关于一类两台机器自由作业的排序问题

以工件完工时间的总和为优化目标的两台机器自由作业问题是NP-hard问题.本文针对加工时间仅依赖于机器并且机器连续加工的问题,给出了机器排序是可行排序的充分必要条件,引入可行排列的极小子排列的概念,运用组合优化方法,研究了最优排序中极小子排列的性质,并由此得到了该问题的最优时间表的一般构造方法.     

两种SINS惯性系四元数粗对准算法等价性分析

针对捷联惯导系统惯性系粗对准两种四元数算法的等价性进行了详细分析。首先,根据姿态矩阵的分解原理将初始对准问题转化为多矢量定姿的Wahba问题,并根据重力矢量连续变化的特点建立了积分形式的优化目标函数。然后,根据基于四元数的坐标变换原理,将目标函数变换为关于姿态四元数的函数,进而根据四元数运算性质分别导出最优四元数的两种求解形式,并根据矩阵特征值和特征向量的性质证明了两种算法的等价性。最后,通过仿真和试验数据进一步验证了理论分析的正确性。     

随机多需求环境下远程中继保障网络设计优化问题建模与求解

为保障海域安全稳定, 当远海海域发生紧急安全问题时, 需要派遣飞机从大陆保障基地出发进行远程支援。本文研究了在随机多需求环境下, 中继保障网络的最优化设计问题, 给出了规范化的问题描述以及问题的混合整数规划模型, 根据事发点发生意外事件的频率以及保障需求量作为需求的权重建立目标函数。模型以中继保障点的位置以及最优支援路线作为决策变量, 以保障资源作为约束条件, 实现了连续与离散相结合的选址方法来优化中继保障点, 并运用几何近似方法将模型中的欧式距离非线性约束转化为线性约束。所建模型可应用数学模型建模语言和求解器进行最优化求解, 直接获得多种不确定需求环境下的期望最优网络设计及支援路径。基于给定的3种任务类型, 经过模拟案例验证, 所建立模型可满足对实际规模的中继保障网络优化设计。     

Distributed Nonsmooth Convex Optimization over Markovian Switching Random Networks with Two Step-Sizes

This paper investigates the distributed convex optimization problem over a multi-agent system with Markovian switching communication networks. The objective function is the sum of each agent's local nonsmooth objective function, which cannot be known by other agents. The communication network is assumed to switch over a set of weight-balanced directed graphs with a Markovian property. The authors propose a consensus sub-gradient algorithm with two time-scale step-sizes to handle the Markovian switching topologies and the absence of global gradient information. With proper selection of step-sizes, the authors prove the almost sure convergence of all agents' local estimates to the same optimal solution when the union graph of the Markovian network' states is strongly connected and the Markovian chain is irreducible. The convergence rate analysis is also given for specific cases.Simulations are given to demonstrate the results.     

铁路线路设计方案综合优选决策系统的研究

介绍了基于多目标模糊综合优选模型的铁路线路设计方案综合优选决策系统软件的研制与开发过程，给出了其应用算例，较好地解决了方法在各方案定量与定性指标出现交叉时难于评优的问题。     

Optimal Switching Integrity Attacks on Sensors in Industrial Control Systems

In this article, an optimal switching integrity attack problem is investigated to study the response of feedback control systems under attack. The authors model the malicious attacks on sensors as additive norm bounded signals. The authors consider an attacker who is only capable of launching attacks to limited number of sensors once a time and changing the combinations of attacked sensors all over the time. The objective of this paper is to find the optimal switching sequence of these combinations and the optimal attack input. The authors solve this problem by transforming it into a traditional optimal control problem with new control variables vary continuously in the range [0, 1]. The optimal solutions of the new control variables are of bang-bang-type. Therefore, an algebraic switching condition and an optimal attack input can be obtained. Finally, numerical results are provided to illustrate the effectiveness of the methods.     

Model and algorithm of flow interception problem with multi-type of flows

To study simultaneous location of different kinds of facilities, a new model of flow interception problem with multi-type of flows is proposed, with the consideration of multi-purpose flows and the influence of facilities on each other. To be more practical, the objective is to maximize the benefits from flow-by customers instead of maximizing flows in the past. Since this problem is NP-hard and there is no optimal solution for large network, greedy and improved greedy heuristic algorithms are proposed. A computational example is presented to show that the optimal location decisions are proved to be strongly dependent on the influence coefficients and average profits by one customer and different types of facilities are almost co-located. Finally the results of sensitivity analysis are reported.     

