糖果厂模型的最优化搜索方法

讨论了用两台装置搜索两个坏硬币的糖果厂模型C2,给出了一个测试过程t,使之与理论上的最优过程最多相差一次测试。     

一类走走停停行程问题的解答

本文讲述了走走停停行程问题中.每行进固定的距离两人就休息相同的时间而产生的追及问题的解法.并把它推广为两人休息时同点不同的一类题的解法.     

成对需求占线服务器问题及公平原则策略

针对在对称度量空间上多服务需求的k-服务器占线问题,研究问题空间为k＋2（度量空间上有k＋2个顶点,但只有k个服务器）时的一个特例：即在任意时刻都同时有两个服务需求提出。建立了该问题的数学模型,给出了公平原则策略,该策略能使得任意两个服务器完成服务后花费费用之差不大于某个固定常数;进行了相应的策略分析和竞争比的证明,并同工作函数策略进行了比较。     

一个砝码问题的数学证明

1　砝码问题　有一家村店 ,店里有一架天平 ,四个砝码 ,店主人夸口说 :用这四个砝码 ,我能称出所有从 1两到 4斤的物品 .村里人不信 ,有人报了几个数字 :1斤 2两、3斤 8两、7两、2斤6两… ,店主人一一把这些重量的物品称了出来 ,没人能难住他 .那么 ,这四只砝码本身分别有多少重呢 ?2　问题的解答　这四个砝码的重量分别是 1两、3两、9两、2斤 7两 ,并且是唯一的 .3　数学模型的建立　下面构造此类问题的数学模型 .设Ａ为 -ｎ个自然数的数列 :ａ1,ａ2 ,ａ3,… ,ａｉ,… ,ａｎ;ａｉ 为Ａ的一般项 .设Ｂ为一整数有限集 ,元素个数为ｍ .我们用…     

与装箱（切割）问题有关的数论结果

在生产与储运领域,把（小的）矩形货物装入（大的）矩形箱子是一项重要的工作。本文回答了以下的问题：设有一个长度为X的一维箱子以及设有两种（或三种）长度分别为α,b （或α,b,c)的人货物许多,问在什么条件下,可以（或不能）用这些货物（假定货物数量不限）装满箱子？或当两（或三）种货物的长度α,b（或α,b,c）给定时,一维箱子的长度X为多大时,用这两（ 或三）种货物能或不能装满箱子？不能被这些货物装满的箱子有多少个？     

基于动态规划的迭代算法设计方法

为了基于动态规划法设计求约束最优化问题(COPs)最优解的迭代算法,在避免使用"标记函数"和递归算法的前提下提出了两种求解模式,给出了设计求COPs最优解的迭代算法一般方法,并利用两个典型优化问题-最长公共子序列问题和矩阵链乘法问题,阐明了如何利用两种求解模式设计求COPs最优解的简捷迭代算法.     

一类具有上下界的均衡问题

本文获得一类具有上、下界的抽象均衡问题解的存在性条件, 回答了Isac, Sehgal和Singh提出的一个公开问题,进一步研究了具上、下界及约束条件的抽象均 衡问题,获得了更为深刻的结果. 最后,把上述公开问题推广到两个空间的情形.     

一道范围问题的简解与推广

石礼标、刘陆军和蒋明建老师先后来稿,给出了一道范围问题的简解,两篇稿件主题相同,各有所长,本刊将两篇稿件合并修改后刊出,以飨读者．     

跨区域生产供给的决策模型及其求解

跨区域生产经营是现代企业集团发展的一种趋势,追求高效益低成本是生产经营者所考虑的首要问题.我们对这类问题进行了描述和定量分析,并在是否允许产品交叉生产两种情形下建立了优化数学模型,经过技术分析,分别将这两种模型转化为运输问题和最优平衡指派问题来处理,从而为这类经济决策问题提供了一种科学的决策依据和可行的决策方法.     

最小最大二点集覆盖问题分析及改进算法设计

本文考虑二中心问题的扩展问题-最小最大二点集覆盖问题。给定两个平面点集P₁和P₂,分别包含m和n个点,求两个圆分别覆盖P₁和P₂,并且要求两圆半径与两圆圆心距三者中的最大值最小。本文主要贡献在于分析半径变化过程中两个点集中心包之间最近距离的变化关系,其中中心包是点集所具有的一个特殊几何结构,所得到的结果改进了Huang等人之前给出的结果,并且通过该结果设计相应算法,所得到的算法复杂性是目前最好的。     

