A Brief Survey of Modern Optimization for Statisticians

Modern computational statistics is turning more and more to high‐dimensional optimization to handle the deluge of big data. Once a model is formulated, its parameters can be estimated by optimization. Because model parsimony is important, models routinely include non‐differentiable penalty terms such as the lasso. This sober reality complicates minimization and maximization. Our broad survey stresses a few important principles in algorithm design. Rather than view these principles in isolation, it is more productive to mix and match them. A few well‐chosen examples illustrate this point. Algorithm derivation is also emphasized, and theory is downplayed, particularly the abstractions of the convex calculus. Thus, our survey should be useful and accessible to a broad audience.     

公开密钥算法RSA策略及程序实现

随着通信的飞速发展，信息安全显得越来越重要，计算机密码体制的基本思想就是将要保护的信息变成伪装信息，在公开密钥算法提出之前，所有密码系统的解密密钥和加密密钥彼此有着直接的联系，这也是秘密密钥的缺陷所在。为此公开密钥算法RSA算法就顺应而生。这种叫加密算法可用VB程序编程实现。     

A hybrid parallel genetic algorithm for yard crane scheduling

This paper aims at postulating a novel strategy in terms of yard crane scheduling. In this study, a dynamic scheduling model using objective programming for yard cranes is initially developed based on rolling-horizon approach. To resolve the NP-complete problem regarding the yard crane scheduling, a hybrid algorithm, which employs heuristic rules and parallel genetic algorithm (PGA), is then employed. Then a simulation model is developed for evaluating this approach. Finally, numerical experiments on a specific container terminal yard are used for system illustration. Computational results suggest that the proposed method is able to solve the problem efficiently.     

A monotonically converging algorithm for the severity of ruin in a discrete semi-markov risk model

This paper deals with the severity of ruin in a discrete semi-Markov risk model. It is shown that the work of Reinhard and Snoussi (Stochastic Models, 18) can be extended to cover the case where the premium is an integer value and no restriction on the annual result is imposed. In particular, it is shown that the severity of ruin without initial surplus is solution of a system of equations. It can be obtained by a monotonically converging algorithm when the claims are bounded.     

Multivariate Cox Hidden Markov models with an application to operational risk

ABSTRACT

Modeling multivariate time-series aggregate losses is an important actuarial topic that is very challenging due to the fact that losses can be serially dependent with heterogeneous dependence structures across loss types and business lines. In this paper, we investigate a flexible class of multivariate Cox Hidden Markov Models for the joint arrival process of loss events. Some of the nice properties possessed by this class of models, such as closed-form expressions, thinning properties and model versatility are discussed in details. We provide the expectation-maximization (EM) algorithm for efficient model calibration. Applying the proposed model to an operational risk dataset, we demonstrate that the model offers sufficient flexibility to capture most characteristics of the observed loss frequencies. By modeling the log-transformed loss severities through mixture of Erlang distributions, we can model the aggregate losses. Finally, out-of-sample testing shows that the proposed model is adequate to predict short-term future operational risk losses.     

基于改进的BP-LM在中国人口老龄化预测中的应用

由于人口老龄化率的预测具有高度非线性特征，这与BP神经网络能够处理非线性问题的特征相符合，但BP神经网络算法易使解陷入局部极小。基于L-M算法的改进BP神经网络可以有效克服这一问题，而且收敛速度快。通过具体的仿真及实践结果验证了改进BP的有效性，并对未来五年的中国老龄化率进行了预测。     

岩土边坡稳定性的遗传算法分析

非线性优化方法主要缺陷在于当边坡土层为非均质复杂条件时,无法保证搜索到安全系数的全局最小解,而只能搜索到局部极小解。基于遗传算法,建立了搜索岩土边坡稳定性分析最小安全系数和滑移面中心坐标与半径的数值方法。问题的可行解在变量搜索区间内搜索,包括滑弧的圆心坐标和半径。数值模拟结果表明,遗传算法搜索到的边坡稳定最小安全系数与理论解是一致的。     

网络考试系统中的命题库设计与组卷算法——以“计算机应用基础”课程为例

以＂计算机应用基础＂课程的网络考试系统开发为基础,讨论了使用面向对象分析方法建立与改进命题库数据模型并将其映射为关系模型的过程。该命题库是网络考试系统的关键组成部分即题库子系统中的核心内容。最后,在网络考试系统组卷功能的实现方面,给出了随机组卷算法的具体实现。     

基于K-means算法的企业服务创新方向选择研究

企业在进行服务创新过程中,首先需要考虑到企业发展战略与其自身优势能力的匹配性,结合这两点来确定服务创新的发展方向。本文研究了企业基于自身已有的优势能力,运用K-means算法建立了企业服务创新战略方向选择模型,识别并确定了企业服务创新战略方向,由此得出企业进行服务创新时的最佳服务定位策略。     

基于无交叉遗传算法的物流车辆路径问题研究

设计并实现了一种求解基本车辆路径问题的无交叉遗传算法,阐述了无交叉遗传算法求解物流车辆路径问题的关键技术,包括编码方案、初始种群生成方案、适应度函数、种群选择方案和变异操作等;并对比了使用目标函数倒数法和目标函数做差法构造适应度函数时的求解效果。实验结果表明,给出的无交叉遗传算法在求解车辆路径问题上具有良好的性能。