Multiobjective design of actively controlled structures using a hybrid optimization method

A multiobjective approach to the combined structure and control optimization problem for flexible space structures is presented. The proposed formulation addresses robustness considerations for controller design, as well as a simultaneous determination of optimum actuator locations. The structural weight, controlled system energy, stability robustness index and damping augmentation provided by the active controller are considered as objective functions of the multiobjective problem which is solved using a cooperative game-theoretic approach. The actuator locations and the cross-sectional areas of structural members are treated as design variables. Since the actuator locations are spatially discrete, whereas the cross-sectional areas are continuous, the optimization problem has mixed discrete-continuous design variables. A solution approach to this problem based on a hybrid optimization scheme is presented. The hybrid optimizer is a synergetic blend of artificial genetic search and gradient-based search techniques. The computational procedure is demonstrated through the design of an ACOSS-FOUR space structure. The optimum solutions obtained using the hybrid optimizer are shown to outperform the optimum results obtained using gradient-based search techniques.     

Development of an efficient algorithm for global optimization by simplex elimination

An efficient multi-start algorithm for global optimization is developed by introducing multi-dimensional simplexes as new expression units of attraction regions. The region elimination method generally consists of making a set of eliminated regions called attraction regions, checking adjacency between the current design point and the attraction region, and quitting local optimization for the attracted design points. The efficiency of the elimination method is considerably enhanced by supplementing general simplexes and their neighborhoods to conventional units of attraction regions of points and lines. To show the effectiveness of the proposed algorithm, mathematical problems from the literature are solved and the results are compared with several well-known multi-start algorithms. The present algorithm produces the global optimum in all problems more efficiently than the variants of the multi-start method. Several types of truss, frame, and composite material structures are optimized as engineering applications. Many local optima are found and the differences among the local optima are not negligibly small. These results suggest that an efficient and reliable global optimizer is strongly required in some fields of engineering optimization.     

Hybrid metamodel-based design space management method for expensive problems

Metamodel-based global optimization methods have been extensively studied for their great potential in solving expensive problems. In this work, a design space management strategy is proposed to improve the accuracy and efficiency of metamodel-based optimization methods. In this strategy, the whole design space is divided into two parts: the important region constructed using several expensive points and the other region. Combined with a previously developed hybrid metamodel strategy, a hybrid metamodel-based design space management method (HMDSM) is developed. In this method, three representative metamodels are used simultaneously in the search of the global optimum in both the important region and the other region. In the search process, the important region is iteratively reduced and the global optimum is soon captured. Tests using a series of benchmark mathematical functions and a practical expensive problem demonstrate the excellent performance of the proposed method.     

An efficient and practical approach to obtain a better optimum solution for structural optimization

For many structural optimization problems, it is hard or even impossible to find the global optimum solution owing to unaffordable computational cost. An alternative and practical way of thinking is thus proposed in this research to obtain an optimum design which may not be global but is better than most local optimum solutions that can be found by gradient-based search methods. The way to reach this goal is to find a smaller search space for gradient-based search methods. It is found in this research that data mining can accomplish this goal easily. The activities of classification, association and clustering in data mining are employed to reduce the original design space. For unconstrained optimization problems, the data mining activities are used to find a smaller search region which contains the global or better local solutions. For constrained optimization problems, it is used to find the feasible region or the feasible region with better objective values. Numerical examples show that the optimum solutions found in the reduced design space by sequential quadratic programming (SQP) are indeed much better than those found by SQP in the original design space. The optimum solutions found in a reduced space by SQP sometimes are even better than the solution found using a hybrid global search method with approximate structural analyses.     