包含随机客户的选择性旅行商问题建模及求解

针对快递配送过程中客户需求具有不确定性的特征,提出一种新的路径优化问题——包含随机客户的选择性旅行商问题,在该问题中客户每天是否具有配送需求存在一定概率,并且对客户进行配送可获取一定利润。同时考虑以上两种因素,建立该问题的数学模型, 目标为在满足行驶距离限制的条件下,找出一条经过部分客户的预优化路径,使得该路径的期望利润最大。其可用于模拟构建最后一公里快递配送的路径问题,提供更具有经济效益的配送路径。随后提出包含精细化局部搜索策略的改进遗传算法,算法根据问题特点构建初始可行解。最后通过多个计算比对结果表明,该算法具有较高的计算效率。     

On the semicontinuity problem of fibers and global F-regularity

In this article, we discuss the semicontinuity problem of certain properties on fibers for a morphism of schemes. One aspect of this problem is local. Namely, we consider properties of schemes at the level of local rings, in which the main results are established by solving the lifting and localization problems for local rings. In particular, we obtain the localization theorems in the case of seminormal and F-rational rings, respectively. Another aspect of this problem is global, which is often related to the vanishing problem of certain higher direct image sheaves. As a test example, we consider the deformation of the global F-regularity.     

Test Problem Generator by Neural Network for Algorithms that Try Solving Nonlinear Programming Problems Globally

A test problem generator, by means of neural networks nonlinear function approximation capability, is given in this paper which provides test problems, with many predetermined local minima and a global minimum, to evaluate nonlinear programming algorithms that are designed to solve the problem globally.     

Stochastic optimization models for a single-sink transportation problem

In this paper, we study a single-sink transportation problem in which the production capacity of the suppliers and the demand of the single customer are stochastic. Shipments are performed by capacitated vehicles, which have to be booked in advance, before the realization of the production capacity and the demand. Once the production capacity and the demand are revealed, there is an option to cancel some of the booked vehicles against a cancellation fee; if the quantity shipped from the suppliers using the booked vehicles is not enough to satisfy the demand, the residual quantity is purchased from an external company. The problem is to determine the number of vehicles to book in order to minimize the total cost. We formulate a two-stage and a multistage stochastic mixed integer linear programming models to solve this problem and test them on a real case provided by Italcementi, the primary Italian cement producer and the fifth largest cement producer in the world. We test the influence of different scenario-tree structures on the solutions of the problem, as well as sensitivity of the results with respect to the cancellation fee.     

On the stable difference scheme for source identification nonlocal elliptic problem

Approximation of source identification problem for elliptic equation with integral-type nonlocal condition is discussed. The first order of accuracy difference scheme for elliptic nonlocal identification problem is studied. By using spectral resolution of a self-adjoint operator, we establish stability inequalities for solution of constructed scheme. Subsequently, the difference scheme for approximate solution of multidimensional boundary value problem with integral-type nonlocal and first kind boundary conditions is investigated on stability. Numerical test examples are presented.     

“问题情境设计式赏识教学法”研究及其教学效果

给出了"问题情境设计式赏识教学法"的界定及研究方法,以及试验班级与对照班级期末高等数学考试成绩结果.通过统计处理,试验班级与对照班级成绩有显著性差异,得到"问题情境设计式赏识教学法"对提高教育质量效果明显的结论,可以推广.     

商人渡河问题的算法实现

"商人渡河问题"是一个传统的智力游戏问题,常常是作为数学模型、数据结构与智能算法分析等学科中很重要的教学或实验案例被引用.其求解算法尚未得到很好的解决,问题解的存在性等还缺少一般性和明确的结论.将首先从算法实现方面对这个问题进行深入地探讨.设计出思想方法较简单的、能在Matlab中编程实现的算法,且算法能求出问题的全部最少步数解.此外还报告了该类问题在各种情形下有趣的计算结果.     

Minimizing shifts for personnel task scheduling problems: A three-phase algorithm

The personnel task scheduling problem is a subject of commercial interest which has been investigated since the 1950s. This paper proposes an effective and efficient three-phase algorithm for solving the shift minimization personnel task scheduling problem (SMPTSP). To illustrate the increased efficacy of the proposed algorithm over an existing algorithm, computational experiments are performed on a test problem set with characteristics motivated by employee scheduling applications. Experimental results show that the proposed algorithm outperforms the existing algorithm in terms of providing optimal solutions, improving upon most of the best-known solutions and revealing high-quality feasible solutions for those unsolved test instances in the literature.     

A two-phase algorithm for the partial accessibility constrained vehicle routing problem

In the partial accessibility constrained vehicle routing problem, a route can be covered by two types of vehicles, i.e. truck or truck + trailer. Some customers are accessible by both vehicle types, whereas others solely by trucks. After introducing an integer programming formulation for the problem, we describe a two-phase heuristic method which extends a classical vehicle routing algorithm. Since it is necessary to solve a combinatorial problem that has some similarities with the generalized assignment problem, we propose an enumerative procedure in which bounds are obtained from a Lagrangian relaxation. The routine provides very encouraging results on a set of test problems.