关键词： Stochastic programming   Integer programming   Chance constraints   Probabilistic constraints   Decomposition  

摘要： We present a new approach for exactly solving chance-constrained mathematical programs having discrete distributions with finite support and random polyhedral constraints. Such problems have been notoriously difficult to solve due to nonconvexity of the feasible region, and most available methods are only able to find provably good solutions in certain very special cases. Our approach uses both decomposition, to enable processing subproblems corresponding to one possible outcome at a time, and integer programming techniques, to combine the results of these subproblems to yield strong valid inequalities. Computational results on a chance-constrained formulation of a resource planning problem inspired by a call center staffing application indicate the approach works significantly better than both an existing mixed-integer programming formulation and a simple decomposition approach that does not use strong valid inequalities. We also demonstrate how the approach can be used to efficiently solve for a sequence of risk levels, as would be done when solving for the efficient frontier of risk and cost.

关键词： Clifford algebra   algorithm construction   network analysis   shortest path algorithm  

摘要： Clifford algebra is introduced as a theoretical foundation for network topology expression and algorithm construction. Network nodes are coded with basis vectors in a vector space Rn, and the edges and k-walk routes can be expressed by 2-blades and k-blades, respectively, in the Clifford algebra Cl(n,0). The topologies among nodes, edges, and routes of networks can be directly calculated, and the network routes can be extended and traversed with oriented join products. The network algorithm construction processes based on Clifford algebra are instantiated by the single source shortest path algorithm. The experimental results on different scale random networks suggest that Clifford algebra is suited for network expression and relation computation. The Clifford algebra-based shortest path algorithm is vivid and clear in geometric meaning and has great advantage on temporal and spatial complexity. Copyright (c) 2013 John Wiley & Sons, Ltd.

关键词： 全球定位系统   用户位置   数学模型  

摘要： 在卫星时钟、系统时钟、用户接收机时钟同步为前提假设的基础上,描述了用户接收机定位的数学原理;又在以上时钟非同步条件下建立用户接收机位置定量求解模型和算法,在线性化的基础上,用迭代法进行位置求解.为定位软件的设计提供了理论依据.

关键词： Top-bead width   Genetic algorithm   Multiple regression   Robotic arc welding   GMA welding  

摘要： Gas metal arc (GMA) welding process has widely been employed due to the wide range of applications, cheap consumables, and easy handling. In order to achieve a high level of welding performance and quality, a suitable model is required to investigate the characteristics of the effects of process parameters on the bead geometry in the GMA welding process. This paper is to represent new algorithms to predict process parameters on top-bead width in robotic GMA welding process. The models have been developed, linear, curvilinear, and intelligent model, based on full factorial design with two replications. Regression analysis was employed for optimization of the coefficients of linear and curvilinear models, while genetic algorithm (GA) was utilized to estimate the coefficients of an intelligent model. Not only the fitting of these models was checked and compared by using a variance test (analysis of variance (ANOVA)) but also the prediction on top-bead width using the developed models was carried out based on the additional experiments. The developed models were employed to investigate the characteristic between process parameters and top-bead width. Resulting solutions and graphical representation showed that the intelligent model developed can be employed for prediction of bead geometry in GMA welding process.

关键词： 冲击线性信号   线性神经网络   双滑动窗口   Matlab仿真  

摘要： 利用线性神经网络方法对由正弦波组成的冲击响应信号进行仿真实验。应用改进的双滑动窗口时滞算法确定网络输入的响应窗口,仿真结果显示利用线性神经网络对线性系统进行建模具有非常高的精度,表明应用线性神经网络来进行实际线性系统预测具有较大的理论实用价值。

关键词： 算法改进   数学建模   改进意见  

摘要： 近年来,随着现代科学的不断发展和数学理论知识的不断进步,数学建模理论的应用范围也越来越广泛。通过数学建模理论,可以使事物更直观、更客观的体现出来。针对高校有关数学建模知识,深入探讨数学建模的分类问题和算法改进问题,并针对其应用问题提出合理性建议。

关键词： 数学形态学   遗传算法   滤波器   优化   量子论  

摘要： 为解决数学形态滤波器结构元素参数优化问题,提出了一种基于量子遗传算法的数学形态滤波器优化设计方法.根据数学形态结构元素参数特点初始化量子遗传种群,通过量子交叉、变异、基于膨胀系数的量子旋转门实现种群的演化进程,进而得到数学形态滤波器的最佳参数.结合仿真实验,研究了不同比例随机噪声、工频干扰噪声下的优化算法性能.仿真结果表明:优化后的数学形态滤波器性能得到较大改善,含随机噪声信号的信噪比由-0.98 dB提高到5.23 dB,含混合噪声信号的信噪比由-3.05 dB提高到0.41 dB,有效滤除了随机噪声、混入工频干扰的混合噪声.