨论了此算法的收敛性.首先给出档案的定义,设计出基于支配关系下的带有存档策略遗传算法,并通过算例检验了算法的有效性;然后引入了两档案间的距离的概念,在此距离定义的基础上证明了算法在概率意义下是收敛的.     

基于离散近似迭代法的多阶段M-V投资组合优化

提出了离散近似迭代方法,并用该方法求解具有交易成本和交易量限制的多阶段均值-方差(M-V)投资组合模型.离散近似迭代方法的基本思路为:首先,将连续型状态变量离散化,根据网络图的构造方法将上述模型转化多阶段赋权有向图;其次,运用嘉量原理求出起点至终点的最长路程,即获得模型的一个可行解;最后,以该可行解为基础,继续迭代直到前后两个可行解非常接近.还证明了该方法的收敛性和复杂性.     

基于DNA遗传算法的随机整数规划期望值模型求解

为了求解随机整数规划问题,提出了随机整数规划期望值模型的概念,分析了利用DNA遗传算法求解此类问题的优点,并设计了求解算法,最后通过报童问题,验证了算法的可行性和有效性.     

P*(κ)阵线性互补问题一种新的宽邻域预估-校正内点算法

基于邻近度量函数的最小值,对P*(κ)阵线性互补问题提出了一种新的宽邻域预估-校正算法,在较一般的条件下,证明了算法的迭代复杂性为O(κ+1)23n log(x0ε)Ts0.算法既可视为Miao的P*(κ)阵线性互补问题Mizuno-Todd-Ye预估-校正内点算法的一种变形,也可以视为最近Zhao提出的线性规划基于邻近度量函数最小值的宽邻域内点算法的推广.     

Towards auction algorithms for large dense assignment problems

In this paper, we focus on the problem of solving large-scale instances of the linear sum assignment problem by auction algorithms. We introduce a modified auction algorithm, called look-back auction algorithm, which extends the forward auction algorithm by the ability of reusing information from previous bids. We show that it is able to reuse information from the previous bids with high efficiency for all tested types of input instances. We discuss then the design and implementation of a suite of sequential and distributed memory auction algorithms on a Linux cluster with the evaluation on several types of input instances of the linear sum assignment problem. Our results show that the look-back auction algorithm solves sequentially nearly all types of dense instances faster than other evaluated algorithms and it is more stable than the forward-reverse auction algorithm for sparse instances. Our distributed memory auction algorithms are fully memory scalable. This research has been supported by IGA CTU under grant CTU0308013 and under research program MSMT 6840770014.     

The use of higher order finite difference schemes is not dangerous

We discuss the issue of choosing a finite difference scheme for numerical differentiation in case the smoothness of the underlying function is unknown. If low order finite difference schemes are used for smooth functions, then the best possible accuracy cannot be obtained. This can be circumvented by using higher order finite difference schemes, but there is concern that this may cause bad error behavior. Here we show, theoretically and by numerical simulation, that this is not the case. However, by doing so, the step-size should be chosen a posteriori.     

A second‐order accurate difference scheme for the two‐dimensional Burgers' system

In this article, a Crank‐Nicolson‐type finite difference scheme for the two‐dimensional Burgers' system is presented. The existence of the difference solution is shown by Brouwer fixed‐point theorem. The uniqueness of the difference solution and the stability and L₂ convergence of the difference scheme are proved by energy method. An iterative algorithm for the difference scheme is given in detail. Furthermore, a linear predictor–corrector method is presented. The numerical results show that the predictor–corrector method is also convergent with the convergence order of two in both time and space. At last, some comments are provided for the backward Euler scheme. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009     

Genetic algorithms applied to the solution of hybrid optimal control problems in astrodynamics

Many space mission planning problems may be formulated as hybrid optimal control problems, i.e. problems that include both continuous-valued variables and categorical (binary) variables. There may be thousands to millions of possible solutions; a current practice is to pre-prune the categorical state space to limit the number of possible missions to a number that may be evaluated via total enumeration. Of course this risks pruning away the optimal solution. The method developed here avoids the need for pre-pruning by incorporating a new solution approach using nested genetic algorithms; an outer-loop genetic algorithm that optimizes the categorical variable sequence and an inner-loop genetic algorithm that can use either a shape-based approximation or a Lambert problem solver to quickly locate near-optimal solutions and return the cost to the outer-loop genetic algorithm. This solution technique is tested on three asteroid tour missions of increasing complexity and is shown to yield near-optimal, and possibly optimal, missions in many fewer evaluations than total enumeration would require.     

Capabilities of a quasi-gasdynamic algorithm as applied to inviscid gas flow simulation

Ten well-known one-dimensional test problems reflecting the characteristic features of unsteady inviscid gas flows are successfully solved by a unified numerical algorithm based on the quasigasdynamic system of equations. In all the cases, the numerical solution converges to a self-similar one as the spatial grid is refined.