黏弹性复合材料结构的多目标优化设计

黏弹性复合材料具有良好的阻尼性能,但黏弹性层的存在对黏弹性复合材料结构的强度性能会有所影响,黏弹性复合材料结构只有同时兼备良好的阻尼和强度才能满足工程要求。该文在经典层合板及小挠度弯曲理论基础上,运用Ritz法建立黏弹性复合材料结构应变能损耗因子和横向均布荷载作用下初始破坏强度计算模型。提出新的遗传算法适应度函数构造办法,克服了多目标优化问题中优化结果的偏移现象,对黏弹性复合材料结构进行单目标和双目标优化设计。优化结果表明：改进的遗传算法适用于黏弹性复合材料结构阻尼和强度性能的优化设计,而且多目标优化设计可以权衡复合结构的阻尼性能和强度性能,有利于发挥黏弹性复合材料结构良好的整体性能。     

非线性函数全局最优化的一种混沌优化混合算法

混沌优化方法是近年出现的利用混沌的遍历性、随机性作为全局优化机制的一种优化技术。已有的混沌优化方法都是利用Logistic映射作为混沌序列发生器,而由Logistic映射产生的混沌序列的概率密度函数服从两头多、中间少的切比雪夫型分布,这种分布特性会严重影响混沌优化全局搜索能力和效率。利用Logistic映射的特点,在混沌搜索时预先筛选掉劣质点,建立改进的混沌BFGS混合优化算法。复杂非线性测试函数计算结果表明,与文献中不加改进的混沌混合算法相比,本算法以同样的混沌搜索次数找到全局最优解的概率提高了10-30%,而以概率1获得全局最优解的最大混沌搜索次数减少了8-10倍。另外,还将细搜索策略引入到改进的混沌BFGS混合算法中,对具有较大边界约束范围的非线性函数进行了优化计算。     

基于混合加点准则的代理模型优化设计方法

在工程优化设计中,采用数值仿真模拟计算结构响应需耗费大量的时间和计算成本,给计算密集型的优化设计带来了巨大挑战,因此基于代理模型的序列优化设计方法得到了深入研究和广泛应用.对代理模型的序列优化方法框架进行了简要的概述;针对现有方法中存在的不足,发展了一类模型无关的混合加点准则,使优化循环过程中产生的新样本点分布在当前最...     

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.     

A hybrid optimization method of harmony search and opposition-based learning

The harmony search (HS) method is an emerging meta-heuristic optimization algorithm. However, like most of the evolutionary computation techniques, it sometimes suffers from a rather slow search speed, and fails to find the global optimum in an efficient way. In this article, a hybrid optimization approach is proposed and studied, in which the HS is merged together with the opposition-based learning (OBL). The modified HS, namely HS-OBL, has an improved convergence property. Optimization of 24 typical benchmark functions and an optimal wind generator design case study demonstrate that the HS-OBL can indeed yield a superior optimization performance over the regular HS method.     

OPTIMAL STRUCTURAL DESIGN BY ANT COLONY OPTIMIZATION

Ant colony optimization (ACO) is a relatively new heuristic combinatorial optimization algorithm in which the search process is a stochastic procedure that incorporates positive feedback of accumulated information. The positive feedback (;i.e., autocatalysis) facility is a feature of ACO which gives an emergent search procedure such that the (common) problem of algorithm termination at local optima may be avoided and search for a global optimum is possible.

The ACO algorithm is motivated by analogy with natural phenomena, in particular, the ability of a colony of ants to ‘optimize’ their collective endeavours. In this paper the biological background for ACO is explained and its computational implementation is presented in a structural design context. The particular implementation of ACO makes use of a tabu search (TS) local improvement phase to give a computationally enhanced algorithm (ACOTS).

In this paper ACOTS is applied to the optimal structural design, in terms of weight minimization, of a 25-bar space truss. The design variables are the cross-sectional areas of the bars, which take discrete values. Numerical investigation of the 25-bar space truss gave the best (i.e., lowest to-date) minimum weight value. This example provides evidence that ACOTS is a useful and technically viable optimization technique for discrete-variable optimal structural design.     