城市交通网络中商业街的选址分析与计算

商业街在城市交通网络体系中的选址是商业街布局的重要方面。本文提出交通网络商业街选址问题并建立数学模型，给出了两种选址原则：（1）城市中所有节点至商业街（只需要达到商业街的其中一个节点）之间的最短路径之和最小。（2）城市中所有点对之间过商业街的最短路径之和最小。针对以上两个方面，分另4给出其计算方法，并进行了算法的时间和空间复杂性分析。     

Method for Risky Multiobjective Group Decision-Making and Its Application

The multiobjective group decision-making problem under risk is common in reality. This paper focuses on the study about risky multiobjective group decision-making problem where the index value is not certain. We give indexes classifying method and index normalizing formula of this type problem. By building objective function that minimizes general weighted distance from every alternative to the relatively best and worst alternative, the optimal membership degree of every decision-maker to every alternative can be obtained, and by building another objective function that minimizes general weighted distance from the optimal membership degree of every decision-maker to every alternative to the group optimal alternative and the group inferior alternative, the optimal membership degree of every decision-maker to every alternative can be obtained, which are both based on probability theory and fuzzy theory. Aftermost a model is established which collects group preferences. This method provides a new idea and     

Optimal antenna placement in distributed antenna systems

To minimize the outage probability of the cell (OPC) in downlink distributed antenna systems with selection transmission, a complex-encoding genetic algorithm (GA) is proposed to find the optimal locations of the antenna elements (AEs). First, the outage probability at a fixed location in the cell is investigated. Next, an analytical expression of the OPC is derived, which is a function of the AE locations. Then the OPC is used as the objective function of the antenna placement optimization problem, and the complexencoding GA is used to find the optimal AE locations in the cell. Numerical results show that the optimal AE locations are symmetric about the cell center, and the outage probability contours are also given with the optimal antenna placement. The algorithm has a good convergence and can also be used to determine the number of AEs which should be installed in order to satisfy the certain OPC value. Lastly, verification of the OPC’s analytical expression is carried out by Monte Carlo simulations. The OPC with optimal AE locations is about 10% lower than the values with completely random located AEs.     

有市场协同作用的竞争设施选址：模型与比较

针对产品或服务市场有协同效应的竞争设施选址问题,首先提出了协同效应的定义和三种不同类型的协同效应函数,并建立了有协同效应的最大俘获选址模型. 对于分段类型的协同函数,分别通过计算试验和理论分析的方法考察了有协同效应的新问题P₁与无协同效应的原问题P₀最优解之间的关系; 并对原问题P₀最优解取不同水平值时,新问题P₁最优解是如何随协同效应函数参数的不同而变化做了具体分析,结果对实践有一定的指导意义.     

一种最优控制问题的直接参数化描述解法

本文采用亏数为2的分段三次样条函数描述最优控制函数,使塔式起重机定位这个奇异最优控制问题转化为多变量参数极小问题。文中讨论了控制约束的加入,使用了直接搜索算法。给出了使用共轭梯度直接最优控制解法与本文方法的结果比较,表明本文方法是解决该类问题的一种直观有效的途径。本文叙述的方法容易被面向实际的工程应用人员所接受。     

用遗传算法求解最优同时镇定控制器

研究了用改进的遗传算法求解同时镇定一族线性定常系统的最优状态 /输出反馈控制律问题。引入了通常的二次型指标作为每一个系统的性能指标。在满足稳定性的条件下 ,通过最小化每个系统性能指标的加权函数值来求得最优同时镇定律。提出了一种求解该优化问题的改进遗传算法。计算结果说明了该方法的有效性。     

Multiple optimal solutions to a sort of nonlinear optimization problem

The optimization problem is considered in which the objective function is pseudolinear（both pseudoconvex and pseudoconcave） and the constraints are linear. The general expression for the optimal solutions to the problem is derived with the representation theorem of polyhedral sets, and the uniqueness condition of the optimal solution and the computational procedures to determine all optimal solutions （if the uniqueness condition is not satisfied ） are provided. Finally, an illustrative example is also given.     

