Multi-objective shape optimization using ant colony coupled computational fluid dynamics solver

An adaptation of a parametric ant colony optimization (ACO) to multi-objective optimization (MOO) is presented in this paper. In this algorithm (here onwards called MACO) the concept of MOO is achieved using the reference point (or goal vector) optimization strategy by applying scalarization. This method translates the multi-objective optimization problem to a single objective optimization problem. The ranking is done using ?-dominance with modified L_p metric strategy. The minimization of the maximum distance from the goal vector drives the solution close to the goal vector. A few validation test cases with multi-objectives have been demonstrated. MACO was found to out perform R-NSGA-II for the test cases considered. This algorithm was then integrated with a meshless computational fluid dynamics (CFD) solver to perform aerodynamic shape optimization of an airfoil. The algorithm was successful in reaching the optimum solutions near to the goal vector on one hand. On the other hand the algorithm converged to an optimum outside the boundary specified by the user for the control variables. These make MACO a good contender for multi-objective shape optimization problems.     

交替方向隐式CFD解法器的GPU并行计算及其优化

交替方向隐格式(ADI)是常见的偏微分方程离散格式之一,目前对ADI格式在计算流体力学（CFD）实际应用中的GPU并行工作开展较少。从一个有限体积CFD应用出发,通过分析ADI解法器的特点和计算流程,基于统一计算架构(CUDA)编程模型设计了基于网格点与网格线的两类细粒度GPU并行算法,讨论了若干性能优化方法。在天河-1A系统上,采用128×128×128网格规模的单区结构网格算例,无粘项、粘性项及ADI迭代计算的GPU并行性能相对于单CPU核,分别取得了100.1、40.1和10.3倍的加速比,整体ADI CFD解法器的GPU并行加速比为17.3     

On improving the GA step-wise shape optimization method through the application of the Fixed Grid FEA paradigm

In previous work by the authors, a Genetic Algorithm (GA) based shape optimization technique was introduced. The method was shown to be capable of producing high-fidelity optimal shapes. However, the process was computationally expensive and required constant re-meshing due to distorted boundary elements resulting from large boundary movements. This paper combines the Fixed Grid (FG) method of Finite Element Analysis (FEA) and the GA shape optimization module to create a hybrid that effectively addresses these problems. The FG solver is found to be significantly faster than conventional FEA, and the fixed FE mesh frees boundary movements from meshing constraints. The Fixed-Grid Genetic-Algorithm (FGGA) shape optimization method is detailed in this paper, and the key algorithms used in the FG and the GA components are explained. The method is also applied to a number of shape optimization problems, and the results are presented and discussed.     

Efficient shape optimization for certain and uncertain aerodynamic design

In this paper, we present novel developments in aerodynamic shape optimization based on shape calculus as well as the proper treatment of aleatoric uncertainties in the field of aerodynamic design.     

基于NURBS方法的气动外形优化设计

采用NURBS曲线曲面,对钝锥弹头和钝双锥弹体建立参数化曲面模型,取NURBS曲线控制点作为设计参数,应用高超声速面元法求解气动力特性,在给定设计约束下,采用遗传算法进行气动外形优化设计,并对优化结果进行了比较分析。结果表明,采用NURBS方法构造参数化外形,并结合优化技术可方便快速地获得所需最优外形;与应用二次曲线构造参数化外形相比,该方法对弹体形状控制更加灵活,并可局部修改弹头曲线形状。因此,基于NURBS方法发展整套的系统优化设计算法很有现实意义和应用价值。     

Multi-operator based evolutionary algorithms for solving constrained optimization problems

Over the last two decades, many sophisticated evolutionary algorithms have been introduced for solving constrained optimization problems. Due to the variability of characteristics in different COPs, no single algorithm performs consistently over a range of problems. In this paper, for a better coverage of the problem characteristics, we introduce an algorithm framework that uses multiple search operators in each generation. The appropriate mix of the search operators, for any given problem, is determined adaptively. The framework is tested by implementing two different algorithms. The performance of the algorithms is judged by solving 60 test instances taken from two constrained optimization benchmark sets from specialized literature. The first algorithm, which is a multi-operator based genetic algorithm (GA), shows a significant improvement over different versions of GA (each with a single one of these operators). The second algorithm, using differential evolution (DE), also confirms the benefit of the multi-operator algorithm by providing better and consistent solutions. The overall results demonstrated that both GA and DE based algorithms show competitive, if not better, performance as compared to the state of the art algorithms.     

