混合人工鱼群算法在约束非线性优化中的应用

为了解决具有约束的非线性优化问题,本文将增广拉格朗日乘子法和鱼群算法相结合用于非线性问题的全局优化,即用人工鱼群算法寻找增广拉格朗日函数的近似最优解,并将该近似解用于拉格朗日乘子和惩罚因子等参数的更新．同时,简要分析了人工鱼群算法的随机收敛性．仿真结果证明,与自适应惩罚遗传算法相比,该混合算法在解决约束优化问题中具有优越性和有效性．     

A new method on hydrothermal scheduling optimization in electric power market

The hydrothermal scheduling in the electric power market becomes difficult because of introducing competition and considering sorts of constraints. An augmented Lagrangian approach is adopted to solve the problem,which adds to the standard Lagrangian function a quadratic penalty term without changing its dual property,and reduces the oscillation in iterations. According to the theory of large system coordination and decomposition,the problem is divided into hydro sub-problem and thermal sub-problem,which are coordinated by updating the Lagrangian multipliers,then the optimal solution is obtained. Our results for a test system show that the augmented Lagrangian approach can make the problem converge into the optimal solution quickly.     

两种保持符号距离函数的水平集分割方法

Chan-Vese模型在图像分割领域正被广泛应用。然而,传统的水平集方法存在两个重要的数值问题:水平集函数不能隐式地保持为符号距离函数;由于采用梯度降方法求解使水平集演化速度缓慢。针对该问题提出两种快速分割方法加快演化速度:对偶方法和分裂Bregman方法。为了让水平集保持符号距离函数特性,利用投影方法加以约束,并采用增广Lagrangian方法加快收敛速度。实验结果表明,提出的两种快速分割方法比传统的梯度降方法分割效果好、计算效率高。     

Image super-pixels segmentation method based on the non-convex low-rank and sparse constraints

Image super-pixels segmentation is considered as the subspace clustering problem. A new constraint condition is presented to be equivalent to using the clean data as the dictionary. The non-convex proximal p-norm of the coefficients matrix is used for the sparse constraint, and, the non-convex proximal p-norm of the singular values of the coefficients matrix is used for the low-rank constraint. Then a non-convex minimization model is proposed. The augmented Lagrangian method and the AM (alternating minimization) method are applied for solving the unknown matrices. The results of numerical experiments show that the constraint condition presented in this paper is better than using the original data as the dictionary, and that the non-convex proximal p-norm has a better segmentation result than the convex nuclear norm and l₁ norm.     

Object tracking via online low rank representation

Object tracking is an active research topic in computer vision. The traditional tracking methods based on the generative model are sensitive to noise and occlusion, which leads to the failure of tracking results. In order to solve this problem, the tracking results of the first few frames are used as the observation matrix, and the low rank features of the observation model are solved by the the RPCA model. When the new video streams come, a new incremental RPCA is proposed to compute the new observation matrix by the augmented Lagrangian algorithm. The tracking model is established in the Bayesian framework, and the dictionary matrix is updated with the low rank feature. We have tested the proposed algorithm and six state-of-the-art approaches on eight publicly available sequences. Experimental results show that the proposed method has a lower pixel center position error and a higher overlap ratio.     

一类新的乘子方法

提出一种乘子方法用于解带不等式约束的非线性规划问题。其具体思路如下：先将原不等式约束问题用Fischer-Burmeister非线性规划互补（NCP）函数转化为一个等价的等式约束问题;在此基础上,经过适当修改后的DI PILLO的方法以及参考Xuewu Du,Liansheng Zhang,Yuelin Gao的方法,将等式约束问题转化为无约束极小化问题。在适当的假定条件下,通过求解一个无约束连续可微函数的最小值来得到原约束问题的解,从而可以使用标准的无约束极小化方法来求其解。最后,讨论了原不等式约束问题和转换后的无约束问题相关的最优性条件之间的等价关系,以及局部最优性和全局最优性结果：即在适当的假设下,只要罚参数充分大,并不要求罚参数趋于无穷,则原约束问题的最优解（或KKT点）对应于增广Lagrangian函数的最优解（或平稳点）。     

