具有不确定参数多目标决策的一类鲁棒有效解

针对具有区间型不确定参数多目标决策问题,探讨了决策人在决策的最优性与决策后果 的不确定性之间的权衡,从而制定决策的方法,提出了鲁棒有效解及ε-鲁棒有效解的概念,并研究 了其最优性条件.     

一种改进的多目标混合差分进化算法

将差分进化算法（DE）用于多目标优化问题,提出了一种精英保留和进化进程中非支配解集迁移操作的差分进化算法,以保证所求得多目标优化问题Pareto最优解的多样性。采用双群体约束处理技术,构建进化群体的Pareto非支配解外部存档集,并进行基于非支配解集的迁移操作,以增加非支配解的数目和质量。用多个经典测试函数测试的结果表明,与标准DE相比,该方法收敛到问题的Pareto前沿效果良好,能有效保持Pareto最优解多样性与收敛之间的平衡。     

3G基站选址的智能优化实现

基站的位置和数量影响网络的服务质量。针对传统选址方法的不足,提出了一种基于免疫遗传算法的选址优化方法;给出了基站选址问题的多目标优化数学模型和实现过程。算法中采用了浓度调节选择概率机制,有效保证了抗体的多样性,避免了早熟收敛,并使用记忆细胞集来保存每代所产生的Pareto最优解;提出了一种邻近排挤算法对记忆细胞集进行更新、删除,保证了Pareto最优解集的分布均匀性。仿真结果表明,算法可以有效找到可行的基站布置方案,为实际工程应用提供了解决思路。     

最小MPR集选取问题的改进蚁群优化算法

多点中继(MPR)是移动自组网中用来降低网络开销所采用的一种机制,但由于最小MPR集的选取属于NP完全问题,传统的贪心算法往往难以取得较好的结果.本文将蚁群优化用于最小MPR集选取问题的求解,给出了一种基于候选解的改进蚁群算法CSACO.通过使用候选解集进行信息素的更新,提高了算法的收敛速度,同时避免了算法陷入早熟.模拟实验表明,CSACO可以有效降低MPR集的大小,同时在较短的时间内收敛到最优解,提高网络性能.     

新的混合智能优化算法及其多目标优化应用

针对人工鱼群算法后期收敛速度较慢、解精度不高的不足,按照分阶段寻优和变参数寻优的改进策略,并结合禁忌搜索算法中的相关规则,提出一种新的混合智能优化算法。该算法将寻优过程分为锁定最优解或者局部解邻域和求得高精度最优解两个阶段,每个阶段设置不同的参数并结合禁忌搜索算法以提高收敛速度和最优解精度。典型函数验证表明,该算法收敛速度快、精度高;同时,对于多目标优化问题,该算法可以提高Pareto最优解集质量,扩大决策分布范围,维持决策多样性,有利于决策者作出决策。     

大型群组多属性决策Bayes 概率修正法

针对大型群组多属性决策问题,给出了备选对象的优势集和Pareto有效率,并讨论了二者的性质.证明并指出了只有备选对象为Pareto解时,其Pareto有效率才可能不为0.将Pareto备选对象的Pareto有效率作为其“最优决策”的先验概率分布,然后利用Bayes公式和群组专家们决策的后验概率对其加以修正,即可得到“最优决策”概率最大的备选对象.该方法在充分利用专家组决策信息的前提下避免了寻找一个主观集结规则的决策问题,不需要集结出一个权重结果,从而减少了决策过程中主观因素的影响,并且当将每位专家的决策看成一个独立的随机实验时,理论上专家人数越多,决策结果越精确.最后以一个算例说明了所提出方法的有效性.     

