非凸区域上的一些Hardy型不等式

研究非凸区域上的Hardy型不等式.通过选取特殊的向量值函数以及仔细的分析与计算,得到了各向异性Heisenberg群上一类非凸区域上的Hardy不等式,更进一步得到了非凸区域上与Greiner型向量场相关的几类Hardy型不等式.     

半圆区域的包含测度

本文研究了半圆区域内定长线段的包含测度问题.利用广义支撑函数和限弦函数,得到了这类区域的包含测度.关于非多边形凸域的包含测度的现有结果不多,本文的结果丰富了凸体包含测度的具体结果.     

路径跟踪方法求解无界非凸区域上的不动点问题

给出了求解一类无界非凸区域上不动点问题的路径跟踪方法.在适当的条件下,给出了不动点存在性的构造性证明,从而得到了路径跟踪方法的全局收敛性结果.研究结果为计算无界非凸区域上不动点问题提供了一种全局收敛性方法.     

Heisenberg群中一类非凸区域上的Hardy不等式

通过构造向量函数,得到了Heisenberg群中一类非凸区域上的Hardy不等式,从而推广了以前的相关结论.     

一类非凸全局最优化问题的最优性条件

本文研究一类非凸连续全局最优化问题的最优性条件.通过构造含有参数的辅助函数,且对辅助函数作极限运算,得到一种基于积分运算的积分型全局最优性条件,并利用该辅助函数得到非凸规划问题全局最优解的一些充分必要条件.     

一类具有连续变量的全局最优化问题的凸化方法

本文研究了一类非凸最优化问题的凸化方法与最优性条件的问题.利用构造含有参数的函数变换方法,将具有次正定性质的目标函数凸化,并获得了这一类非凸优化问题全局最优解的充要条件,推广了凸化方法在求解全局最优化问题方面的应用.     

关于非凸的有限理性的稳定性

关于有限理性方面的文献, 大多数都是在满足凸性条件下研究有限理性的相关性质, 在一定程度上限制了其应用范围. 应用Ekeland变分原理, 减弱了有限理性模型的假设条件, 考虑在不满足凸性条件下的有限理性模型的稳定性问题. 具体给出了非凸的Ky Fan点问题解的稳定性, 非凸非紧的Ky Fan点问题解的稳定性, 非凸向量值函数Ky Fan点解的稳定性和非凸非紧向量值函数Ky Fan点解的稳定性. 作为应用, 还给出了非凸的n人非合作博弈有限理性模型解的稳定性和非凸的多目标博弈有限理性模型解的稳定性.     

平均凸曲线缩短流的非坍塌性

本文主要研究了平面凸曲线缩短流的非坍塌性质.首先,我们给出了平面凸曲线非坍塌性的定义,并通过定义一个函数Z,我们证明了平面凸曲线非坍塌与函数Z的非负性是等价的.接着,我们利用极值原理证明平面凸曲线缩短流保持非坍塌性质.     

数据挖掘中聚类中心问题的光滑化和填充函数方法

本文提出了数据挖掘中求解聚类中心问题的一种新方法.这类问题属于非凸非光滑全局最优化问题.我们首先利用光滑化方法将非光滑聚类函数用光滑函数逼近,然后对光滑化问题利用填充函数搜索其全局最优点.对不同数据库的数值试验表明,本文提出的算法是可行和有效的.     

非线性规划的(H,Ω)对偶理论

对偶理论是非线性规划理论的一个重要组成部分,目前较成熟和完善的仅是凸规划的对偶理论.对于非凸规划对偶问题的研究仅有少量的工作完成,其结果也不令人满意.文献[1]就凸共轭函数进行了推广,建立了(H,(?))共轭函数理论,这一理论为凸对偶向非凸对偶迈进提供了基础.本文应用这一(H,(?))共轭函数理论,提出并建立了非线性规划的(H,(?))对偶理论.应用表明,在特殊簇 H 及(?)下,迄今为止几乎所有非线性规划的对偶理论都是这一对偶框架下的特殊形式,因此可以说,它是对偶理论的一个突破.     

基于网络分析方法的物流配送中心选址的研究

经济全球化。信息技术和电子商务的发展对物流产生了深刻的影响。使之呈现出新的特点。这些特点对配送中心选址的研究提出了更高，更新的要求。本在对GIS网络分析方法的阐述和P中心选址模型的分析的基础上，建立了配送中心选址优化模型。该模型通过引入商品保管费用、处理费用、配送中心建造费用对P中心选址模型进行了拓展，并通过总费用最小化确定配送中心的数量、位置以及资源点与配送中心、配送中心与用户之间的供需关系。     

Improving biorefinery planning: Integration of spatial data using exact optimization nested in an evolutionary strategy

Biorefineries can provide a product portfolio from renewable biomass similar to that of crude oil refineries. To operate biorefineries of any kind, however, the availability of biomass inputs is crucial and must be considered during planning. Here, we develop a planning approach that uses Geographic Information Systems (GIS) to account for spatially scattered biomass when optimizing a biorefinery’s location, capacity, and configuration. To deal with the challenges of a non-smooth objective function arising from the geographic data, higher dimensionality, and strict constraints, the planning problem is repeatedly decomposed by nesting an exact nonlinear program (NLP) inside an evolutionary strategy (ES) heuristic, which handles the spatial data from the GIS. We demonstrate the functionality of the algorithm and show how including spatial data improves the planning process by optimizing a synthesis gas biorefinery using this new planning approach.     