Mesh optimization for surface approximation using an efficient coarse-to-fine evolutionary algorithm

The investigated mesh optimization problem C(N,n) for surface approximation, which is NP-hard, is to minimize the global error between a digital surface and its approximating mesh surface by efficiently locating a limited number n of grid points which are a subset of the original N sample points. This paper proposes an efficient coarse-to-fine evolutionary algorithm (CTFEA) with a novel orthogonal array crossover (OAX) for solving the mesh optimization problem. OAX adaptively divides the meshes of parents into a number of parts using a tuning parameter for applying a coarse-to-fine technique. Meshes of children are formed from an intelligent combination of the good parts from their parents rather than the conventional random combination. The better one of two parts in two parents is chosen by evaluating the contribution of the individual parts to the fitness function based on orthogonal experimental design. The coarse-to-fine technique of CTFEA can advantageously solve large mesh optimization problems. Furthermore, CTFEA using an additional inheritance technique can further efficiently locate the grid points in the mesh surface. It is shown empirically that CTFEA outperforms the existing evolutionary algorithm in terms of both approximation quality and convergence speed, especially in solving large mesh optimization problems.     

An efficient dynamical evolutionary algorithm for global optimization

In this paper, we introduce a new dynamical evolutionary algorithm (DEA) that aims to find the global optimum and give the theoretical explanation from statistical mechanics. The algorithm has been evaluated numerically using a wide set of test functions which are nonlinear, multimodal and multidimensional. The numerical results show that it is possible to obtain global optimum or more accurate solutions than other methods for the investigated hard problems.     

Multiobjective optimization of trusses using genetic algorithms

In this paper we propose the use of the genetic algorithm (GA) as a tool to solve multiobjective optimization problems in structures. Using the concept of min–max optimum, a new GA-based multiobjective optimization technique is proposed and two truss design problems are solved using it. The results produced by this new approach are compared to those produced by other mathematical programming techniques and GA-based approaches, proving that this technique generates better trade-offs and that the genetic algorithm can be used as a reliable numerical optimization tool.     

Structural shape optimization using self-adjusted convex approximation

This study researches the applications of Self-Adjusted Convex Approximation (SACA) in structural shape optimization problems. The B-spline curve is adopted as the mathematical representation of the structural shapes. The SACA method is based on the CONvex LINearization (CONLIN) method and has better accuracy and convergent rate. Numerical examples are offered and the results show that the proposed method is effective in the structural shape design.     

基于遗传算法的模糊Hamming网络参数优化

根据遗传算法的演化原理,提出了一种新的度量模糊Hamming网络参数性能优劣的适应度函数,在此基础上,将遗传算法作为模糊Hamming网络的训练算法,进行网络参数寻优,并采用UCI机器学习数据库中不同的数据集进行对比测试。试验结果表明:将遗传算法与模糊Hamming网络相结合,可以快速求得最优网络参数组合,避免原有参数调整时的盲目性和随机性,训练后的网络具有分类迅速、准确、稳定的特点。     

Integrated optimal topology design and shape optimization using neural networks

In this paper, neural network- and feature-based approaches are introduced to overcome current shortcomings in the automated integration of topology design and shape optimization. The topology optimization results are reconstructed in terms of features, which consist of attributes required for automation and integration in subsequent applications. Features are defined as cost-efficient simple shapes for manufacturing. A neural network-based image-processing technique is presented to match the arbitrarily shaped holes inside the structure with predefined features. The effectiveness of the proposed approach in integrating topology design and shape optimization is demonstrated with several experimental examples.     

