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...     

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...     

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.     

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.     

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.     

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.     

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.     

一种基于光流的障碍物估计算法

移动机器人在行进过程中必须能够检测和躲避障碍物,文章提出了一种使用光流场估计障碍物区域的算法。使用结合从粗到精策略的最小加权二乘法的方法计算光流,从而估计图像序列中可能的障碍物位置,为后续的接近时间计算提供了良好的基础。大量实地实验验证了该方法的有效性和可行性。     

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.

     

Improving local torque optimization techniques for redundant robotic mechanisms

Two techniques that improve existing local torque optimization methods for redundant robotic mechanisms are proposed. The first technique is based on a balancing scheme, which balances a joint torque norm against a norm of joint accelerations. Expressions have been derived utilizing the Lagrangian multipliers method. The other technique is based on a torque optimization method which minimizes torques through accelerations, obtained from the null-space of the Jacobian matrix. These accelerations are balanced against the minimum-norm acceleration component in order to improve the performance. Numerical simulations have been carried out which in most cases illustrate good performance capability from the viewpoint of torque optimization and global stability.     

Conservative interpolation between volume meshes by local Galerkin projection

The problem of interpolating between discrete fields arises frequently in computational physics. The obvious approach, consistent interpolation, has several drawbacks such as suboptimality, non-conservation, and unsuitability for use with discontinuous discretisations. An alternative, Galerkin projection, remedies these deficiencies; however, its implementation has proven very challenging. This paper presents an algorithm for the local implementation of Galerkin projection of discrete fields between meshes. This algorithm extends naturally to three dimensions and is very efficient.     

Direct gradient projection method with transformation of variables technique for structural topology optimization

This paper proposes an efficient and reliable topology optimization method that can obtain a black and white solution with a low objective function value within a few tens of iterations. First of all, a transformation of variables technique is adopted to eliminate the constraints on the design variables. After that, the optimization problem is considered as aiming at the minimum compliance in the space of design variables which is supposed to be solved by iterative method. Based on the idea of the original gradient projection method, the direct gradient projection method (DGP) is proposed. By projecting the negative gradient of objective function directly onto the hypersurface of the constraint, the most promising search direction from the current position is obtained in the vector space spanned by the gradients of objective and constraint functions. In order to get a balance between efficiency and reliability, the step size is constrained in a rational range via a scheme for step size modification. Moreover, a grey elements suppression technique is proposed to lead the optimization to a black and white solution at the end of the process. Finally, the performance of the proposed method is demonstrated by three numerical examples including both 2D and 3D problems in comparison with the typical SIMP method using the optimality criteria algorithm.     

Global-local structural optimization using response surfaces of local optimization margins

A general decomposition method developed by Haftka and Watson is applied to global-local structural optimization problems. First, a large number of component optimizations for maximization of margins are performed. Response surface approximations (RSAs) for maximum margins of component optimization are constructed. At the system-level optimization, the RSAs of maximum margins are used as surrogates for the components. One advantage of the decomposition approach is that it allows much of the search for a global optimum to be conducted in low dimensions for each component separately. Minimization of a portal frame weight with eight local optima is used to demonstrate the approach.     

Distributed optimization with arbitrary local solvers

With the growth of data and necessity for distributed optimization methods, solvers that work well on a single machine must be re-designed to leverage distributed computation. Recent work in this area has been limited by focusing heavily on developing highly specific methods for the distributed environment. These special-purpose methods are often unable to fully leverage the competitive performance of their well-tuned and customized single machine counterparts. Further, they are unable to easily integrate improvements that continue to be made to single machine methods. To this end, we present a framework for distributed optimization that both allows the flexibility of arbitrary solvers to be used on each (single) machine locally and yet maintains competitive performance against other state-of-the-art special-purpose distributed methods. We give strong primal–dual convergence rate guarantees for our framework that hold for arbitrary local solvers. We demonstrate the impact of local solver selection both theoretically and in an extensive experimental comparison. Finally, we provide thorough implementation details for our framework, highlighting areas for practical performance gains.