集合竞价问题研究

20世纪中期以来,随着纳什均衡理论的提出和发展,博弈论(game theory)逐渐成为一门新兴的科学,它涉及了经济学、管理学、计算机科学、社会学等各个领域,对社会的发展起了极大的推动作用。本文侧重在博弈论中一些具体问题的优化算法的实现与比较,以及其在高性能平台下的并行度和改进情况的分析和研究。     

粒子滤波算法(PF)在疲劳驾驶检测系统中的应用研究

目前,实现定位跟踪的算法有很多,如卡尔曼滤波算法、扩展卡尔曼滤波算法、粒子滤波算法等。由于我们实际生活中的系统基本上都是非线性的,因此本文研究的是专门用于非线性非高斯系统跟踪的粒子滤波算法(PF)的基本原理及其具体应用。     

一种基于遗传算法求解车间调度问题的优化方法

遗传算法是解决车间调度问题的有效方法之一。但在构造适应度函数时由于调度问题诸多的束条件使得直接求解十分困难。罚函数法将约束条件加到目标函数上，变有约束为无约束．能较易求解该类问题。     

单件离散型生产作业排程的多目标协同优化

以某重机企业为背景,分析了单件离散型生产作业排程的特征,提出多目标协同优化问题。基于改进的田口质量损失函数,确立质量、工期与成本之间的非线性关系,综合考虑单件离散型的约束条件,构建了生产作业排程多目标协同优化模型。集成仿真技术和遗传算法,为模型求解提供了有效方法。最后将模型和算法应用到企业的生产实践中,验证了其实用性和有效性,为解决单件离散型生产排程问题提供了科学方法。     

Interval programming model for risk-based partner selection of virtual enterprise

The problem of risk-based partner selection of virtual enterprise is investigated. By choosing optimal partner for each project task, the project risk is minimized. The risk parameters are expressed in the form of interval numbers when the precise values are difficult to obtain, and the model is formulated into a 0-1 nonlinear programming with interval coefficients in its objective function. In order to solve the problem, the definition of order relation between interval numbers is given, and the original model is converted into an equivalent crisp bi-objective programming model. Because of the highly constrained nature and multiple objective of the model, a genetic algorithm is proposed to find the set of Pareto or near Pareto optimal solutions. The approach is demonstrated by some numerical examples, and the result shows that the suggested approach has high efficiency and the model has potential to practical applications.     

城市物流基地选址问题研究

本文将物流基地纳入城市交通网络中，以体现交通状况对物流基地选址的影响。在进行选址时，以运输费用和基地的投资、管理费用总和最小为规划者的主要目标，建立目标函数。选址的上层模型体现了运输费用和基地投资费用、管理费用最小的原则，下层模型体现了入选点的不同对交通流量分配的影响，下层模型是求解上层模型的基础。     

A multivariate Poisson mixture model for marketing applications

This paper describes a multivariate Poisson mixture model for clustering supermarket shoppers based on their purchase frequency in a set of product categories. The multivariate nature of the model accounts for cross-selling effects between the purchases made in different product categories. However, for computational reasons, most multivariate approaches limit the covariance structure by including just one common interaction term, or by not including any covariance at all. Although this reduces the number of parameters significantly, it is often too simplistic as typically multiple interactions exist on different levels. This paper proposes a theoretically more complete variance/covariance structure of the multivariate Poisson model, based on domain knowledge or preliminary statistical analysis of significant purchase interaction effects in the data. Consequently, the model does not contain more parameters than necessary, whilst still accounting for the existing covariance in the data. Practically, retail category managers can use the model to devise customized merchandising strategies.     

基于两层架构协调的应急物资分配与车辆调度集成优化方法

针对突发事件下的应急物资调运问题,考虑了多个地区同时受灾以及多个出救点需要对其进行救灾并且各出救点的运力有限的情况,以最小化总的车辆运输费用,最大化救灾效率、各受灾点的救灾满意度,以及各受灾点得到救助的公平性为目标,建立了该问题的多目标混合整数非线性规划模型,并提出了一个基于两层架构协调的迭代式遗传算法进行求解。基于仿真数据的实验结果证明了所提出的模型和算法的有效性。     

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.     

Numerical Maximisation of Likelihood: A Neglected Alternative to EM?

There is by now a long tradition of using the EM algorithm to find maximum‐likelihood estimates (MLEs) when the data are incomplete in any of a wide range of ways, even when the observed‐data likelihood can easily be evaluated and numerical maximisation of that likelihood is available as a conceptually simple route to the MLEs. It is rare in the literature to see numerical maximisation employed if EM is possible. But with excellent general‐purpose numerical optimisers now available free, there is no longer any reason, as a matter of course, to avoid direct numerical maximisation of likelihood. In this tutorial, I present seven examples of models in which numerical maximisation of likelihood appears to have some advantages over the use of EM as a route to MLEs. The mathematical and coding effort is minimal, as there is no need to derive and code the E and M steps, only a likelihood evaluator. In all the examples, the unconstrained optimiser nlm available in R is used, and transformations are used to impose constraints on parameters. I suggest therefore that the following question be asked of proposed new applications of EM: Can the MLEs be found more simply and directly by using a general‐purpose numerical optimiser?