稳定相容节点积分无网格法动力学分析

利用添加多项式项的（Radial Point Interpolation Method，RPIM）形函数，形成了动力学问题的无网格全局弱形式．生成了伴随于域节点的Voronoi图，利用基于应变光滑稳定方案的稳定相容节点积分得到了改进后的总体刚度矩阵离散化形式，并利用直接法施加位移边界条件．自由振动分析得到了与有限元参考解吻合良好的数值解，受迫振动分析采用了无条件稳定的Newmark法，从而验证了本方法在求解动力学问题所展现的稳定性、精确性及收敛性．     

路径流量估计方法在高速公路收费分配中的应用

为解决高速公路收费分配问题,提出了一个用于高速公路多路径费用拆分的路径流量估计模型.模型假设出行者选择路径时遵循随机用户平衡行为,并给出了一个增广的拉克朗日算法用于计算路径流量状态.最终,通过在真实的苏南路网中进行相应的实验研究,将苏南路网中调查得到的数据代入模型中.结果表明,路段流量估计精度达到了99%,路径流量估计精度也达到了90%.     

稳定相容节点积分无网格法动力学分析

利用添加多项式项的(Radial Point Interpolation Method,RPIM)形函数,形成了动力学问题的无网格全局弱形式.生成了伴随于域节点的Voronoi图,利用基于应变光滑稳定方案的稳定相容节点积分得到了改进后的总体刚度矩阵离散化形式,并利用直接法施加位移边界条件.自由振动分析得到了与有限元参考解吻合良好的数值解,受迫振动分析采用了无条件稳定的Newmark法,从而验证了本方法在求解动力学问题所展现的稳定性、精确性及收敛性.     

多星观测任务问题的规划调度

研究了多星多观测任务调度这一NP完全问题,建立了多星任务规划调度的混合整数规划模型,并对模型的求解进行了研究,提出运用改进的拉格朗日松弛算法来求解。仿真结果表明,改进的拉格朗日松弛算法可明显提高模型的求解效率,对大规模问题效果更为显著。     

基于Q学习算法的随机离散时间系统的随机线性二次最优追踪控制

针对随机线性离散时间系统,利用Q学习算法求解无限时域的随机线性二次最优追踪控制(SLQT)问题.首先,假设通过命令生成器生成追踪所需的参考信号,并建立一个由原随机系统和参考轨迹系统组成的增广系统,把最优追踪问题转化为最优调节问题的形式.其次,为了在线求解随机系统的最优追踪问题,将随机系统转为确定性系统,并根据增广系统定义随机线性二次最优追踪控制的Q函数,在无需知道系统模型参数的情况下在线求解增广随机代数方程(GSAE).再次,证明了Q学习算法和增广随机代数方程的等价性,给出了Q学习算法实现步骤.最后,给出一个仿真实例说明Q学习算法的有效性.     

Interactive operation of physically-based slender flexible parts in an augmented reality environment

In order to deal with the problems of laying and assembly planning of slender flexible parts in electromechanical products, a novel approach to operate the physically-based slender flexible parts in an augmented reality environment is presented in this paper. A discrete dynamic method is used to efficiently build the physical model of slender flexible parts, which is very well suited for interactive operation in the augmented reality environment. In this model, bending penalty force can be calculated by the bending energy function to improve dynamic bending behavior, and a penalty method is used to simplify the calculation of geometric torsion. With a reasonable construction of augmented reality environment, a real-time interactive algorithm based on the operating panel is proposed to enable users to interact with the virtual slender flexible parts in the mixed reality-based scene. A case study in the augmented reality environment shows that the proposed approach is efficient and feasible.     

