A Fastly Convergent Directly Feasible Directions Method for Nonlinearly Inequality Constrained Optimization

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A Superlinearly Convergent Combined PhaseⅠ-PhaseⅡ Subfeasible Method

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求解非线性互补问题的混合光滑型算法

光滑型算法已经成功地用来求解各种优化问题. 基于一类新的光滑函数族， 提出了一个带有混合线搜 索的光滑型算法求解非线性互补问题. 在适当的条件下， 证明了算法是适定的， 且保持全局 收敛性和局部超线性收敛性. 最后对提出的算法进行了数值计算. 数值结果显示出该算法的有效性.     

A line search filter secant method for nonlinear equality constrained optimization

<正> This paper formulates and analyzes a line search method for general nonlinear equalityconstrained optimization based on filter methods for step acceptance and secant methods for searchdirection.The feature of the new algorithm is that the secant algorithm is used to produce a searchdirection,a backtracking line search procedure is used to generate step size,some filtered rules areused to determine step acceptance,second order correction technique is used to reduce infeasibility andovercome the Maratos effect.Global convergence properties of this method are analyzed:under mildassumptions it is showed that every limit point of the sequence of iterates generated by the algorithmis feasible,and that there exists at least one limit point that is a stationary point for the problem.Moreover,it is also established that the Maratos effect can be overcome in our new approach by addingsecond order correction steps so that fast local superlinear convergence to a second order sufficient localsolution is achieved.Finally,the results of numerical experiments are reported to show the effectivenessof the line search filter secant method.     

Grover quantum searching algorithm based on weighted targets

The current Grover quantum searching algorithm cannot identify the difference in importance of the search targets when it is applied to an unsorted quantum database, and the probability for each search target is equal. To solve this problem, a Grover searching algorithm based on weighted targets is proposed. First, each target is endowed a weight coefficient according to its importance. Applying these different weight coefficients, the targets are represented as quantum superposition states. Second, the novel Grover searching algorithm based on the quantum superposition of the weighted targets is constructed. Using this algorithm, the probability of getting each target can be approximated to the corresponding weight coefficient, which shows the flexibility of this algorithm. Finally, the validity of the algorithm is proved by a simple searching example.     

Nonmonotonic Reduced Projected Hessian Method Via an Affine Scaling Interior Modified Gradient Path for Bounded-Constrained Optimization

The authors propose an affine scaling modified gradient path method in association with reduced projective Hessian and nonmonotonic interior backtracking line search techniques for solving the linear equality constrained optimization subject to bounds on variables. By employing the QR decomposition of the constraint matrix and the eigensystem decomposition of reduced projective Hes- sian matrix in the subproblem, the authors form affine scaling modified gradient curvilinear path very easily. By using interior backtracking line search technique, each iterate switches to trial step of strict interior feasibility. The global convergence and fast local superlinear/quadratical convergence rates of the proposed algorithm are established under some reasonable conditions. A nonmonotonic criterion should bring about speeding up the convergence progress in some ill-conditioned cases. The results of numerical experiments are reported to show the effectiveness of the proposed algorithm.     

混合混沌量子进化算法

针对量子进化算法计算量大、收敛速度慢以及容易出现早熟等问题, 提出混合混沌量子进化算法. 该算法采用混沌 初始化方法产生初始种群, 使种群具有较好的多样性;采用简单量子旋转门更新当前种群中的非最优个体, 降低算法的计算量; 提出混合混沌搜索策略以提高算法的收敛速度和全局搜索能力. 大量的测试表明, 与量子进化算法、实数编码量子进化算法和 混合量子遗传算法相比, 所提出的算法具有较快的收敛速度和较好的寻优能力. 大量的测试也表明, 若将混沌引入量子进化算法, 则混合混沌搜索策略的综合性能明显优于载波混沌策略, 在大多数情况下优于混沌变异策略. 本文提出的算法是惟一的每次测试 都收敛的算法, 且实现简单, 便于工程应用. 将其用于求解城市道路的交通信号配时优化问题, 实际效果令人满意.     

基于对角隐式Runge-Kutta公式的无约束优化方法

通过把一个无约束优化问题转化为一个等价的常微分方程,利用二阶半对角隐式Runge Kutta公式构造了求解无约束优化问题的LRKOPT算法。LRKOPT算法具有与IMPBOT方法相似的数值特性,但LRKOPT算法可以看成是最速下降方向与牛顿法方向的非线性组合,而IMPBOT方法为它们两者之间的线性组合。在目标函数为一致凸函数的假设条件下,证明了LRKOPT方法的具有全局收敛和局部超线性收敛性。数值结果表明LRKOPT方法具有很好的数值稳定性并且LRKOPT方法的计算效率优于IMPBOT方法。     

约束优化问题的一个超线性收敛的广义梯度投影法

对线性约束的非线性优化问题提出了一个新的广义梯度投影法，该算法我们采用了非精确线性搜索，并在每次迭代运算中运用了广义投影矩阵和变尺度方法的思想确定其搜索方向。在通常的假设条件下，证明了算法的整体收敛性和超线性收敛速度。     

UUV编队协同最优扩方应召搜索方法

针对螺旋应召搜索方法理论上可行但实际上无法实现的问题，提出了基于改进的粒子群优化（particle swarm optimization，PSO）算法的无人水下航行器（unmanned underwater vehicle，UUV）编队协同最优扩方应召搜索水下匀速直线运动目标的方法。首先，根据UUV的搜索宽度，建立了最优转向角模型，给出了采用改进的PSO算法的具体求解流程，并在此基础上继续探讨当目标速度未知情况下的搜索计划。然后，根据投放方式的不同，探讨了UUV编队的几种协同搜索方法。最后，通过仿真实验，证明了该方法的有效性，并根据仿真结果给出了对未来UUV 装备技术发展方向的建议。     

Global and Superlinear Convergence for Generalized Broyden＇s Class Methods

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体液免疫算法及其对证券组合投资分析的应用

基于Jia&Dyer的一般性失望模型,给出一种新的非对称风险度量方法,建立该风险度量下考虑证券最小交易单位约束的组合投资二次整数规划模型;进而依据体液免疫原理设计实用、简单的新体液免疫算法,并寻求该模型的最优方案.算法设计中引入优秀抗体演化操作,搜集和更新进化中最好解,以及建立能增强群体多样性及具有较强整体、局部、并行搜索能力的免疫操作,从多方位搜索最优解.实证及比较表明,所获算法的整体和局部搜索能力强、能快速获取最优投资决策方案,所建模型的合理性和有效性被论证.     

