Advances in concrete arch dams shape optimization

This paper presents an efficient methodology to find the optimum shape of arch dams. In order to create the geometry of arch dams a new algorithm based on Hermit Splines is proposed. A finite element based shape sensitivity analysis for design-dependent loadings involving body force, hydrostatic pressure and earthquake loadings is implemented. The sensitivity analysis is performed using the concept of mesh design velocity. In order to consider the practical requirements in the optimization model such as construction stages, many geometrical and behavioral constrains are included in the model in comparison with previous researches. The optimization problem is solved via the sequential quadratic programming (SQP) method. The proposed methods are applied successfully to an Iranian arch dam, and good results are achieved. By using such methodology, efficient software for shape optimization of concrete arch dams for practical and reliable design now is available.     

Constrained Global Optimization of Expensive Black Box Functions Using Radial Basis Functions

We present a new strategy for the constrained global optimization of expensive black box functions using response surface models. A response surface model is simply a multivariate approximation of a continuous black box function which is used as a surrogate model for optimization in situations where function evaluations are computationally expensive. Prior global optimization methods that utilize response surface models were limited to box-constrained problems, but the new method can easily incorporate general nonlinear constraints. In the proposed method, which we refer to as the Constrained Optimization using Response Surfaces (CORS) Method, the next point for costly function evaluation is chosen to be the one that minimizes the current response surface model subject to the given constraints and to additional constraints that the point be of some distance from previously evaluated points. The distance requirement is allowed to cycle, starting from a high value (global search) and ending with a low value (local search). The purpose of the constraint is to drive the method towards unexplored regions of the domain and to prevent the premature convergence of the method to some point which may not even be a local minimizer of the black box function. The new method can be shown to converge to the global minimizer of any continuous function on a compact set regardless of the response surface model that is used. Finally, we considered two particular implementations of the CORS method which utilize a radial basis function model (CORS-RBF) and applied it on the box-constrained Dixon–Szegö test functions and on a simple nonlinearly constrained test function. The results indicate that the CORS-RBF algorithms are competitive with existing global optimization algorithms for costly functions on the box-constrained test problems. The results also show that the CORS-RBF algorithms are better than other algorithms for constrained global optimization on the nonlinearly constrained test problem.     

2D shape optimization under proximity constraints by CFD and response surface methodology

In this paper we consider two-dimensional CFD-based shape optimization in the presence of obstacles, which introduce nontrivial proximity constraints to the optimization problem. Built on Gregory’s piecewise rational cubic splines, the main contribution of this paper is the introduction of such parametric deformations to a nominal shape that are guaranteed to satisfy the proximity constraints. These deformed shape candidates are then used in the identification of a multivariate polynomial response surface; proximity-constrained shape optimization thus reduces to parametric optimization on this polynomial model, with simple interval bounds on the design variables. We illustrate the proposed approach by carrying out lift and/or drag optimization for the NACA 0012 airfoil containing a rectangular fuel tank: By identifying polynomial response surfaces using a large batch of 1800 design candidates, we conclude that the lift coefficient can be optimized by a linear model, whereas the drag coefficient can be optimized by using a quadratic model. Higher order polynomial models yield no improvement in the optimization.     

Optimum design of “road-friendly” vehicle suspension systems subjected to rough pavement surfaces

This paper presents an optimum concept to design “road-friendly” vehicles with the recognition of pavement loads as a primary objective function of vehicle suspension design. A walking-beam suspension system is used as an illustrative example of vehicle model to demonstrate the concept and process of optimization. The hypothesis of isotropy is applied to the measured one-dimensional road profile so that a two-dimensional random field model of pavement surface roughness can be achieved. Dynamic response of the walking-beam suspension system is obtained by means of stochastic process theory. Three commonly used objective of suspension optimum design, including ride quality, suspension stroke, and road adhesion, are briefly reviewed. The minimization of the probability of peak value of the tire load exceeding a given value is proposed as an objective function. Using the direct update method, optimization is carried out when tire loads is taken as the objective function of suspension design. The results show that tires with high air pressure and suspension systems with small damping will lead to large tire loads. The concept proposed in this paper is applicable to generic cases, where more complex vehicle model and pavement surface condition apply.     