带时效性约束的配送中心多源选址问题研究

应用启发式算法求解带时效性约束的多源选址问题.分析物流配送的时效性问题,建立带时效性约束的配送中心多源选址模型.构造两步启发式算法:1)借助传统迭代算法,求解物流服务分配矩阵,把多源选址问题转化为单源选址问题;2)基于M ATLAB函数,设计优化程序,计算带时效性约束的单源选址模型.并给出算例,验证模型和算法的可行性.研究表明两步启发式算法是求解带时效性约束的物流配送中心多源连续选址问题的有效算法.     

一个带产品定价约束的竞争选址双层规划模型及其求解算法

以大型连锁卖场的选址为研究背景,提出了一个在竞争环境下使获利最大的竞争选址定价双层规划模型,其中上层模型做出选址决策,下层模型确定产品的纳什均衡价格.将设施效用引入到模型中,用指数效用函数来刻画顾客的购物行为偏好,首次证明了不合作状态下双方价格均衡解的存在性和唯一性,并给出了求解最优设施点设置方案和价格均衡解的算法思想及数值算例.     

Strategic design of competing supply chain networks for inelastic demand

A model for designing the network of a new entrant supply chain under inelastic demand and in the presence of pre-existing competing chains is proposed. These supply chains provide an identical product for a market area. The model considers the location of distribution centres and retail outlets on a discrete set of potential locations. The assumptions of the model are: (1) static competition between the new and pre-existing chains and (2) a probabilistic customer behaviour based on an attraction function depending on both the location and the quality of the retailers. This model also incorporates the impact of the facilities’ location decisions on the operational inventory and shipment decisions. The resulting model is formulated as a mixed integer non-linear programme (MINLP). To solve the MINLP it is transformed to a linear one. We illustrate the model, discuss the results of a real-world case, and investigate the effectiveness of the proposed algorithm using randomly generated examples.     

Internal modelling of objective functions for global optimization

Global optimization requires an adequate internal representation of the objective function for success in a reasonable number of function evaluations. A method for determining the location of a new function evaluation, based on a representation using a stationary stochastic process model, is investigated and some results are given.     

The Spatial Analysis of Community Health Services on Wirral Using Geographic Information Systems

This paper discusses the development of a geographical information system (GIS) for analysing the spatial distribution of community-based health services and the patients who use them on the Wirral peninsula in North West England. Information, with full geographical coding, has been obtained about General Practitioners (GPs) on the Wirral and the services they provide, together with the location, age and sex of the patients registered with them. Data have also been assembled on the services provided at local clinics. This is augmented with information on administrative boundaries and the street network held in digital form, and with statistical information for small areas covering demographic structure, social conditions and deprivation. The GIS is being used to identify catchment areas for different services and to produce demographic, social and residential profiles for the patients who use them.     

考虑居民选择行为的应急避难场所选址问题研究

突发事件发生后,应急管理部门将面临选择启用哪些应急避难场所供居民避难的决策。与其它设施选址不同,处于有限理性状态下的居民可选择是否去避难以及去哪个避难所避难。为使未被服务的居民数量最小化,考虑居民的有限理性选择行为至关重要。为此,考虑居民避难距离及避难所吸引力等因素,基于竞争选址理论构建避难所对居民的效用函数。在此基础上,运用多项logit模型刻画居民的有限理性选择行为,建立基于有限理性选择行为的选址模型,并与基于效用最优选择行为和基于系统最优原则的选址模型进行对比以验证模型的合理性。为了高效地求解模型,设计了模拟退火算法和遗传算法两种启发式算法。算例分析结果验证了模型和算法的可行性和有效性,并揭示了居民理性程度、选址个数及财政预算均对选址结果有重要影响。     

基于时间满意度的应急物资储备库选址问题

基于应急物资配送过程中时间因素的重要性,将时间满意度引人应急物资储备库选址问题中.针对时间满意度为线性分段函数,建立了以时间满意度最小的需求点的时间满意度尽量大以及系统总费用最小为目标的双目标混合整数规划模型,对目标函数的最小最大值问题进行转化,在此基础上构造新的优化模型,并设计了相应的启发式算法求解.最后通过算例说明算法的可行性和有效性.     

A continuous covering location model with risk consideration

This paper proposes a continuous covering location model with risk consideration. The investigated model is an extension of the discrete covering location models in continuous space. The objective function consists of installation and risk costs. Because of uncertain covering radius, customer satisfaction degree of covering radius is introduced by fuzzy concept. Since, the uncertainty may cause risk of uncovering customers; the risk cost is added to the objective function. The installation cost is assigned to a zone with a predetermined radius from its center. The model is solved by a fuzzy method named α$\alpha$-cut. After solving the model based on different α$\alpha$-values, the zones with the largest possibilities are determined for locating new facilities and the best locations are calculated based on the obtained possibilities. Then, the model is solved to determine the best covering values. This paper, also introduces a risk analysis method based on Response Surface Methodology (RSM) to consider risk management in the location models. Finally, a numerical example is expressed to illustrate the proposed model.