分批加工中迟后范围的极小化问题

排序中以工件迟后范围作为极小化的目标函数体现了生产中对顾客的平等对待，对此目标函数以往的研究局限于非成批加工．随着成批加工大量出现于柔性制造系统中，其它一些目标函数如加权完工时间之和，最大迟后己出现在成批加工问题中，但还无人讨论工件迟后范围问题．本文对工件加工顺序给定时如何使迟后范围极小的最优分批问题建立了所需时间为多项式的动态规划算法，并进一步给出了一些性质．     

旅行商问题的基因整合算法

本文针对旅行商问题提出了基因整合算法。它是通过设置扰动矩阵构造与原商问题等价的近似问题，使用最优罚函数选择回路分枝得到一系列局部最优回路，从中提取频度高的分技——基因进行整合，得到更优的回路。该算法计算量小，对大规模问题计算效果显著。利用该算法对CHN144问题给出了目前最件的结果。     

需要安装时间的两台多功能机排序问题的计算复杂性

提出需要安装时间的多功能机排序问题,一般情况下,这是NP-困难的;主要研究只有两台机器时一些特殊情况下的计算复杂性.根据加工集合为机器全集的工件组数的不同,分别给出多项式时间算法和分枝定界算法.对各工件组的工件数和加工时间都相等的情况,给出一个多项式时间的最优算法-奇偶算法,从而证明此问题是多项式时间可解的.     

一类无需线性搜索的记忆梯度法

提出一类新的求解无约束优化问题的记忆梯度法,证明了算法的全局收敛性.当目标函数为一致凸函数时,对其线性收敛速率进行了分析.新算法在迭代过程中无需对步长进行线性搜索,仅需对算法中的一些参数进行预测估计,从而减少了目标函数及梯度的迭代次数,降低了算法的计算量和存储量.数值试验表明算法是有效的.     

一种原始——对偶单纯形算法的枢轴准则选择

Curet曾提出了一种有趣的原始一对偶技术,在优化对偶问题的同时单调减少原始不可行约束的数量,当原始可行性产生时也就产生了原问题的最优解.然而该算法需要一个初始对偶可行解来启动,目标行的选择也是灵活、不确定的.根据Curet的原始一对偶算法原理,提出了两种目标行选择准则,并通过数值试验进行比较和选择.对不存在初始对偶可行解的情形,通过适当改变目标函数的系数来构造一个对偶可行解,以求得一个原始可行解,再应用原始单纯形算法求得原问题的最优解.数值试验对这种算法的计算性能进行验证,通过与经典两阶段单纯形算法比较,结果表明,提出的算法在大部分问题上具有更高的计算效率.     

求线性比试和问题的确定性全局优化算法

为求线性比试和问题的全局最优解,本文给出了一个分支定界算法.通过一个等价问题和一个新的线性化松弛技巧,初始的非凸规划问题归结为一系列线性规划问题的求解.借助于这一系列线性规划问题的解,算法可收敛于初始非凸规划问题的最优解.算法的计算量主要是一些线性规划问题的求解.数值算例表明算法是切实可行的.     

加工时间依赖于机器的自由作业排序问题

1992年M．Dror提出工件的加工时间依赖于机器的排序问题（schedulingwithmachinedependentprocessingtimes），并研究以最大完工时间（makespan）和以总的完工时间为优化目标的两种这类排序问题．然而，M．Dror对以总的完工时间为优化目标提出的“最优算法”是错误的．本文用算例表明他提出的算法不是最优的，并在机器连续加工的条件下，把这个排序问题转化成指派问题（assignmentproblem），从而可以用匈牙利算法得到最优解．最后，我们提出几个尚未解决的问题，以期引起国内外同行进一步研究．     

带折扣因子的单机干扰管理研究

针对可预见的干扰管理问题,考虑单机环境下,加权折扣最短加工时间优先(WDSPT)序为原目标的最优加工次序,研究了如何对初始加工时间表进行修改。在干扰事件影响下,初始加工时间表将不再是最优,甚至不再可行。和大多数重排序研究不同,构建了同时考虑原目标和由干扰事件造成的扰动目标的重排序模型,并基于理想点法提出一种动态规划算法来求解所建模型中的双目标排序问题。最后通过一个数值算例来说明该重调度模型对于求解带折扣因子的单机干扰管理问题是有效的。     

基于两步子抽样算法的多目标抽样统计推断研究

针对海量数据,子抽样算法是当前一种流行的简化计算和降低计算成本的方法。现阶段的研究主要集中于单目标变量的估计上。多目标抽样也是现实生活中经常遇到的问题。本文提出基于广义线性模型,多目标抽样的均值两步子抽样算法。两步子抽样算法是Wang等(2018)^[1]提出的基于L-最优和A-最优的思想,确定每个抽样单元的入样概率。本文在此基础上,定义多目标抽样的各单元的入样概率,并推导模型参数估计量的渐近性质,最后用模拟数据和实际例子对均值两步子抽样算法和多目标两步子抽样方法进行比较。结果表明,在样本量相同时,A-最优准则下均值两步子抽样算法在估计精度上优于基于两步子抽样算法的MPPS抽样和L-最优准则下均值多目标两步子抽样算法。在计算效率上也较全样本估计有显著的提高,节约了计算时间。     