A genetic algorithm approach to single and multiobjective structural optimization with discrete–continuous variables

A search procedure with a philosophical basis in molecular biology is adapted for solving single and multiobjective structural optimization problems. This procedure, known as a genetic algorithm (GA). utilizes a blending of the principles of natural genetics and natural selection. A lack of dependence on the gradient information makes GAs less susceptible to pitfalls of convergence to a local optimum. To model the multiple objective functions in the problem formulation, a co-operative game theoretic approach is proposed. Examples dealing with single and multiobjective geometrical design of structures with discrete–continuous design variables, and using artificial genetic search are presented. Simulation results indicate that GAs converge to optimum solutions by searching only a small fraction of the solution space. The optimum solutions obtained using GAs compare favourably with optimum solutions obtained using gradient-based search techniques. The results indicate that the efficiency and power of GAs can be effectively utilized to solve a broad spectrum of design optimization problems with discrete and continuous variables with similar efficiency.     

A Genetic Algorithm Hybrid for Constructing Optimal Response Surface Designs

Hybrid heuristic optimization methods can discover efficient experiment designs in situations where traditional designs cannot be applied, exchange methods are ineffective, and simple heuristics like simulated annealing fail to find good solutions. One such heuristic hybrid is GASA (genetic algorithm–simulated annealing), developed to take advantage of the exploratory power of the genetic algorithm, while utilizing the local optimum exploitive properties of simulated annealing. The successful application of this method is demonstrated in a difficult design problem with multiple optimization criteria in an irregularly shaped design region. Copyright © 2004 John Wiley & Sons, Ltd.     

混合遗传算法在结构动力反演中的应用研究

研究了输入荷载未知条件下的结构参数识别及荷载反演问题,该问题最终归结为一个非线性的优化问题求解,根据目标函数、约束条件的具体特性,采用BFGS算法作为局部搜索算子,构造了基于浮点编码的混合遗传算法.针对系统输入未知的激励特性,采用分解反演的计算策略,从而提高了动力反演中混合遗传算法的稳健性和收敛速度.数值算例表明,这种方法具有很好的参数识别精度及荷载反演效果,对测试噪声有较强的适应能力.     

有限元法和退火进化算法相结合分析结构模糊可靠性

结构的失效除了具有随机性,还应具有模糊性。本文在介绍一种修正的联合概率密度函数的基础上,采用有限元法和退火进化算法相结合来研究结构的模糊可靠度。在每一模糊失效水平下,有限元法用来计算荷载效应项,并将荷载效应项代入原联合概率密度函数形成修正的联合概率密度函数。为了解决进化算法的早熟收敛问题,采用模拟退火算法与进化算法相结合,以保证更有效地搜索到最可能失效点(设计点)。解决不存在显式极限状态方程的大部分实际结构的可靠度研究的困难。数例结果表明该法可直接应用现有的确定性的有限元程序,并且具有很好的效率和精度。     

An optimization design of vehicle axle system based on multiobjective cooperative optimization algorithm

ABSTRACT

To address multiobjective, multi constraint and time-consuming structural optimization problems in a vehicle axle system, a multiobjective cooperative optimization model of a vehicle axle structure is established. In light of the difficulty in the nondominated sorting of the NSGA-II algorithm caused by inconsistent effects of the uniformity objective function and physical objective function, this paper combines a multiobjective genetic algorithm with cooperative optimization and presents a strategy for handling the optimization of a vehicle axle structure. The uniformity objective function of the sub discipline is transformed to its self-constraint. Taking the multiobjective optimization of a vehicle axle system as an example, a multiobjective cooperative optimization design for the system is carried out in ISIGHT. The results show that the multiobjective cooperative optimization strategy can simplify the complexity of optimization problems and that the multiobjective cooperative optimization method based on an approximate model is favorable for accuracy and efficiency, thereby providing a theoretical basis for the optimization of similar complex structures in practical engineering.     

