一种求解约束minimax问题的罚函数法的补充定理

文[1]建立了针对带约束连续型minimax问题的罚函数法,将其转化为无约束两层规划问题,然后利用无约束两层规划问题的区间算法来进行求解,本文研究了这种罚函数与约束问题的局部极大或极小之间的关系,对这种罚函数收敛性定理中的一假设给出了一补充定理。     

用LINGO处理规划问题的探讨

运用LINGO软件辅助教学是运筹学教学模式的重大变革,实际上LINGO还是最优化问题的一种建模语言,易于方便地输入、求解和分析最优化问题。由于这些特点,LINGO软件在教学、科研和工业、商业、服务等领域得到广泛应用,同时也便于高职高专学生掌握和应用。     

需求不确定的再制造第四方物流网络优化研究

考虑到第四方物流再制造过程中消费区客户需求的不同,采用区间描述了客户需求的不确定性,建立了一个多目标的再制造第四方物流LRP整数规划模型。用LINGO 10进行求解,得出最优的运输方案。设计的数值算例结果验证了模型和方法的有效性。     

有价证券投资的优化研究

<正>本文研究的是将资金用于有价证券投资,使收益最大化的问题。首先对题干要求进行分析,接着找出约束条件并建立线性规划模型,最后利用LINGO软件进行求解。一、问题提出为了使规定的资金在各个方面的限制下,制定最优策略使得到的收益最大,某经理希望通过数学建模来解决对1000万元资金的投资安排,具体问题如下:①若该经理拥有1000万元资金,在证券数量、信用等级、到期年限、到期税前收益的约束     

线性规划问题的软件求解

本文通过实例介绍MATLAB、MATHMATICAL、LINGO三种求解线性规划问题的软件,并对三种求解方式在操作过程及使用局限性方面进行简单分析和比较,为线性规划问题的教学提供帮助.     

二次约束下的边界约束非凸二次规划问题的最优化算法

二次规划是非线性规划问题中较为重要的一种,非线性规划问题的发展方向是使非线性规划问题变换成以序列为基础的对二次规划问题的求解与计算。文中将二次约束下的边界约束非凸二次规划问题作为研究目标,运用改进的分支定界算法对该问题进行最优化求解。首先,利用非线性二次函数的特性对原问题实现等价问题的变换,采用新型改进的线性松弛策略实现对原问题函数的松弛效果,利用外接最小体积椭球松弛法求解目标函数最优解下界值,再用最大体积椭球紧缩法求解目标函数最优解上界值,重复迭代步骤至下界与上界相等;其次,在确定原问题的最优下界和上界后,利用超矩形缩减法及标准二分法在松弛结果基础上对超矩形实现削减,使全局中不是最优解的部分得到剔除,最终实现非凸二次规划问题最优解。通过仿真实验证明,利用文中改进型分支定界算法使非凸二次规划问题达到了全局最优解。     

谈隐枚举法中过滤约束的使用与解题技巧

首先,举例说明"0-1整数规划"中隐枚举法的求解步骤和解题技巧,重点阐述过滤约束的构造和选择。然后,通过对两种求解顺序的比较,说明过滤约束的作用以及"隐"字的含义;最后,在分析解题过程中常见错误的原因之后,总结出使用隐枚举法的注意事项:根据目标函数确定求解顺序;过滤约束必须满足约束条件;合理选择过滤约束;避免解组合的遗漏。     

线性半无限规划的全局算法

本文给出了一个解决线性半无限规划问题的离散化方法,通过对独立参数集的网格离散化,以达到将无限个约束转变为有限个约束的目的。由一个初始的粗略网格出发,通过加细网格,不断修正网格,利用单纯形法求解所得到的子线性规划问题,最终求得一个较为理想的解,这对一般精度要求的问题很有效。最后给出一个关于切比雪夫逼近的数值例子。     

线性半无限规划的全局算法

本文给出了一个解决线性半无限规划问题的离散化方法,通过对独立参数集的网格离散化,以达到将无限个约束转变为有限个约束的目的。由一个初始的粗略网格出发,通过加细网格,不断修正网格,利用单纯形法求解所得到的子线性规划问题,最终求得一个较为理想的解,这对一般精度要求的问题很有效。最后给出一个关于切比雪夫逼近的数值例子。     