A VARIATION OF GOLDFARB'S METHOD FOR LINEARLY CONSTRAINED OPTIMIZATIONPROBLEMS AND ITS SUPERLINEAR CONVERGENCE RATE

1.IntroductionRosen'sgradientprojectionmethodisaveryinterestingtechniqueinoptimization(see[1,2]),butitsglobalconvergenceisalong-standingopenproblemintheliterature.Thefirstconvergentversionwasfoundbyp.l.k[3].ButPolak'sversionistoocomplicated.Du[4]alsofoundasimplerconvergentversionbydeletingPolak'sspecialprocedure.CombiningRosen'smethodwithvariablemetricmethods,Goldfarb[sl,MurtaghandSargentl'lobtainedtwoefficientalgorithms.Theconvergenceofsuchalgorithmsisstillanopenproblem.However,severalcon…     

运动目标的多无人机编队覆盖搜索决策

针对无人机搜索运动目标时,由于目标运动状态的不确定性,传统静态环境下的无人机覆盖搜索航迹规划算法不再适用的问题,分析了无人机覆盖搜索的基本原则,提出了运动目标垂线搜索（moving target with vertical line search pattern, MTVL）算法,证明了在MTVL策略下的任务完成条件。对MTVL算法进行了改进,通过控制无人机的运动方向与搜索区域边界的角度,提出了运动目标斜线搜索（moving target with slanting line search pattern, MTSL）算法,从理论上分析了在MTSL策略下的任务完成条件并进行了仿真验证。仿真结果表明,提出的两种搜索策略在满足一定条件下都能够完成对指定区域的搜索任务,而无人机完成任务的能力取决于无人机速度与目标速度的比值、无人机数目等因素;完成同样的搜索任务,与MTVL算法相比,MTSL算法对无人机速度和无人机数目的要求更低。     

AN ADAPTIVE TRUST REGION METHOD FOR EQUALITY CONSTRAINED OPTIMIZATION

In this paper, a trust region method for equality constrained optlmization based on nondiferentiable exact penalty is proposed. In this algorithin, the trail step is characterized by computation of its normal component being separated from computation of its tangential component, i.e., only the tangential component of the trail step is constrained by trust radius while the normal component and trail step itself have no constraints. The other main characteristic of the algorithm is the decision of trust region radius. Here, the decision of trust region radius uses the information of the gradient of objective function and reduced Hessian. However, Maratos effect will occur when we use the nondifferentiable exact penalty function as the merit function. In order to obtain the superlinear convergence of the algorithm, we use the twice order correction technique. Because of the speciality of the adaptive trust region method, we use twice order correction when p= 0 (the definition is as in Section 2) and this is different from the traditional trust region methods for equality constrained opthnization. So the computation of the algorithm in this paper is reduced. What is more, we can prove that the algorithm is globally and superlinearly convergent.     

基于数据矩阵分解的相干源方向估计新方法

提出一种相干源存在情况下的波达方向估计新算法。利用阵列快拍数据构造数据矩阵,相关去噪后,通过奇异值分解获得低维信号子空间的估计,然后运用ESPRIT思想估计出波达方向。无论是否存在相干源,新算法均能有效估计出波达方向,并且无需角度搜索,运算量小。该算法虽基于一维线阵,但可直接推广到具有线性性质的二维平面阵,如L形阵、十字阵、双平行线阵等。计算机仿真验证了算法的有效性     

基于正交试验和元胞自动机模型的加速并行遗传算法

针对标准遗传算法中存在早熟收敛、后期收敛速度慢以及解精度低的问题,结合正交试验设计和元胞自动机模型,提出了一种改进的加速并行遗传算法(APGA)。APGA利用正交试验设计确定较好的初始种群,利用元胞自动机模型固有的并行计算能力设计并行遗传算法,借助元胞信息的动态性和多元性实现正交加速过程。仿真结果表明,APGA能够有效地防止早熟收敛,可以极大地提高遗传算法的搜索效率和解的精度。     

A CLASS OF REVISED BROYDEN ALGORITHMS

In this paper, we discuss the convergence of the Broyden algorithms with revised search direction. Under some inexact llne searches, we prove that the algorithms are globally convergent for continuously differentiable functions and the rate of convergence of the algorithms is one-step superlinear and n-step second-order for uniformly convex objective functions.     

A SUPERLINEAR CONVERGENT FEASIBLE METHOD FOR NONLINEAR PROGRAMMING WITH NONLINEAR CONSTRAINTS

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基于均匀设计的多目标遗传算法在柔性工作车间调度中的应用

采用均匀设计技术合成多个适应度函数以提高搜索方向的空间均匀性,并针对多目标柔性工作车间调度问题的特点,设计了基于工序顺序和基于机器分配两种交叉变异的操作以及小生境技术、精英保留策略和遗传操作自适应调整策略来提高种群的多样性和搜索的效率。实验证明,本文提出的算法所得结果比较理想。