离散变量结构优化设计的拟满应力遗传算法

以力学准则法为基础,提出了一种求解离散变量结构优化设计的拟满应力方法;这种方法能直接求解具有应力约束和几何约束的离散变量结构优化设计问题.通过在遗传算法中定义拟满应力算子,建立了一种离散变量结构优化设计的混合遗传算法拟满应力遗传算法.算例表明;这种混合遗传算法对于离散变量结构优化设计问题具有较高的计算效率.     

基于Matlab的两级星型齿轮传动的优化设计

建立了两级内外啮合星型齿轮传动优化设计的数学模型,分析了系统的传动方案和约束条件,以中心距最小为目标函数,确定了主要优化设计参数。采用了以齿数、模数为离散变量和变位系数,齿数比等为连续变量的优化设计方法。过多的等式约束造成最优化时可行域减少,甚至找不到可行域,严重影响了优化设计的运行结果。鉴于此,发展了分级优化的方法,以齿数、模数为离散变量,变位系数、齿数比等为连续变量,运用Matlab中非线性有约束的多元函数fmincon求解,经过优化计算,得到主要优化设计参数。     

基于复合形算子的基础支护桩优化设计智能算法研究

本文通过遗传算法和传统复合形搜索法相结合,基于对遗传算法算子计算结构的调整,并将遗传算法与神经网络相结合,提出并研究了一种新的优化设计方法,协同求解复杂工程中的优化问题.并针对悬臂式支护桩的优化设计的数学模型,采用该算法进行了优化设计分析;计算结果表明,该算法可克服遗传算法最终进化至最优解较慢和人工神经网络易陷入局部解的缺陷,具有较好的全局性和收敛速度.     

离散变量结构优化的拟满应力设计方法

本文以满应力设计思想为基础,提出了适用于离散变量结构优化设计计算的拟满应力设计方法。该方法能直接计算具有应力约束和截面尺寸约柬的离散变量结构优化设计问题,也能处理同时具有稳定性约束和位移约束的多工况、多约束、多变量的离散变量结构优化设计问题。算例结果表明,拟满应力设计方法对于离散变量结构优化计算是非常有效的。     

力学映射下板壳结构的截面离散优化设计

依据力学映射的方法把离散变量优化问题转换为连续变量优化问题,通过在连续优化最优解附近构造两节模型,采用无穷小单元的无穷组合方法和变量连接术对板壳结构进行优化.同时在MSC公司的Nastran软件平台上利用其PCL语言开发出优化模块,并进行了算例的优化设计.     

混合离散变量模拟退火方法及其应用

基于海洋工程中存在的设计变量为离散型和连续型的混合离散变量的情况,探讨了一种优化设计问题的方法———混合离散模拟退火法.该方法相对常规模拟退火方法有一定改进并且针对混合离散变量进行了特定处理.实际算例计算表明,该方法可用于海洋工程优化设计中,其结果不需圆整,而且其解题可靠性和效率相当高.     

求解实对称矩阵区间特征值问题的直接优化法

提出了一种用于对称区间矩阵特征值问题求解的直接优化法。将区间矩阵中为区间量的各元素作为优化设计变量,将区间量的分布区间作为相应的设计变量的边界约束,运用约束优化法求出区间矩 最大特征值和最小特征值,从而获得区间矩阵特征值问题的解。本文提出的直接优化法适用于对称区间矩阵的标准特征值问题和广义特征值问题。文中给出的两个计算实例显示了该法的有效性。     

基于梯度优化方法的钢结构标准截面选型优化设计

实际的工程应用中,钢框架的基本构件大多是根据钢结构设计规范要求,从标准型钢库中选取,所组成的框架结构的截面尺寸非连续变化。因此,钢结构截面优化设计是典型的离散设计变量优化问题。若采用基于启发式的算法(如遗传算法等)进行求解,当可选截面类型较多时,其计算量巨大,求解效率低下。该文通过引入高维拉格朗日插值函数对该离散设计问题进行连续化,建立了可采用梯度优化方法进行求解的钢结构标准截面选型设计模型,并且使得连续化以后的设计变量个数大幅度减少。对给定截面类型种数为2n个的可选截面集合,其设计变量只需n个即可。具体算例表明：与基于遗传算法的优化方法相比,该方法的计算效率提高1~2个数量级,并且在结构性能基本相当的情况下,得到的型钢种类更少,便于工程应用。     