基于人工免疫系统的多目标函数优化

为克服传统遗传算法退化和早熟等缺点,同时降低优化算法的复杂度,提出基于人工免疫系统（Artificial Immune System, AIS）实现无约束多目标函数的优化。使用随机权重法和自适应权重法计算种群个体的适应值,使Pareto最优解均匀分布的同时,加快算法的收敛;通过引入人工免疫系统的三个基本算子：克隆、超变异和消亡,保持种群的多样性;在进化种群外设立Pareto 解集,保存历代的近似最优解。使用了两个典型的多目标检测函数验证了该算法的有效性。优化结果表明,基于AIS的多目标优化算法可使进化种群迅速收敛到Pareto前沿,并能均匀分布,是实现多目标函数优化的有效方法。     

连续过程的多目标优化

在模块环境(Aspen Plus)下,建立了基于多目标遗传算法NSGA-Ⅱ求解多目标优化问题的系统结构,并对含循环物流的连续过程废料最小化问题进行求解。在求解过程中遗传算法需要反复调用流程模拟,而流程中循环物流的迭代收敛使优化计算效率较低。为减少流程迭代次数本文提出2个加速策略:一是变收敛精度策略,在优化计算初始阶段,使流程在较低精度下收敛,快速淘汰劣点,随着优化的进行,将流程收敛精度逐步提高,得到高质量的非劣解;二是循环流初值策略,利用已有的计算值,回归决策变量与循环流变量的对应关系,改善循环流初值。实例结果表明,加速策略减少了一半左右的流程迭代次数,效率提高50%,本文提出的求解多目标问题的方法能方便地得到问题的Pareto最优解集,可应用于一般连续化工过程的多目标优化。     

基于树模型和输入参数关系的组合测试集精简方法*

提出了一种精简组合测试用例集的方法,该方法基于解空间树模型,利用输入参数之间的依赖关系来剪裁解空间树中的枝叶,从而获得精简的组合测试用例集。该方法采用回溯算法来实现,在遍历树的同时,剪裁解空间树并输出组合测试用例。在算法的实现过程中,采用了一些策略以便提高算法的效率并节省空间。实验结果证明该方法是可行和有效的,对于一些输入参数依赖关系明确的被测系统,该方法能够较大幅度地精简全组合测试用例集。     

基于改进的NSGA-II多目标优化方法研究*

针对传统多目标优化算法在其领域存在的多个子目标不能同时取优的问题,提出了一种基于改进的非支配排序遗传算法（Non-dominated Sorting Genetic Algorithm-II, NSGA-II）多目标优化方法,以多目标优化遗传算法为基础,多输入多输出的反向传播（Back-Propagation, BP）神经网络为适应度函数评价体系,保证算法快速收敛并搜索到全局最优解集,该算法在建模前对实验数据进行主成分分析,降低了运算时间和算法难度,通过在遗传进化过程中引进正态分布交叉算子（Normal Distribution Crossover, NDX）和改进的自适应调整变异算子,实现了多个目标同时取优,保证Pareto最优解集快速、准确地获取。仿真实验使用UCI数据集,通过与其他常用的多目标优化算法对比,验证了改进的NSGA-II算法精确度更高、收敛速度更快、稳定性更强。     

一种在多Agent系统中求帕累托效率解的方法

著名的Robert Axelrod实验证明了具备善意的、宽容的、强硬的和简单明了的算法将总会是赢家。基于这种思想,设计了PESCO算法。它可以在合作博弈中,面对合作的对手,寻求帕累托效率解,尽可能地达到双赢的局面。也可以在非合作博弈中,或对手不合作时,保证安全收益。以可合作的供零博弈、Stackelberg博弈和非合作的猜硬币博弈为背景,将PESCO算法与几个算法进行博弈,PESCO算法取得了较好的效果。     

上下层具有合作关系的两层决策问题研究

针对两层线性规划问题解的无效性,在决策者合作情形下,利用双准则线性规划的有关技术,提出事先不需求解问题而是采用次最优解作为参考点,直接在目标集中有效满意解的方法。数值计算结果表明该方法有效可行的。     

Human Motion Planning Based on Recursive Dynamics and Optimal Control Techniques

This paper presents an efficient optimal control and recursive dynamics-based computer animation system for simulating and controlling themotion of articulated figures. A quasi-Newton nonlinear programmingtechnique (super-linear convergence) is implemented to solve minimumtorque-based human motion-planning problems. The explicit analyticalgradients needed in the dynamics are derived using a matrix exponentialformulation and Lie algebra. Cubic spline functions are used to make thesearch space for an optimal solution finite. Based on our formulations,our method is well conditioned and robust, in addition to beingcomputationally efficient. To better illustrate the efficiency of ourmethod, we present results of natural looking and physically correcthuman motions for a variety of human motion tasks involving open andclosed loop kinematic chains.     