Lexicographical dynamic goal programming approach to a robust design optimization within the pharmaceutical environment

The primary objective of this paper is to develop a new robust design (RD) optimization procedure based on a lexicographical dynamic goal programming (LDGP) approach for implementing time-series based multi-responses, while the conventional experimental design formats and frameworks may implement static responses. First, a parameter estimation method for time-dependent pharmaceutical responses (i.e., drug release and gelation kinetics) is proposed using the dual response estimation concept that separately estimates the response functions of the mean and variance, as a part of response surface method. Second, a multi-objective RD optimization model using the estimated response functions of both the process mean and variance is proposed by incorporating a time-series components within a dynamic modeling environment. Finally, a pharmaceutical case study associated with a generic drug development process is conducted for verification purposes. Based on the case study results, we conclude that the proposed LDGP approach effectively provides the optimal drug formulations with significantly small biases and MSE values, compared to other models.     

Optimization of technology parameters for the plane-strain component in the process of gas quenching

The paper introduces an optimization method for the technology parameters of the plane-strain component in the process of gas quenching. Distortion, residual stress, average surface hardness and standard deviation of surface hardness are regarded as the optimization objectives. A new heat transfer coefficient model is presented, five distinct heat transfer coefficients are used at various regions of the model. The five heat transfer coefficients are regarded as the design variables, and four regressive equations are established by using response surface method. The four equations, respectively represent the relations between the four optimization objectives and the design variables. A multi-objectives optimization model is established, and the multi-objectives optimization model is optimized by the non-linear method. The optimized technology parameters are used to simulate the gas quenching process by FEM software. The quenching results after optimization are compared with those before optimization. The comparison shows that the quenching quality after optimization is better than that before optimization. After optimization, the four optimization objectives are all improved.     

基于卷积神经网络气动力降阶模型的翼型优化方法

针对非线性大扰动翼型气动力优化问题,提出了基于卷积神经网络气动力降阶模型的优化方法.该方法用不同形状参数下翼型的气动力数据作为训练信号,训练卷积神经网络翼型气动力降阶模型.采用该气动力降阶模型,以最大升阻比为目标,对翼型进行优化,结果表明该方法可用于大扰动下翼型气动力的预测和优化.该文同时还讨论了池化法和径向基法的训练...     

On the Design of Optimization Strategies Based on Global Response Surface Approximation Models

Striking the correct balance between global exploration of search spaces and local exploitation of promising basins of attraction is one of the principal concerns in the design of global optimization algorithms. This is true in the case of techniques based on global response surface approximation models as well. After constructing such a model using some initial database of designs it is far from obvious how to select further points to examine so that the appropriate mix of exploration and exploitation is achieved. In this paper we propose a selection criterion based on the expected improvement measure, which allows relatively precise control of the scope of the search. We investigate its behavior through a set of artificial test functions and two structural optimization problems. We also look at another aspect of setting up search heuristics of this type: the choice of the size of the database that the initial approximation is built upon.     

Multi-fidelity design optimization of transonic airfoils using physics-based surrogate modeling and shape-preserving response prediction

A computationally efficient design methodology for transonic airfoil optimization has been developed. In the optimization process, a numerically cheap physics-based low-fidelity surrogate (the transonic small-disturbance equation) is used in lieu of an accurate, but computationally expensive, high-fidelity (the compressible Euler equations) simulation model. Correction of the low-fidelity model is achieved by aligning its corresponding airfoil surface pressure distribution with that of the high-fidelity model using a shape-preserving response prediction technique. The resulting method requires only a single high-fidelity simulation per iteration of the design process. The method is applied to airfoil lift maximization in two-dimensional inviscid transonic flow, subject to constraints on shock-induced pressure drag and airfoil cross-sectional area. The results showed that more than a 90% reduction in high-fidelity function calls was achieved when compared to direct high-fidelity model optimization using a pattern-search algorithm.     