追究根基的结构拓扑优化方法

结合作者在结构拓扑优化方面的研究工作,围绕了ICM(独立、连续、映射)方法涉及的基本概念上的突破,叙述了将本质上为0-1离散变量的拓扑优化问题转化为连续变量优化问题的具体做法,其中介绍了若干要点:以阶跃函数把离散问题化为连续问题即完成关键的等价性转换是第一步;定义磨光函数逼近阶跃函数的可操作的近似是第二步;引入作为磨光函数反函数的过滤函数实现映射性建模是第三步;采用某些光滑算法求解连续变量模型则是第四步。通过连续体结构的典型数值算例说明了将结构拓扑优化的模型转化为独立层次的拓扑优化过程。该方法对于纯数学的0-1离散变量优化的求解也适用,方法与数值都表明了这一点。     

拓扑优化方法在复合材料设计中的研究进展

按照设计变量,叙述了连续变量和离散变量拓扑优化设计的一些常用算法,其中包括均匀化方法、变密度法、变厚度法、移动渐进算法、模拟退火法、遗传算法、相对差商法和Tabu搜索法,并对各种方法的优缺点进行了比较;对二维和三维复合材料的拓扑学优化设计研究现状和方法进行了阐述;提出了拓扑优化设计复合材料的未来研究方向.     

A new harmony search algorithm for solving mixed–discrete engineering optimization problems

In general design optimization problems, it is usually assumed that the design variables are continuous. However, many practical problems in engineering design require considering the design variables as integer or discrete values. The presence of discrete and integer variables along with continuous variables adds to the complexity of the optimization problem. Very few of the existing methods can yield a globally optimal solution when the objective functions are non-convex and non-differentiable. This article presents a mixed–discrete harmony search approach for solving these nonlinear optimization problems which contain integer, discrete and continuous variables. Some engineering design examples are also presented to demonstrate the effectiveness of the proposed method.     

Multi-objective optimization of engineering systems using game theory and particle swarm optimization

This study proposes particle swarm optimization (PSO) based algorithms to solve multi-objective engineering optimization problems involving continuous, discrete and/or mixed design variables. The original PSO algorithm is modified to include dynamic maximum velocity function and bounce method to enhance the computational efficiency and solution accuracy. The algorithm uses a closest discrete approach (CDA) to solve optimization problems with discrete design variables. A modified game theory (MGT) approach, coupled with the modified PSO, is used to solve multi-objective optimization problems. A dynamic penalty function is used to handle constraints in the optimization problem. The methodologies proposed are illustrated by several engineering applications and the results obtained are compared with those reported in the literature.     

An effective hybrid cuckoo search and genetic algorithm for constrained engineering design optimization

This article presents an effective hybrid cuckoo search and genetic algorithm (HCSGA) for solving engineering design optimization problems involving problem-specific constraints and mixed variables such as integer, discrete and continuous variables. The proposed algorithm, HCSGA, is first applied to 13 standard benchmark constrained optimization functions and subsequently used to solve three well-known design problems reported in the literature. The numerical results obtained by HCSGA show competitive performance with respect to recent algorithms for constrained design optimization problems.     

A global single-loop deterministic approach for reliability-based design optimization of truss structures with continuous and discrete design variables

A single-loop deterministic method (SLDM) has previously been proposed for solving reliability-based design optimization (RBDO) problems. In SLDM, probabilistic constraints are converted to approximate deterministic constraints. Consequently, RBDO problems can be transformed into approximate deterministic optimization problems, and hence the computational cost of solving such problems is reduced significantly. However, SLDM is limited to continuous design variables, and the obtained solutions are often trapped into local extrema. To overcome these two disadvantages, a global single-loop deterministic approach is developed in this article, and then it is applied to solve the RBDO problems of truss structures with both continuous and discrete design variables. The proposed approach is a combination of SLDM and improved differential evolution (IDE). The IDE algorithm is an improved version of the original differential evolution (DE) algorithm with two improvements: a roulette wheel selection with stochastic acceptance and an elitist selection technique. These improvements are applied to the mutation and selection phases of DE to enhance its convergence rate and accuracy. To demonstrate the reliability, efficiency and applicability of the proposed method, three numerical examples are executed, and the obtained results are compared with those available in the literature.     