带准备时间的单机指数时间学习效应排序问题

研究带有准备时间的单机学习效应模型,其中工件加工时间具有指数时间学习效应,即工件的实际加工时间是已经排好的工件加工时间的指数函数。学习效应模型考虑工件的实际加工时间同时依赖于工件本身的加工时间和已加工工件的累计加工时间,目标函数为最小化总完工时间。这个问题是NP-难的,提出了一个数学规划模型来求解该问题的最优解。通过分析几个优势性质和下界,提出分支定界算法来求解此问题,并设计启发式算法改进分支定界算法的上界值。通过仿真实验验证了分支定界算法在求解质量和时间方面的有效性。     

Pendants-median支撑树及其一个相关问题:复杂性和算法

The complexity status of Pendants-median spanning tree problem is an open problem. Using the complexity of the X3C problem, the paper proves that Pendants-median spanning tree problem is NP-complete. Global-median spanning tree problem is a related problem. Using the complexity of 3SAT, the paper proves that this problem is also NP-complete, and a polynomial -time algorithm to this problem is given, whose time complexity is O(n^3).     

Polynomial Algorithms for a Class of Discrete Minmax Linear Programming Problems

We consider the problem of obtaining integer solutions to a minmax linear programming problem. Although this general problem is NP-complete, it is shown that a restricted version of this problem can be solved in polynomial time. For this restricted class of problems two polynomial time algorithms are suggested, one of which is strongly polynomial whenever its continuous analogue and an associated linear programming problem can be solved by a strongly polynomial algorithm. Our algorithms can also be used to obtain integer solutions for the minmax transportation problem with an inequality budget constraint. The equality constrained version of this problem is shown to be NP-complete. We also provide some new insights into the solution procedures for the continuous minmax linear programming problem.     

有资格限制的指派问题的求解方法

在实际的指派工作中，常会遇到某个人有没有资格去承担某项工作的问题，因此，本建立了有资格限制的指派问题的数学模型。在此数学模型中，将效益矩阵转化为判定矩阵，由此给出了判定此种指派问题是否有解的方法；在有解的情况下，进一步将效益矩阵转化为求解矩阵，从而将有资格限制的指派问题化为传统的指派问题来求解。最后给出了一个数值例子来说明这样的处理方法是有效的。     

A branch and bound network approach to the canonical constrained entropy problem

In this paper, we present a branch and bound algorithm for solving the constrained entropy mathematical programming problem. Unlike other methods for solving this problem, our method solves more general problems with inequality constraints. The advantage of the proposed technique is that the relaxed problem solved at each node is a singly constrained network problem. The disadvantage is that the relaxed problem has twice as many variables as the original problem. An application to regional planning is given, and an example problem is solved.     

三维种群生态动力系统的参数识别

研究具有反应一扩散现象的三维种群生态动力系统的参数识别问题，依该系统正问题解的性质，建立了参数识别的数学模型；论证了系统正问题解关于待识别参数的连续依赖性与参数识别问题最优解的存在性。     

哈明距离下圈图上1-重心问题的反问题

主要讨论哈明距离下圈图上1-重心问题的反问题.1-重心问题的反问题主要研究如何尽可能少地改变网络中的参数值,使得给定的顶点到其它顶点的加权距离之和不超过一个给定的上界.通过将该问题转化为0-1背包问题,证明了在哈明距离下该问题是NP困难的,并运用动态规划的思想,在考虑改变边的长度的情况下,对圈图进行了求解.     

Problem difficulty of real instances of convoy planning

Moving men and materials in large numbers and quantities is a long-standing military problem faced by all arms. An important part of this is the routing of convoys so that they reach their correct destinations in the shortest time. The optimization problem at the heart of this problem is referred to as the convoy movement problem. Previous work on the convoy movement problem has made the assumption that the problem is difficult in practice because of the NP-hardness of the problem in combination with the limited success of early approaches based on genetic algorithms. As a result subsequent work has focused on mathematical programming-based methods, principally Lagrangian relaxation. In this paper, we demonstrate that a straightforward reformulation of the problem renders the real-world like instances, used to benchmark previous approaches, amenable to solution by simple heuristics. The main lessons learnt from this work is that analysis of the problem in conjunction with simple algorithms can, in practice, yield surprisingly effective solutions.     

A primal–dual algorithm for minimizing a sum of Euclidean norms

We study the problem of minimizing a sum of Euclidean norms. This nonsmooth optimization problem arises in many different kinds of modern scientific applications. In this paper we first transform this problem and its dual problem into a system of strongly semismooth equations, and give some uniqueness theorems for this problem. We then present a primal–dual algorithm for this problem by solving this system of strongly semismooth equations. Preliminary numerical results are reported, which show that this primal–dual algorithm is very promising.     

On an optimal shape design problem to control a thermoelastic deformation under a prescribed thermal treatment

A shape optimization problem concerned with thermal deformation of elastic bodies is considered. In this article, measure theory approach in function space is derived, resulting in an effective algorithm for the discretized optimization problem. First the problem is expressed as an optimal control problem governed by variational forms on a fixed domain. Then by using an embedding method, the class of admissible shapes is replaced by a class of positive Borel measures. The optimization problem in measure space is then approximated by a linear programming problem. The optimal measure representing optimal shape is approximated by the solution of this finite-dimensional linear programming problem. Numerical examples are also given.     

求解点覆盖问题的拟物转换及算法

本文首先基于CNF－SAT问题已有的拟物型的求解思想,将点覆盖问题转换为连续情形的目标优化问题,进而提出一种新的竞争式下降梯度方法,从而获得了求解点覆盖问题的高效实用的快速算法．