MultiGLODS: global and local multiobjective optimization using direct search

The optimization of multimodal functions is a challenging task, in particular when derivatives are not available for use. Recently, in a directional direct search framework, a clever multistart strategy was proposed for global derivative-free optimization of single objective functions. The goal of the current work is to generalize this approach to the computation of global Pareto fronts for multiobjective multimodal derivative-free optimization problems. The proposed algorithm alternates between initializing new searches, using a multistart strategy, and exploring promising subregions, resorting to directional direct search. Components of the objective function are not aggregated and new points are accepted using the concept of Pareto dominance. The initialized searches are not all conducted until the end, merging when they start to be close to each other. The convergence of the method is analyzed under the common assumptions of directional direct search. Numerical experiments show its ability to generate approximations to the different Pareto fronts of a given problem.     

Robust optimization for multiple responses using response surface methodology

Typically in the analysis of industrial data for product/process optimization, there are many response variables that are under investigation at the same time. Robustness is also an important concept in industrial optimization. Here, robustness means that the responses are not sensitive to the small changes of the input variables. However, most of the recent work in industrial optimization has not dealt with robustness, and most practitioners follow up optimization calculations without consideration for robustness. This paper presents a strategy for dealing with robustness and optimization simultaneously for multiple responses. In this paper, we propose a robustness desirability function distinguished from the optimization desirability function and also propose an overall desirability function approach, which makes balance between robustness and optimization for multiple response problems. Simplex search method is used to search for the most robust optimal point in the feasible operating region. Finally, the proposed strategy is illustrated with an example from the literature. Copyright © 2009 John Wiley & Sons, Ltd.     

具有动应力、位移和稳定性约束的离散变量桁架结构布局优化设计算法

给出了在动应力、动位移和动稳定约束下离散变量结构布局优化设计问题的数学模型,用“拟静力”算法,将具有动应力约束、动位移约束和动稳定约束的离散变量结构布局优化设计问题化为静应力、静位移和静稳定约束的优化问题,然后利用两级优化算法求解该模型．优化过程由两级组成,拓扑级优化和形状级优化．在每一级,都使用了综合算法,并且在搜索过程中都根据两类设计变量的相对差商值进行搜索．对包含稳定约束和不包含稳定约束的优化结果做了比较,结果显示稳定性约束对优化结果产生较大的影响．     

An inverse eigenvalue method for frequency isolation in spring–mass systems

The action of external vibrating forces on mechanical structures can cause severe damages when resonance occurs. The removal of natural frequencies of the structure from resonance bands is therefore of great importance. This problem is called frequency isolation problem and is the subject of this paper. A new inverse eigenvalue method is proposed and applied to spring–mass systems, which have generated much interest in the literature as prototypes of vibrating structures. The novelty of the method lies in using the zeros of the frequency response function at the last mass as control variables in an optimization problem to minimize the impact of redesign. Numerically accurate algorithms for computing the sensitivity with respect to the control variables are presented, which form the basis of an efficient multidimensional search strategy to solve the frequency isolation problem. Copyright © 2001 by John Wiley & Sons, Ltd.     

Transformation technologies in forming composite structures

A design model of axisymmetric transformation of a helically wound shell preform into a given shape is considered. Types of design problems are determined, and examples of their solution are given. Examples of fabrication techniques for structural prototypes by using the transformation method are included.     

An efficient algorithm for optimal design of area traffic control with network flows

An equilibrium network design (EQND) is a problem of finding the optimal design parameters while taking into account the route choice of users. This problem can be formulated as an optimization by taking the user equilibrium traffic assignment as a constraint. In this paper, the methods solving the EQND problem with signal settings are investigated via numerical calculations on two example road networks. An efficient algorithm is proposed in which improvement on a locally optimal search by combining the technique of parallel tangents with the gradient projection method is presented. As it shows, the method combines the locally optimal search and globally search heuristic achieved substantially better performance than did those other approaches.     

Particle swarm optimization with age-group topology for multimodal functions and data clustering

This paper proposes particle swarm optimization with age-group topology (PSOAG), a novel age-based particle swarm optimization (PSO). In this work, we present a new concept of age to measure the search ability of each particle in local area. To keep population diversity during searching, we separate particles to different age-groups by their age and particles in each age-group can only select the ones in younger groups or their own groups as their neighbourhoods. To allow search escape from local optima, the aging particles are regularly replaced by new and randomly generated ones. In addition, we design an age-group based parameter setting method, where particles in different age-groups have different parameters, to accelerate convergence. This algorithm is applied to nonlinear function optimization and data clustering problems for performance evaluation. In comparison against several PSO variants and other EAs, we find that the proposed algorithm provides significantly better performances on both the function optimization problems and the data clustering tasks.     