Engineering optimization using a real-parameter genetic-algorithm-based hybrid method

A hybrid optimization algorithm which combines the respective merits of the genetic algorithm and the simulated annealing algorithm is proposed. The proposed algorithm incorporates adaptive mechanisms designed to adjust the probabilities of the cross-over and mutation operators such that its hill-climbing ability towards the optimum solution is improved. The algorithm is used to optimize the weight of four planar or space truss structures and the results are compared with those obtained using other well-known optimization schemes. The evaluation trials investigate the performance of the algorithm in optimizing over discrete sizing variables only and over both discrete sizing variables and continuous configuration variables. The results show that the proposed algorithm consistently outperforms the other optimization methods in terms of its weight-saving capabilities. It is also shown that the global searching ability and convergence speed of the proposed algorithm are significantly improved by the inclusion of adaptive mechanisms to adjust the values of the genetic operators. Hence the hybrid algorithm provides an efficient and robust technique for solving engineering design optimization problems.     

A comparison of the continuous and discrete adjoint approach extended based on the standard lattice Boltzmann method in flow field inverse optimization problems

The objective of this research is the numerical implementation and comparison between the performance of the continuous and discrete adjoint Lattice Boltzmann (LB) methods in optimization problems of unsteady flow fields. For this purpose, a periodic two-dimensional incompressible channel flow affected by the constant and uniform body forces is considered as the base flow field. The standard LB method and D2Q9 model are employed to solve the flow field. Moreover, the inverse optimization of the selected flow field is defined by considering the body forces as the design variables and the sum of squared errors of flow field variables on the whole field as the cost function. In this regard, the continuous and discrete adjoint approaches extended based on the LB method are used to achieve the gradients of the cost function with respect to the design variables. Finally, the numerical results obtained from the continuous adjoint LB method are compared with the discrete one, and the accuracy and efficiency of them are discussed. In addition, the validity of the obtained cost function gradients is investigated by comparing with the results of the standard forward finite difference and complex step methods. The numerical results show that regardless of the implementation cost of the two approaches, the computational cost to evaluate the gradients in each optimization cycle for the discrete adjoint LB approach is slightly more than the other one but has a little higher convergence rate and needs a smaller number of cycles to converge. Besides, the gradients obtained from the discrete version have a better agreement with those of the complex step method. Eventually, based on the structural similarities of the continuous LB equation and its corresponding adjoint one and using the simple periodic and complete bounce-back boundary conditions for the LB equation, the improved boundary conditions for the continuous adjoint LB equation are presented. The numerical results show that the use of these boundary conditions instead of the original adjoint boundary conditions significantly improves the relative accuracy and also the convergence rate of the continuous adjoint LB method.     

The harmony search heuristic algorithm for discrete structural optimization

Many methods have been developed and are in use for structural size optimization problems, in which the cross-sectional areas or sizing variables are usually assumed to be continuous. In most practical structural engineering design problems, however, the design variables are discrete. This paper proposes an efficient optimization method for structures with discrete-sized variables based on the harmony search (HS) heuristic algorithm. The recently developed HS algorithm was conceptualized using the musical process of searching for a perfect state of harmony. It uses a stochastic random search instead of a gradient search so that derivative information is unnecessary. In this article, a discrete search strategy using the HS algorithm is presented in detail and its effectiveness and robustness, as compared to current discrete optimization methods, are demonstrated through several standard truss examples. The numerical results reveal that the proposed method is a powerful search and design optimization tool for structures with discrete-sized members, and may yield better solutions than those obtained using current methods.     

Classifier-guided sampling for discrete variable,discontinuous design space exploration: Convergence and computational performance

A classifier-guided sampling (CGS) method is introduced for solving engineering design optimization problems with discrete and/or continuous variables and continuous and/or discontinuous responses. The method merges concepts from metamodel-guided sampling and population-based optimization algorithms. The CGS method uses a Bayesian network classifier for predicting the performance of new designs based on a set of known observations or training points. Unlike most metamodelling techniques, however, the classifier assigns a categorical class label to a new design, rather than predicting the resulting response in continuous space, and thereby accommodates non-differentiable and discontinuous functions of discrete or categorical variables. The CGS method uses these classifiers to guide a population-based sampling process towards combinations of discrete and/or continuous variable values with a high probability of yielding preferred performance. Accordingly, the CGS method is appropriate for discrete/discontinuous design problems that are ill suited for conventional metamodelling techniques and too computationally expensive to be solved by population-based algorithms alone. The rates of convergence and computational properties of the CGS method are investigated when applied to a set of discrete variable optimization problems. Results show that the CGS method significantly improves the rate of convergence towards known global optima, on average, compared with genetic algorithms.