A projection approach for topology optimization of porous structures through implicit local volume control

Structural and Multidisciplinary Optimization - Porous structures are of valuable importance in additive manufacturing. They can also be exploited to improve damage tolerance and fail-safe...     

图像局部映射二进制串描述符

为了提高图像局部特征算法的计算速率与匹配速度,并保持其准确率,提出了一种局部映射二进制串描述符算法。它通过映射的方法将图像局部区域转化成二进制串,从而提高其计算效率与匹配速度,并通过机器学习的方法寻找最佳映射矩阵,保持其准确率。从实验结果表明,只需32比特的二进制串就可以在准确率上媲美现有的局部描述符算法,并在匹配速度上有较大的优势。     

变直径次梯度投影函数优化方法

拉格朗日松弛法的关键是求解对偶函数，而在对偶函数不可微的情况下人们经常采用次梯度法，为此提出一种变直径次梯度投影法，该方法根据投影性质确定对偶问题定义域的有效直径，从而使其收敛性不依赖于最优目标值和对偶问题定义域直径等任何先验知识，并证明了其收敛性，给出了收敛效率，通过一个指派问题说明了所提出方法的有效性。     

基于竞争性协同表示的局部判别投影特征提取

特征提取算法中利用样本间的协同表示关系构造邻接图只考虑所有训练样本的协同能力,而忽视了每一类训练样本的内在竞争能力。为此,本文提出一种基于竞争性协同表示的局部判别投影特征提取算法（competitive collaborative repesentation-based local discrininant projection for feature extraction,CCRLDP）,该算法利用基于具有竞争性协同表示的方法构造类间图和类内图,考虑到邻接图中各类型系数的影响,引入保留正表示系数的思想稀疏化邻接图,通过计算类内散度矩阵和类间散度矩阵来刻画图像的局部结构并得其最优投影矩阵。在一些数据集上的实验结果表明,相比同类基于局部判别投影的特征提取算法,该算法具有很高的识别率,并在噪声和遮挡上具有良好的鲁棒性,该算法能有效地提高图像的识别效率。     

基于几何投影的多目标优化降维方法

实际优化问题中可能包含很多目标,这些目标并不都是相互冲突的,有些目标是相互冗余的,因此实际的Pareto前沿面的维数比目标空间的维数要少。为了提高进化算法的效率,减少计算量,提出一种基于几何投影的方法来实现多目标优化问题的降维。首先通过辨别Pareto前沿在二维坐标面上的投影形状,寻找投影区的边界曲线;然后根据投影区的面积和边界曲线的单调性来计算目标之间的冲突度。数值仿真表明了该方法的有效性。     

Generalized gradient projection neural networks for nonsmooth optimization problems

Generalized gradient projection neural network models are proposed to solve nonsmooth convex and nonconvex nonlinear programming problems over a closed convex subset of R n . By using Clarke’s generalized gradient, the neural network modeled by a differential inclusion is developed, and its dynamical behavior and optimization capabilities both for convex and nonconvex problems are rigorously analyzed in the framework of nonsmooth analysis and the differential inclusion theory. First for nonconvex optimizati...     

多智能体系统的多步近似次梯度随机投影优化算法

基于切换网络下带有随机时延和随机通讯噪声的多智能体系统模型,提出分布式多步近似次梯度随机投影算法,并对算法的收敛性进行分析.首先,利用网络扩维的方法将含随机时延的通讯网络转化为无时延网络;其次,提出近似次梯度概念,并设计多步近似次梯度随机批量投影算法,批量随机投影可以避免在实际问题中整体约束集合不易获得而导致投影算子不...     

Two-dimensional supervised local similarity and diversity projection

This paper presents a novel manifold learning method, namely two-dimensional supervised local similarity and diversity projection (2DSLSDP), for feature extraction. The proposed method defines two weighted adjacency graphs, namely similarity graph and diversity graph. The affinity matrix of similarity graph is determined by the spatial relationship between vertices of this graph, while affinity matrix of diversity graph is determined by the diversity information of vertices of its graph. Using these two graphs, the proposed method constructs local similarity scatter and diversity scatter, respectively. A concise feature extraction criterion is then raised via minimizing the ratio of the local similarity scatter to local diversity scatter. Thus, 2DSLSDP can well preserve not only the adjacency similarity structure, but also the diversity of data points, which is important for the classification. Experiments on the AR and UMIST databases show the effectiveness of the proposed method.     

Genetic algorithms and particle swarm optimization for exploratory projection pursuit

Exploratory Projection Pursuit (EPP) methods have been developed thirty years ago in the context of exploratory analysis of large data sets. These methods consist in looking for low-dimensional projections that reveal some interesting structure existing in the data set but not visible in high dimension. Each projection is associated with a real valued index which optima correspond to valuable projections. Several EPP indices have been proposed in the statistics literature but the main problem lies in their optimization. In the present paper, we propose to apply Genetic Algorithms (GA) and recent Particle Swarm Optimization (PSO) algorithm to the optimization of several projection pursuit indices. We explain how the EPP methods can be implemented in order to become an efficient and powerful tool for the statistician. We illustrate our proposal on several simulated and real data sets.     

克服早熟收敛现象的粒子群优化算法

为了在不了解优化函数是否存在多个局部点对早熟收敛现象进行准确判定,提出了早熟收敛判定方法;为了突破局部极值的限制以再次寻优计算,引入了基于混沌变异的粒子群算法,对出现早熟收敛现象的粒子群进行混沌变异,使得最优点不会在一点重复出现,并采用平均截止代数和截止代数分布熵组成的平面测度对算法的优化效率进行度量.仿真结果表明此算法能有效地克服早熟收敛现象,全局寻优能力较强,寻优速度较快,有效地解决了收敛性能和全局寻优能力之间的矛盾.     