HYBRID MULTIMODAL OPTIMIZATION WITH CLUSTERING GENETIC STRATEGIES

Abstract

Two-stage hybrid multimodal optimization approaches that combine cluster identification techniques in genetic algorithms with sharing and gradient-based local search methods are proposed. The multimodal optimization comprises the use of a sharing function implementation in genetic searches to pursue multiple local optima and subsequent executions of local searches to locate each local optimum when an extreme-containing region is identified. A new cluster identification technique is proposed for automatic and adaptive identification of the locations and sizes of design clusters in genetic algorithms with sharing. The first stage of the hybrid multimodal optimization is to use sharing-enhanced genetic algorithms for the identification of the near-optimum designs inside extreme-containing regions. The second stage simply involves consecutive employment of efficient gradient-based local searches by using the near-optimum designs as initial designs. Two strategies defining the coupling of the genetic search and local searches are proposed. The proposed hybrid optimization strategies are tested in a number of illustrative multimodal optimization problems.     

Computational strategy for multiobjective optimization of composite stiffened panels

This paper presents a multiobjective optimization methodology for composite stiffened panels. The purpose is to improve the performances of an existing design of stiffened composite panels in terms of both its first buckling load and ultimate collapse or failure loads. The design variables are the stacking sequences of the skin and of the stiffeners of the panel. The optimization is performed using a multiobjective evolutionary algorithm specifically developed for the design of laminated parts. The algorithm takes into account the industrial design guidelines for stacking sequence design. An original method is proposed for the initialization of the optimization that significantly accelerates the search for the Pareto front. In order to reduce the calculation time, Radial Basis Functions under Tension are used to approximate the objective functions. Special attention is paid to generalization errors around the optimum. The multiobjective optimization results in a wide set of trade-offs, offering important improvements for both considered objectives, among which the designer can make a choice.     

An extension of the directed search domain algorithm to bilevel optimization

A method is developed for generating a well-distributed Pareto set for the upper level in bilevel multiobjective optimization. The approach is based on the Directed Search Domain (DSD) algorithm, which is a classical approach for generation of a quasi-evenly distributed Pareto set in multiobjective optimization. The approach contains a double-layer optimizer designed in a specific way under the framework of the DSD method. The double-layer optimizer is based on bilevel single-objective optimization and aims to find a unique optimal Pareto solution rather than generate the whole Pareto frontier on the lower level in order to improve the optimization efficiency. The proposed bilevel DSD approach is verified on several test cases, and a relevant comparison against another classical approach is made. It is shown that the approach can generate a quasi-evenly distributed Pareto set for the upper level with relatively low time consumption.     

A changing range genetic algorithm

During the last decade various methods have been proposed to handle linear and non‐linear constraints by using genetic algorithms to solve problems of numerical optimization. The key to success lies in focusing the search space towards a feasible region where a global optimum is located. This study investigates an approach that adaptively shifts and shrinks the size of the search space to the feasible region; it uses two strategies for estimating a point of attraction. Several test cases demonstrate the ability of this approach to reach effectively and accurately the global optimum with a low resolution of the binary representation scheme and without additional computational efforts. Copyright © 2004 John Wiley & Sons, Ltd.     

Mathematical Modeling and Optimization of Two-Layer Sintering Process for Sinter Quality and Fuel Efficiency Using Genetic Algorithm

Two-layer sintering by charging a green sinter mix with normal coke rate in the upper layer and reduced coke rate in the lower layer can substantially reduce the coke rate and improve the sinter quality by producing more uniform thermal profile throughout the bed height. The two-layer sintering process has been analyzed by numerical simulation using a detailed CFD-based model, considering all the important phenomena (i.e., gas-solid reaction, melting and solidification, flow through porous bed, heat, and mass transfer etc.). A genetic algorithm optimization technique is then applied to evaluate the optimum coke rate in the two layers of the bed to produce the ideal thermal profile and melting fraction in the sinter bed for optimum sinter quality. By this optimization method a high-quality sinter with minimum return fines can be achieved along with reduced coke rate. Application of genetic algorithm for this type of process optimization has several advantages over traditional optimization techniques, because it can identify the global optimum condition and perform multiobjective optimization very easily for a complex industrial process such as iron ore sintering.