Robust Multigrid Methods for Vector-valued Allen–Cahn Equations with Logarithmic Free Energy

We present efficient and robust multigrid methods for the solution of large, nonlinear, non-smooth systems as resulting from implicit time discretization of vector-valued Allen-Cahn equations with isotropic interfacial energy and logarithmic potential. The algorithms are shown to be robust in the sense that convergence is preserved for arbitrary values of temperature, including the deep quench limit. Numerical experiments indicate that the convergence speed as well is independent of temperature.Dedicated to Peter Deuflhard on the occasion of his 60th birthday.     

A Parametrical Generalized Solution in Linear Vector Optimization

A parametrical representation of a linear problem of Pareto optimization is considered. The notion of a generalized solution is introduced for an appropriate pair of dual problems. The structure of a parametrical generalized solution is investigated. A relation between generalized and efficient solutions of problems is established.     

极大熵和声搜索算法求解多目标优化*

给出了求解多目标优化问题的一个新算法。首先利用极大熵函数,将多目标优化问题转换为一个单目标优化问题;然后利用和声搜索算法对其进行求解,进而得到多目标优化问题的有效解。该算法对目标函数的解析性质没有要求且容易实现,数值结果表明了该方法是有效的。     

Scheduling of tasks in the parareal algorithm

Parallelization of partial differential equations (PDEs) by time decomposition has attracted much interest, mainly due to its potential to enable very long time simulations beyond what is possible using spatial domain decomposition. However, there has only been limited performance analysis of the parareal algorithm in the literature, ignoring the efficient scheduling of tasks. This paper presents a detailed study of the scheduling of tasks in the parareal algorithm that achieves significantly better efficiency than the usual algorithm. Two algorithms are proposed, one which uses a manager-worker paradigm with overlap of sequential and parallel phases, and a second that is completely distributed. Experiments were conducted with the 2D heat equation. It was found that the rate of convergence decreases as the number of processors increases, in the case of strong scaling (fixed time interval). However, for weak scaling results the rate of convergence was unaffected by the number of processors. The results of this paper suggest that the parareal algorithm is a promising approach to solving long time evolution problems, particularly when the goal is simulation of longer times using more processors. It also exhibits characteristics that make it particularly suitable for execution on heterogeneous computational grids, such as low communication overhead and easy accommodation of different processor and network speeds.     

Efficient asymptotically-optimal path planning on manifolds

This paper presents an efficient approach for asymptotically-optimal path planning on implicitly-defined configuration spaces. Recently, several asymptotically-optimal path planners have been introduced, but they typically exhibit slow convergence rates. Moreover, these planners cannot operate on the configuration spaces that appear in the presence of kinematic or contact constraints, such as when manipulating an object with two arms or with a multifingered hand. In these cases, the configuration space usually becomes an implicit manifold embedded in a higher-dimensional joint ambient space. Existing sampling-based path planners on manifolds focus on finding a feasible solution, but they do not optimize the quality of the path in any sense and, thus, the returned solution is usually not adequate for direct execution. In this paper, we adapt several techniques to accelerate the convergence of the asymptotically-optimal planners and we use higher-dimensional continuation tools to deal with the case of implicitly-defined configuration spaces. The performance of the proposed approach is evaluated through various experiments.     

Alternative forms with orders of the lax equivalence theorem in Banach spaces

The Lax equivalence theorem on the convergence of the solution of the discrete problem to that of the given properly posed initial-value problem states that if the difference scheme is consistent, then stability is necessary and sufficient for convergence. In a recent paper by Butzer-Weis this theorem was equipped with orders in the setting of arbitrary Banach spaces in the sense that consistency, stability and convergence were considered with orders. By modifying the concepts involved suitably, an alternative form of the Lax theorem reads that consistency and stability is equivalent to convergence. This result is also generalized to one containing orders, in fact, both forms of the Lax theorem are valid under the same definitions of consistency, stability, and convergence with orders. An example is given showing that the latter theorem is in a certain sense best possible.     

Spline approximation for first Order fredholm delay integro-differential equations

In this paper, a new method for approximating the solution of nonlinear first order Fredholm delay integro-differential equation is presented. Boundness of the approximate solution, convergence results as well as numerical examples are given.