Evolutionary parallel local search for function optimization

This paper proposes a kind of evolutionary parallel local search technique (EPLS) that integrates the reproduction mechanisms from evolutionary algorithms and simplex method. The major aim is to explore the tradeoff between exploration and exploitation for optimizing multimodal functions. It has been cost-efficiently reached by means of parallel local search using simplex method. In each generation, EPLS partitions the population into a group of subpopulations, each of which consists of several individuals with adjacent space locations. EPLS independently locates multiple local optima in these disjoint neighborhoods, thus to reduce the probability of losing the global optimum. The local search in a neighborhood speeds up the convergence rate of simplex method. Recombination, adaptive Gaussian mutation and selection are incorporated into EPLS to further enhance the ability of global exploration and exploitation. The experimental observations and the extensive comparisons show that EPLS remarkably outperforms the standard evolutionary algorithms (EA) and some hybrid ones for almost all the problems tested, thus justifying the rationality and the competitive potential of EPLS for optimizing multimodal functions, especially for those with very rugged and deceptive topological structures.     

Embedded local search approaches for routing optimization

This paper presents a new class of heuristics which embed an exact algorithm within the framework of a local search heuristic. This approach was inspired by related heuristics which we developed for a practical problem arising in electronics manufacture. The basic idea of this heuristic is to break the original problem into small subproblems having similar properties to the original problem. These subproblems are then solved using time intensive heuristic approaches or exact algorithms and the solution is re-embedded into the original problem. The electronics manufacturing problem where we originally used the embedded local search approach, contains the Travelling Salesman Problem (TSP) as a major subproblem. In this paper we further develop our embedded search heuristic, HyperOpt, and investigate its performance for the TSP in comparison to other local search based approaches. We introduce an interesting hybrid of HyperOpt and 3-opt for asymmetric TSPs which proves more efficient than HyperOpt or 3-opt alone. Since pure local search seldom yields solutions of high quality we also investigate the performance of the approaches in an iterated local search framework. We examine iterated approaches of Large-Step Markov Chain and Variable Neighbourhood Search type and investigate their performance when used in combination with HyperOpt. We report extensive computational results to investigate the performance of our heuristic approaches for asymmetric and Euclidean Travelling Salesman Problems. While for the symmetric TSP our approaches yield solutions of comparable quality to 2-opt heuristic, the hybrid methods proposed for asymmetric problems seem capable of compensating for the time intensive embedded heuristic by finding tours of better average quality than iterated 3-opt in many less iterations and providing the best heuristic solutions known, for some instance classes.     

基于梯度投影法与随机优化算法的约束优化方法

针对带有线性等式和不等式约束的无确定函数形式的约束优化问题,提出一种利用梯度投影法与遗传算法、同时扰动随机逼近等随机算法相结合的优化方法。该方法利用遗传算法进行全局搜索,利用同时扰动随机逼近算法进行局部搜索,算法在每次进化时根据线性约束计算父个体处的梯度投影方向,以产生新个体,从而能够严格保证新个体满足全部约束条件。将上述约束优化算法应用于典型约束优化问题,其仿真结果表明了所提出算法的可行性和收敛性。     

The gradient projection method for structural topology optimization including density-dependent force

This paper proposes a modified gradient projection method (GPM) that can solve the structural topology optimization problem including density-dependent force efficiently. The particular difficulty of the considered problem is the non-monotonicity of the objective function and consequently the optimization problem is not definitely constrained. Transformation of variables technique is used to eliminate the constraints of the design variables, and thus the volume is the only possible constraint. The negative gradient of the objective function is adopted as the most promising search direction when the point is inside the feasible domain, while the projected negative gradient is used instead on condition that the point is on the hypersurface of the constraint. A rational step size is given via a self-adjustment mechanism that ensures the step size is a good compromising between efficiency and reliability. Furthermore, some image processing techniques are employed to improve the layouts. Numerical examples with different prescribed volume fractions and different load ratios are tested respectively to illustrate the characteristics of the topology optimization with density-dependent load.     

Tracking local optimality for cost parameterized optimization problems

In this paper, a procedure for computing local optimal solution curves of the cost parameterized optimization problem is presented. We recast the problem to a parameterized nonlinear equation derived from its Lagrange function and show that the point where the positive definiteness of the projected Hessian matrix vanishes must be a bifurcation point on the solution curve of the equation. Based on this formulation, the local optimal curves can be traced by the continuation method, coupled with the testing of singularity of the Jacobian matrix. Using the proposed procedure, we successfully compute the energy diagram of rotating Bose–Einstein condensates.     

Combining weighted adaptive CS-LBP and local linear discriminant projection for gait recognition

With the increasing demands of the remote surveillance system, the gait based personal identification research has obtained more and more attention from biometric recognition researchers. The gait sequence is easier to be affected by factors than other biometric feathers. In order to achieve better performance of the gait based identification system, in the paper, a local discriminant gait recognition method is proposed by integrating weighted adaptive center symmetric local binary pattern (WACS-LBP) with local linear discriminate projection (LLDP). The proposed method consists of two stages. In the first stage, the robust local weighted histogram feature vector is extracted from each gait image by WACS-LBP. In the second stage, the dimensionality of the extracted feature vector is reduced by LLDP. The highlights of the proposed method are (1) the extracted feature is robust to rotation invariant, and is also tolerant to illumination and pose changes; (2) the low dimensional feature vector reduced by LLDP can preserve the discriminating ability; and (3) the small-sample-size (SSS) problem is avoided naturally. The proposed method is validated and compared with the existing algorithms on a public gait database. The experimental results show that the proposed method is not only effective, but also can be clearly interpreted.