能力限制条件下内河集装箱枢纽港选址问题研究:以长江为例

相比于海洋运输,内河运输中集装箱船舶较小,船舶装载能力受到一定的限制.本文研究能力限制条件下内河集装箱枢纽港选址问题,建立一个混合整数非线性规划模型.不同于传统的枢纽选址问题的研究大多是基于枢纽之间的运输折扣因子的假设,本文采用基于流量的非线性费用函数来表示规模经济.从而使得所研究的问题是一个凹函数优化问题.为简化本文的问题,将目标函数分段线性化.基于线性化后的模型,根据能力限制的条件,提出一个启发式求解算法,以及一个加速技巧.最后,通过以长江为例,进行算例分析,来说明模型和算法的效果.     

Bilevel programming model and solution method for mixed transportation network design problem

By handling the travel cost function artfully, the authors formulate the transportation mixed network design problem (MNDP) as a mixed-integer, nonlinear bilevel programming problem, in which the lower-level problem, comparing with that of conventional bilevel DNDP models, is not a side constrained user equilibrium assignment problem, but a standard user equilibrium assignment problem. Then, the bilevel programming model for MNDP is reformulated as a continuous version of bilevel programming problem by the continuation method. By virtue of the optimal-value function, the lower-level assignment problem can be expressed as a nonlinear equality constraint. Therefore, the bilevel programming model for MNDP can be transformed into an equivalent single-level optimization problem. By exploring the inherent nature of the MNDP, the optimal-value function for the lower-level equilibrium assignment problem is proved to be continuously differentiable and its functional value and gradient can be obtained efficiently. Thus, a continuously differentiable but still nonconvex optimization formulation of the MNDP is created, and then a locally convergent algorithm is proposed by applying penalty function method. The inner loop of solving the subproblem is mainly to implement an all-or-nothing assignment. Finally, a small-scale transportation network and a large-scale network are presented to verify the proposed model and algorithm. This research is supported by the National Basic Research Program of China under Grant No. 2006CB705500, the National Natural Science Foundation of China under Grant No. 0631001, the Program for Changjiang Scholars and Innovative Research Team in University, and Volvo Research and Educational Foundations.     

基于MQNM的双基地雷达目标定位改进算法

针对求解双基地雷达目标定位问题常用的Gauss-Newton法自身固有的缺点,如收敛精度和收敛速度依赖于迭代初值与真实值的接近程度和函数的非线性程度,进一步考虑了目标函数Hessian阵的二阶信息,结合MQNM法(修正拟牛顿法)提出了一种双基地雷达目标定位问题的优化改进算法。计算机仿真结果表明了该算法的可行性和有效性。     

A simple smooth exact penalty function for smooth optimization problem

For smooth optimization problem with equality constraints,new continuously differentiate penalty function is derived.It is proved exact in the sense that local optimizers of a nonlinear program are precisely the optimizers of the associated penalty function under some nondegeneracy assumption. It is simple in the sense that the penalty function only includes the objective function and constrained functions,and it doesn’t include their gradients.This is achieved by augmenting the dimension of the program by a variable that controls the weight of the penalty terms.     

基于TDOA/AOA混合的高精度室内可见光定位算法

为了提高室内三维空间的定位精度,提出了一种基于联合到达时间差与到达角度(time difference of arrival/angle of arrival,TDOA/AOA)信息的混合定位算法。由于构建的目标函数具有非凸性,采用传统定位算法在目标函数求解过程中会出现局部最优解的问题。因此,针对该问题,将目标函数转成二次约束二次规划问题,通过引入半定松弛(semi-definite relaxation,SDR)方法将目标函数转换为二阶锥规划(second order cone programming, SOCP)问题,寻找全局最优解。其次,针对SOCP无法对凸包外的目标进行有效定位的问题,在该算法的基础上引入了惩罚项,使松弛后的约束条件进一步逼近原始约束条件,解决了定位过程中的凸包问题。数值仿真结果表明:在10 m×10 m×3 m的三维定位空间内,选取40×40个测试点,平均定位误差为1.39 cm,可实现室内三维空间高精度定位。与传统的混合定位算法相比,均能够获得较高的定位精度。     

一类资源约束单机排序问题

讨论具有连续资源的单机排序问题．在这一模型中，工件的释放时间是所消耗资源的非负严格减少连续函数，工件的加工时间是开工时间的严格增加线性函数．考虑两类问题，第一类问题的目标函数是在满足最大完工时间限制条件下极小化资源消耗总量、第二类问题的目标函数是在满足资源消耗总量限制条件下极小化最大完工时间．对两类问题讨论了最优排序的某些特征．基于对问题的分析，分别给出了求解最优资源分配的方法．结果表明，加工时间为常数情况的结论对于加工时间是开工时间线性函数的情况仍然成立。