面向对象的遗传算法及其在神经网络辅助设计中的应用

在现有的遗传算法的基础上,采用面向对象技术设计了面向对象的遗传算法,建立了遗传算法的类层次。这种方法改变了在传统的遗传算法中各个函数之间只有参数的传递,而没有代码的继承性的状况从概念上提高了软件的可重用性。该方法在人工神经网络的辅助设计问题中的应用表明,这一算法由于采用面向对象的分析与设计方法,从而具有比传统的遗传算法更好的通用性,用户可以更方便地设计和实现自己的编码方案和遗传算子,大大提高了软件的可重用性。     

工程优化问题中神经网络与进化算法的比较

目前工程优化问题不仅种类繁多,而且各自采用的模型与方法迥异。从方法论的高度,将现有工程优化问题分为黑箱优化与白箱优化,然后推出各自的优化模型。对于黑箱优化问题,阐述了前向神经网络在系统逼近上的优势,以及进化算法与BP算法在求解神经网络权值上的优劣;对于白箱优化问题,阐述了进化算法与反馈神经网络的优缺点和目前流行的进化算法及其通用改进策略。通过分析,可以对目前的优化问题,以及神经网络与进化算法在其中的作用,有更加全面的认识。     

The particle swarm optimization algorithm in size and shape optimization

Shape and size optimization problems instructural design are addressed using the particle swarm optimization algorithm (PSOA). In our implementation of the PSOA, the social behaviour of birds is mimicked. Individual birds exchange information about their position, velocity and fitness, and the behaviour of the flock is then influenced to increase the probability of migration to regions of high fitness. New operators in the PSOA, namely the elite velocity and the elite particle, are introduced. Standard size and shape design problems selected from literature are used to evaluate the performance of the PSOA. The performance of the PSOA is compared with that of three gradient based methods, as well as the genetic algorithm (GA). In attaining the approximate region of the optimum, our implementation suggests that the PSOA is superior to the GA, and comparable to gradient based algorithms. Received December 18, 2000     

分布式进化算法的性能测试与分析

针对分布式进化算法设计过程中由于缺乏对性能影响因素的分析而导致算法无法达到预期加速比的问题,提出一种全面的性能分析方法。根据分布式进化算法的组成结构,将影响分布式进化算法性能的因素分为进化操作开销、适应值计算开销和通信开销三个部分。首先研究进化算法在不同个体编码维数下进化操作开销的特性;其次,在进化操作开销相对固定的情况下,通过使用操作系统的延时函数控制适应值计算开销,通过改变个体编码维数控制通信开销;最后,应用控制变量方法,逐一测试各因素对算法加速比的影响。实验结果展现了三种因素的相互制约关系,给出了分布式进化算法获得更好加速比的条件。     

Methodology for shape optimization of ultrasonic amplifier using genetic algorithms and simplex method

Designing devices for ultrasonic vibration applications is mostly done by intuitively adjusting the geometry to obtain the desired mode of vibration at a specific operating frequency. Recent studies have shown that with optimization methods, new devices with improved performance can be easily found. In this investigation, a new methodology for designing an ultrasonic amplifier through shape optimization using genetic algorithms and simplex method with specific fitness functions is presented. Displacements at specific functional areas, main functionality, and mode frequency are considered to determine the properties of an individual shape to meet the stated criteria. Length, diameter, position of mountings, and further specific geometric parameters are set up for the algorithm search for an optimized shape. Beginning with genetic algorithms, the basic shape fitting the stated requirements is found. After that the simplex method further improves the found shape to most appropriately minimize the fitness function. At the end, the fittest individual is selected as the final solution. Finally, resulting shapes are experimentally tested to show the effectiveness of the methodology.     

Integrated multiobjective optimization and a priori preferences using genetic algorithms

One of the tasks of decision-making support systems is to develop methods that help the designer select a solution among a set of actions, e.g. by constructing a function expressing his/her preferences over a set of potential solutions. In this paper, a new method to solve multiobjective optimization (MOO) problems is developed in which the user’s information about his/her preferences is taken into account within the search process. Preference functions are built that reflect the decision-maker’s (DM) interests and use meaningful parameters for each objective. The preference functions convert these objective preferences into numbers. Next, a single objective is automatically built and no weight selection is performed. Problems found due to the multimodality nature of a generated single cost index are managed with Genetic Algorithms (GAs). Three examples are given to illustrate the effectiveness of the method.