基于净现值的离散型多项目多期投资优化模型

关于资本结构优化模型的讨论已经有了很好的结论,即基于项目组合的净现值最大化,对于多项目单期优化模型已经有了比较满意的结论.在已有结论的基础上研究了离散型多项目多期投资组合优化模型的一般形式,首先针对离散型多项目分期持续期相等的投资组合提出了一般优化模型,然后讨论离散型多项目分期持续期不全相等的投资组合优化模型,最后讨论了引进组合风险的投资组合优化模型。     

离散变量结构优化设计的组合算法*

本文首先给出了离散变量优化设计局部最优解的定义,然后提出了一种综合的组合算法.该算法采用分级优化的方法,第一级优化首先采用计算效率很高且经过随机抽样性能实验表明性能较高的启发式算法─—相对差商法,求解离散变量结构优化设计问题近似最优解 X ;第二级采用组合算法,在 X 的离散邻集内建立离散变量结构优化设计问题的(-1,0.1)规划模型,再进一步将其化为(0,1)规划模型,应用定界组合算法或相对差商法求解该(0,1)规划模型,求得局部最优解.解决了采用启发式算法无法判断近似最优解是否为局部最优解这一长期未得到解决的问题,提高了计算精度,同时,由于相对差商法的高效率与高精度,以上综合的组合算法的计算效率也还是较高的.     

求解复杂优化问题的基于信息熵的自适应蚁群算法

针对基本蚁群算法存在收敛速度慢、易陷入局部最优、计算复杂且不易求解连续优化问题等缺陷 ,提出了一种基于信息熵的改进自适应蚁群算法 ,采用由信息熵控制的路径选择及随机扰动策略实现了算法的自适应调节 ,克服了基本蚁群算法的不足 .典型的 NP-hard问题的计算实例表明 ,该方法具有较好的收敛性、稳定性和鲁棒性 ,可用于离散及连续的组合优化问题求解中 ,其不失为求解复杂组合优化问题的一种较好的方法 .     

组合拓扑方法在组合学和图论中的应用

本文介绍组合拓扑方法在图论和组合学中的应用，探索一些新的离散问题和连续问题的关系，介绍目前有关这方面的新结果及发展动向。本文主要介绍同调理论在图论中的应用，与图有关的复形及性质，不动点定理在离散问题中的应用等。文中提出了一些新结果及可供研究的新问题。     

证券投资组合优化问题的强健性的锥优化方法(英文)

本文研究了具有强健性的证券投资组合优化问题.模型以最差条件在值风险为风险度量方法,并且考虑了交易费用对收益的影响.当投资组合的收益率概率分布不能准确确定但是在有界的区间内,尤其是在箱型区间结构和椭球区域结构内时,我们可以把具有强健性的证券投资组合优化问题的模型分别转化成线性规划和二阶锥规划形式.最后,我们用一个真实市场数据的算例来验证此方法.     

离散优化问题最优值函数的连续性质

对优化问题的最优值研究是有意义的, 尽管有时并不知道怎样寻求最优值. 研究了几个重要的组合最优化问题的目标值随着输入值变化的连续化性质, 重点研究几个经典的、有代表性的离散优化问题：极小化最大完工时间的排序问题、背包问题、旅行商问题等, 以连续的数学分析思维模式审视离散问题. 最后, 研究了一些近似算法对应的目标函数的性质.     

一类组合优化函数的若干研究

本文研究了一个组合优化问题.利用组合数论的理论,给出了计算优化函数的一个新方法,并确定了4≤4m≤120时优化函数g(4m,6)的准确值,以及相心的优化向量.     

基于指数支撑度的最优组合预测模型及其性质研究

在支撑度定义的基础上,提出平均指数支撑度、平均离散度等概念,构建了平均指数支撑度最优组合预测模型,并考虑其等价的平均离散度最优组合预测模型.针对该模型,提出优性组合预测等概念,给出了非劣性组合预测和优性组合预测存在的充分条件、冗余预测方法的存在性和冗余信息的判定等结果,最后的实例说明了该模型的有效性.     

离散单因素投资组合模型的对偶算法

本文研究金融优化中的离散单因素投资组合问题,该问题与传统投资组合模型的不同之处是决策变量为整数(交易手数),从而导致要求解一个二次整数规划问题．针对该模型的可分离性结构,我们提出了一种基于拉格朗日对偶和连续松弛的分枝定界算法。我们分别用美国股票市场的交易数据和随机产生的数据对算法进行了测试．数值结果表明该算法是有效的,可以求解多达150个风险证券的离散投资组合问题．     

一般组合弹性结构的有限元分析

提出一个求解一般组合弹性结构问题的有限元方法:对体件的位移、 板件的纵向位移和杆件的纵向位移用线性协调元离散, 对杆件的纵向转角用二次协调元离散, 对板件的横向位移和杆件的横向位移分别用Morley元和三次Hermite元离散. 在相应的非协调元空间上建立了广义Korn不等式, 进而证得有限元方法的唯一可解性. 最后导出方法在能量模意义下的最优误差估计.     

The Cross-Entropy Method for Continuous Multi-Extremal Optimization

In recent years, the cross-entropy method has been successfully applied to a wide range of discrete optimization tasks. In this paper we consider the cross-entropy method in the context of continuous optimization. We demonstrate the effectiveness of the cross-entropy method for solving difficult continuous multi-extremal optimization problems, including those with non-linear constraints.      