遗传算法在求解时间表问题中的应用研究

时间表问题（TTP）是一类特殊的资源调度问题，属于NP完全问题．排课问题是时间表问题的一个实例，属于多目标优化问题，本文给出了其数学模型．由于遗传算法具有良好的全局搜索能力，在优化问题中有着广泛的应用．本文根据排课问题的特点对普通遗传算法作了改进，设计了一种新的染色体编码方法，通过线性加权法将各目标优化函数进行整合转化成为单目标优化问题，并将此作为遗传算法的适应度函数．最后给出了一个计算实例，用MATLAB进行了仿真，算法最终收敛到稳定状态，所得的结果能够满足要求．     

基于ALR的Hopfield神经网络在高程拟合中的应用

运用具有正规化项的增广拉格朗日函数作为神经网络的能量函数，辅助二次曲面拟合，进一步探索Hopfield神经网络在高程拟合中的应用。实际算例表明，该方法可以大大提高神经网络的计算效率和可靠性。     

解决扩充现实中的遮挡问题

提出了一种新的解决扩充现实中遮挡问题的方法。该算法的核心是在每一帧图像中追踪至少四个基准点,构成仿射基,进而对虚拟物体与真实物体之间的遮挡轮廓进行重建和重投影,且在前两帧图像中交互指定这些阻挡轮廓相对于虚拟物体的前后位置,从而解决了扩充现实的阻挡问题。两个典型实例表明,此算法是可行的。     

遗传算法在MATLAB环境中的实现

探讨了在MATLAB环境中实现遗传算法仿真的方法,并以一个简单的求函数最值的问题作为遗传算法的应用实例,说明遗传算法的全局寻优性及用MATLAB实现仿真的可行性.     

基于物元矩阵的多指标理想决策法

针对权重未知的多指标决策问题,利用物元矩阵和理想点法进行了研究．在自定义方案指标矩阵、方案标准指标矩阵、正理想方案指标矩阵和负理想方案指标矩阵等的基础上,依据决策方案到正负理想方案指标矩阵距离大小,建立了决策模型,并给出了模型的求解过程．依据极值原理,利用拉格朗日函数得到各个指标的权重值．实例应用表明,基于物元矩阵的理想决策模型,计算过程简单、实用性强、具有广泛推广价值．     

非线性电路的插值迭代计算法

本文提出一种新的迭代计算法──拉格朗日插值迭代计算法。借助于拉格朗日插值公式，先假设一个电流Ｉ０，可算得与假设电流Ｉ０相对应的非线性电阻上的电压Ｕ０，根据欧姆定津算得非线性电阻阻值，再结合节点电压方程，算得节点电压ＵＮ，然后再运用电路中的ＶＣＲ确定电流Ｉ１的数值，并与假设电流Ｉ０进行比较直至其误差在规定范围之内。此方法尤其适用于含有多个非线性电阻元件和受控源电路的分析和设计。计算方法简单，迭代次数少，精度较高。     

非凸优化问题的局部鞍点和凸化

研究了2个方面的问题:一是L(x,μ)的局部鞍点,二是L(x,μ)的局部凸化.提出了一类新的转换方法,通过此类转换,在某种更弱的条件下,可以得到一个关于局部鞍点的结论,并证明了等价问题的拉格朗日函数是局部凸的.     

Two personification strategies for solving circles packing problem

Two personification strategies are presented, which yield a highly efficient and practical algorithm for solving one of the NP hard problems——circles packing problem on the basis of the quasi-physical algorithm. A very clever polynomial time complexity degree approximate algorithm for solving this problem has been reported by Dorit S.Hochbaum and Wolfgang Maass in J. ACM. Their algorithm is extremely thorough-going and of great theoretical significance. But, just as they pointed out, their algorithm is feasible only in conception and even for examples frequently encountered in everyday life and of small scale, it is the case more often than not that up to a million years would be needed to perform calculations with this algorithm. It is suggested toward the end of their paper that a heuristic algorithm of higher practical effectiveness should be sought out. A direct response to their suggestion is intented to provide.