基于期望函数的土遗址锚固参数组合优化方法

针对土遗址锚固工程需求，提出了一种基于期望函数的锚固参数组合优化方法.该方法通过对锚固长度、锚孔直径等参数的组合优化,获得了最大锚固力与最小遗址伤害的良好平衡.试验设计为全因子试验，利用响应面方法构建分析模型，而后将统计中的期望函数法引入锚固参数优化中，建立了多重目标响应指标与锚固参数水平的关系.研究结果表明:当分别满足锚固力最大化和遗址伤害最小化目标时，相应的锚固参数取值间存在冲突；多重响应优化能够确定目标响应需求下锚固参数的可行域范围，方便工程设计人员根据实际工程条件对锚固参数进行可视化取值.     

A constrained optimization based method for acoustic finite element model updating of cavities using pressure response

A method based on constrained optimization for updating of an acoustic finite element model using pressure response is proposed in this paper. The constrained optimization problem is solved using sequential quadratic programming algorithm. Updating parameters related to the properties of the sound absorbers and the measurement errors are considered. Effectiveness of the method is demonstrated by numerical studies on a 2D rectangular cavity and a car cavity. It is shown that the constrained formulation, that includes lower and upper bounds on the updating parameters in the form of inequality constraints, is important for obtaining a correct updated model. It is seen that the proposed updating method is not only able to effectively update the model to obtain a close match between the finite element model pressure response and the reference pressure response, but is also able to identify the correction factors to the parameters in error with reasonable accuracy.     

An Inverse Reliability-based Approach for Designing under Uncertainty with Application to Robust Piston Design

In this work, we propose an optimization framework for designing under uncertainty that considers both robustness and reliability issues. This approach is generic enough to be applicable to engineering design problems involving nonconvex objective and constraint functions defined in terms of random variables that follow any distribution. The problem formulation employs an Inverse Reliability Strategy that uses percentile performance to address both robustness objectives and reliability constraints. Robustness is achieved through a design objective that evaluates performance variation as a percentile difference between the right and left trails of the specified goals. Reliability requirements are formulated as Inverse Reliability constraints that are based on equivalent percentile performance levels. The general proposed approach first approximates the formulated problem via a Gaussian Kriging model. This is then used to evaluate the percentile performance characteristics of the different measures inherent in the problem formulation for various design variable settings via a Most Probable Point of Inverse Reliability search algorithm. By using these percentile evaluations in concert with the response surface methodology, a polynomial programming approximation is generated. The resulting problem formulation is finally solved to global optimality using the Reformulation–Linearization Technique (RLT) approach. We demonstrate this overall proposed approach by applying it to solve the problem of reducing piston slap, an undesirable engine noise due to the secondary motion of a piston within a cylinder.     

An ellipsoidal distance-based search strategy of ants for nonlinear single and multiple response optimization problems

Various continuous ant colony optimization (CACO) strategies are proposed by researchers to resolve continuous single response optimization problems. However, no such work is reported which also verifies suitability of CACO in case of both single and multiple response situations. In addition, as per literature survey, no variant of CACO can balance simultaneously all the three important aspects of an efficient search strategy, viz. escaping local optima, balancing between intensification and diversification scheme, and handling correlated variable search space structure. In this paper, a variant of CACO, so-called ‘CACO-MDS’ is proposed, which attempts to address all these three aspects. CACO-MDS strategy is based on a Mahalanobis distance-based diversification, and Nelder–Mead simplex-based intensification search scheme. Mahalanobis distance-based diversification search ensures exact measure of multivariate distance for correlated structured search space. The proposed CACO-MDS strategy is verified using fourteen single and multiple response multimodal function optimization test problems. A comparative analysis of CACO-MDS, with three different metaheuristic strategies, viz. ant colony optimization in real space (ACO_R), a variant of local-best particle swarm optimization (SPSO) and simplex-simulated annealing (SIMPSA), also indicates its superiority in most of the test situations.