一类约束连续型minimax问题的改进算法研究

本文研究了一类约束连续型minimax问题,其中目标函数关于外层决策变量二阶连续可微,约束函数只含内层或者外层决策变量。针对由极大熵函数以及罚函数将约束问题转化而成的无约束可微优化问题,本文利用可微优化方法 Newton法进行求解,建立基本算法,给出数值算例,表明算法的可靠性和有效性。     

动态规划算法分析与研究

分析多阶段决策问题,总结动态规划的基本概念、原理以及解题。通过0－1背包问题的具体解题步骤,阐述动态规划算法一般解题思路。并分析常用经典算法在解决最优问题中的差异性,比较各自优缺点,探讨其研究方向。     

Honey-bee mating optimization (HBMO) algorithm for optimal reservoir operation

In recent years, evolutionary and meta-heuristic algorithms have been extensively used as search and optimization tools in various problem domains, including science, commerce, and engineering. Ease of use, broad applicability, and global perspective may be considered as the primary reason for their success. The honey-bee mating process has been considered as a typical swarm-based approach to optimization, in which the search algorithm is inspired by the process of real honey-bee mating. In this paper, the honey-bee mating optimization (HBMO) algorithm is presented and tested with a nonlinear, continuous constrained problem with continuous decision and state variables to demonstrate the efficiency of the algorithm in handling the single reservoir operation optimization problems. It is shown that the performance of the model is quite comparable with the results of the well-developed traditional linear programming (LP) solvers such as LINGO 8.0. Results obtained are quite promising and compare well with the final results of the other approach.     

Optimal linear attack for multi-sensor network against state estimation

This paper is concerned with a security problem about malicious integrity attacks in state estimation system, in which multiple smart sensors locally measure information and transmit it to a remote fusion estimator though wireless channels. A joint constraint is considered for the attacker behaviour in each channel to keep stealthiness under a residual-based detector on the remote side. In order to degrade the estimator performance, the attacker will maximize the trace of the remote state estimation error covariance which is derived based on Kalman filter theory. It is proved that the optimal linear attack strategy design problem is convex and finally turned into a semi-definite programming problem. In addition, the tendency of attack behaviour on recursive and fixed Kalman filter system is analyzed. Several examples are given to illustrate the theoretical results.     

一种新的椭球算法

基于更动约束的思想[1 ] 与方法 ,提出了求解线性规划问题的新椭球算法 .它与L .G .Khachian的椭球算法[2 ] 不同 ,在新算法的椭球迭代过程中 ,不仅用约束不等式割掉不含约束集的半个椭球 (椭球中心不在约束集内时 ) ,称之为约束割 ;而且在椭球中心落在约束集内时 ,它用目标不等式割掉含约束集的半个椭球 ,称之为目标割 .新算法的不等式系统是由原规划 (或对偶规划 )的约束不等式与目标不等式组成的 (规模小 ) ,而不是由原椭球算法的K K T条件[5] 组成的不等式系统 (规模大 ) .这种新椭球算法即有多项式计算复杂性的特性 ,又在迭代过程中得到一系列单调趋向最优解的可行解 (在解存在时 ) .如果认为已得满意解 ,可随时停机 .对于实际问题 ,大多数是变量有界的 ,初始椭球不大 ,因此新算法更为实际 ,有效 .     

Spacecraft output feedback attitude control based on extended state observer and adaptive dynamic programming

This paper investigates spacecraft output feedback attitude control problem based on extended state observer (ESO) and adaptive dynamic programming (ADP) approach. For the plant described by the unit quaternion, an ESO is first presented in view of the property of the attitude motion, and the norm constraint on the unit quaternion can be satisfied theoretically. The practical convergence proof of the developed ESO is illustrated by change of coordinates. Then, the controller is designed with an involvement of two parts: the basic part and the supplementary part. For the basic part, a proportional-derivative control law is designed. For the supplementary part, an ADP method called action-dependent heuristic dynamic programming (ADHDP) is adopted, which provides a supplementary control action according to the differences between the actual and the desired system signals. Simulation studies validate the effectiveness of the proposed scheme.     