A critical review of discrete filled function methods in solving nonlinear discrete optimization problems

Many real life problems can be modeled as nonlinear discrete optimization problems. Such problems often have multiple local minima and thus require global optimization methods. Due to high complexity of these problems, heuristic based global optimization techniques are usually required when solving large scale discrete optimization or mixed discrete optimization problems. One of the more recent global optimization tools is known as the discrete filled function method. Nine variations of the discrete filled function method in literature are identified and a review on theoretical properties of each method is given. Some of the most promising filled functions are tested on various benchmark problems. Numerical results are given for comparison.     

非线性整数规划的一个新的无参数填充函数算法

离散填充函数是一种用于求解多极值优化问题最优解的一种行之有效的方法.已被证明对于求解大规模离散优化问题是有效的.本文基于改进的离散填充函数定义,构造了一个新的无参数填充函数,并在理论上给出了证明,提出了一个新的填充函数算法.该填充函数无需调节参数,而且只需极小化一次目标函数.数值结果表明,该算法是高效的、可行的.     

Applying Ant System for solving Unequal Area Facility Layout Problems

Ant Colony Optimization (ACO) is a young metaheuristic algorithm which has shown promising results in solving many optimization problems. To date, a formal ACO-based metaheuristic has not been applied for solving Unequal Area Facility Layout Problems (UA-FLPs). This paper proposes an Ant System (AS) (one of the ACO variants) to solve them. As a discrete optimization algorithm, the proposed algorithm uses slicing tree representation to easily represent the problems without too restricting the solution space. It uses several types of local search to improve its search performance. It is then tested using several case problems with different size and setting. Overall, the proposed algorithm shows encouraging results in solving UA-FLPs.     

Benchmarking ordering techniques for nonserial dynamic programming

Five ordering algorithms for the nonserial dynamic programming algorithm for solving sparse discrete optimization problems are compared in this paper. The benchmarking reveals that the ordering of the variables has a significant impact on the run-time of these algorithms. In addition, it is shown that different orderings are most effective for different classes of problems. Finally, it is shown that, amongst the algorithms considered here, heuristics based on maximum cardinality search and minimum fill-in perform best for solving the discrete optimization problems considered in this paper.     

Discrete Gradient Method: Derivative-Free Method for Nonsmooth Optimization

A new derivative-free method is developed for solving unconstrained nonsmooth optimization problems. This method is based on the notion of a discrete gradient. It is demonstrated that the discrete gradients can be used to approximate subgradients of a broad class of nonsmooth functions. It is also shown that the discrete gradients can be applied to find descent directions of nonsmooth functions. The preliminary results of numerical experiments with unconstrained nonsmooth optimization problems as well as the comparison of the proposed method with the nonsmooth optimization solver DNLP from CONOPT-GAMS and the derivative-free optimization solver CONDOR are presented.     

Matching inductive search bias and problem structure in continuous Estimation-of-Distribution Algorithms

Research into the dynamics of Genetic Algorithms (GAs) has led to the field of Estimation-of-Distribution Algorithms (EDAs). For discrete search spaces, EDAs have been developed that have obtained very promising results on a wide variety of problems. In this paper we investigate the conditions under which the adaptation of this technique to continuous search spaces fails to perform optimization efficiently. We show that without careful interpretation and adaptation of lessons learned from discrete EDAs, continuous EDAs will fail to perform efficient optimization on even some of the simplest problems. We reconsider the most important lessons to be learned in the design of EDAs and subsequently show how we can use this knowledge to extend continuous EDAs that were obtained by straightforward adaptation from the discrete domain so as to obtain an improvement in performance. Experimental results are presented to illustrate this improvement and to additionally confirm experimentally that a proper adaptation of discrete EDAs to the continuous case indeed requires careful consideration.     

Strong relaxations for continuous nonlinear programs based on decision diagrams

Decision Diagrams (DDs) have arisen as a powerful tool to solve discrete optimization problems. The extension of this emerging concept to continuous problems, however, has remained a challenge. In this paper, we introduce a novel framework that utilizes DDs to model continuous nonlinear programs. This framework, when combined with the array of techniques available for discrete problems, illuminates a new pathway to solving mixed integer nonlinear programs with the help of DDs.     

离散变量的分级优化方法及其应用

在工程优化设计中,绝大多数实际问题的设计变量往往限定取离散值,为了求得问题的真正最优解,就必须采用离散变量的优化方法进行求解.本文根据离散变量数学规划的特性,提出了一种分级优化搜索算法.这种方法的基本思想是在约束集合内,寻求一可行的离散初始点,然后在该点的邻域内,进行分级寻优搜索,以求得一个改进的新离散点,随之,以该点作为初始点,重复执行分级寻优搜索过程,直至求得问题的最优解.通过对工程实例的计算,证明本文所提出的新方法具有快速、简便的特点,能有效地应用各种工程优化设计问题.     

Generating equidistant representations in biobjective programming

In recent years, emphasis has been placed on generating quality representations of the nondominated set of multiobjective optimization problems. This paper presents two methods for generating discrete representations with equidistant points for biobjective problems with solution sets determined by convex, polyhedral cones. The Constraint Controlled-Spacing method is based on the epsilon-constraint method with an additional constraint to control the spacing of generated points. The Bilevel Controlled-Spacing method has a bilevel structure with the lower-level generating the nondominated points and the upper-level controlling the spacing, and is extended to multiobjective problems. Both methods are proven to produce (weakly) nondominated points and are demonstrated on a variety of test problems.