混合时间窗下多目标电商物流路径优化研究

结合电商物流特点,探讨混合时间窗车辆路径问题,设计了混合时间窗惩罚函数和模糊预约时间函数,建立了基于混合时间窗约束的多目标车辆路径模型。设计了改进智能水滴算法对模型进行求解,改进节点概率选择方式来保护优秀水滴,设置路径泥土量最大和最小限制以防止算法提前进入收敛。最后,运用实际案例模拟计算,与传统智能水滴算法计算结果对比分析。结果表明,改进智能水滴算法求解混合时间窗下多目标电商物流路径优化问题,能够以很高的概率获得更优的全局最优解,是求解这类问题有效算法。     

Dynamic event-triggered optimal tracking control for constrained nonlinear stochastic systems

This paper investigates the optimal tracking control problem (OTCP) for nonlinear stochastic systems with input constraints under the dynamic event-triggered mechanism (DETM). Firstly, the OTCP is converted into the stabilizing optimization control problem by constructing a novel stochastic augmented system. The discounted performance index with nonquadratic utility function is formulated such that the input constraint can be encoded into the optimization problem. Then the adaptive dynamic programming (ADP) method of the critic-only architecture is employed to approximate the solutions of the OTCP. Unlike the conventional ADP methods based on time-driven mechanism or static event-triggered mechanism (SETM), the proposed adaptive control scheme integrates the DETM to further lighten the computing and communication loads. Furthermore, the uniform ultimately boundedness (UUB) of the critic weights and the tracking error are analysed with the Lyapunov theory. Finally, the simulation results are provided to validate the effectiveness of the proposed approach.     

Source localization using TDOA and FDOA measurements based on semidefinite programming and reformulation linearization

The problem of source localization using time-difference-of-arrival (TDOA) and frequency-difference-of-arrival (FDOA) measurements has been widely studied. It is commonly formulated as a weighted least squares (WLS) problem with quadratic equality constraints. Due to the nonconvex nature of this formulation, it is difficult to produce a global solution. To tackle this issue, semidefinite programming (SDP) is utilized to convert the WLS problem to a convex optimization problem. However, the SDP-based methods will suffer obvious performance degradation when the noise level is high. In this paper, we devise a new localization solution using the SDP together with reformulation-linearization technique (RLT). Specifically, we firstly apply the RLT strategy to convert the WLS problem to a convex problem, and then add the SDP constraint to tighten the feasible region of the resultant formulation. Moreover, this solution is also extended for cases when there are sensor position and velocity errors. Numerical results show that our solution has significant accuracy advantages over the existing localization schemes at high noise levels.     

Integer Linear Programming for Constrained Multi-Aspect Committee Review Assignment

Automatic review assignment can significantly improve the productivity of many people such as conference organizers, journal editors and grant administrators. A general setup of the review assignment problem involves assigning a set of reviewers on a committee to a set of documents to be reviewed under the constraint of review quota so that the reviewers assigned to a document can collectively cover multiple topic aspects of the document. No previous work has addressed such a setup of committee review assignments while also considering matching multiple aspects of topics and expertise. In this paper, we tackle the problem of committee review assignment with multi-aspect expertise matching by casting it as an integer linear programming problem. The proposed algorithm can naturally accommodate any probabilistic or deterministic method for modeling multiple aspects to automate committee review assignments. Evaluation using a multi-aspect review assignment test set constructed using ACM SIGIR publications shows that the proposed algorithm is effective and efficient for committee review assignments based on multi-aspect expertise matching.     

关于0/1背包问题的粒子群优化算法

背包问题作为运筹学中一个典型的组合优化难题,有着广泛的应用背景,有许多不同的求解方法。给出了基于粒子群优化算法的一种求解方法,利用遗传算法的部分思想将粒子群优化算法应用到0/1背包问题中,得到了比较满意的计算结果。