MULTIOBJECTIVE DESIGN OPTIMIZATION BY AN EVOLUTIONARY ALGORITHM

This paper presents an evolutionary algorithm for generic multiobjective design optimization problems. The algorithm is based on nondominance of solutions in the objective and constraint space and uses effective mating strategies to improve solutions that are weak in either. Since the methodology is based on nondominance, scaling and aggregation affecting conventional penalty function methods for constraint handling does not arise. The algorithm incorporates intelligent partner selection for cooperative mating. The diversification strategy is based on niching which results in a wide spread of solutions in the parametric space. Results of the algorithm for the design examples clearly illustrate the efficiency of the algorithm in solving multidisciplinary design optimization problems.     

小生境遗传算法在反演堤坝地震勘探数据中的应用

基于反演问题的不确定性和目标函数的多峰性,本文提出引入小生境遗传算法,采用自适应控制交配概率和变异概率,求解出目标函数的若干个局部峰(或全局峰),然后利用先验知识,判定得到满意解。本文对实测资料进行了层速度与厚度的反演,通过实际值与反演值的比较,验证了进行多峰优化的有效性。     

Structural optimization of rotating tapered laminated thick composite plates with ply drop-offs

In this study, structural optimization of rotating tapered thick laminated composite plates with ply drop-offs has been investigated numerically. The governing differential equations of motion of the tapered composite plate have been presented including the energy associated with the inertia force, coriolis force, displacement dependent centrifugal force and initial stress resultants due to steady state rotation. Four noded quadrilateral finite element has been formulated based on the first order shear deformation theory. Finite element analysis results are validated with experimental results for natural frequencies of the tapered plate with various configurations. Various cases of optimization problems are formulated with different objective functions in terms of maximization of natural frequencies and damping factors (individually and combined) and solved using genetic algorithm in order to obtain optimal ply sequence and ply orientation. It is shown that the optimization problem with maximization of fundamental modal damping factor without rotating condition yields the optimal layout as 90° for all the layers in the plate. It is also observed that maximization of the fundamental modal damping factor yields identical optimal orientation for uniform and all the configurations of a tapered composite plate.     

Parameter Identification Method of Large Macro-Micro Coupled Constitutive Models Based on Identifiability Analysis

Large and complex macro-micro coupled constitutive models, which describe metal flow and microstructure evolution during metal forming, are sometimes overparameterized with respect to given sets of experimental datum. This results in poorly identifiable or non-identifiable model parameters. In this paper, a systemic parameter identification method for the large macro-micro coupled constitutive models is proposed. This method is based on the global and local identifiability analysis, in which two identifiability measures are adopted. The first measure accounts for the sensitivity of model results with respect to single parameters, and the second measure accounts for the degree of near-linear dependence of sensitivity functions of parameter subsets. The global identifiability analysis adopts a sampling strategy with only a limited number of model evaluations, and the strategy is a combination of Latin-hypercube sampling, one-factor-at-a-time sampling and elitism preservation strategy. The global identifiability index is the integration of the corresponding local index. A hybrid global optimization method is designed to identify the parameter. Firstly, the genetic algorithm is adopted to identify the model parameter rudely, and then the obtained parameter is further refined through the improved Levenberg-Marquardt algorithm. The niching method is used to maintain the population diversity and to choose the initial value for the Levenberg-Marquardt algorithm. A transition criterion between the genetic algorithm and the Levenberg-Marquardt algorithm is proposed, through the improvement on the average objective function value of the chromosomes and the objective function value of the best chromosome. During optimization by the Levenberg-Marquardt algorithm, the local identifiability analysis is taken at the beginning stage of each iteration, and then the variable with poor identifiability remains unchanged in this iteration; the problem of violation constraint for some solution is solved through adjusting the search step length. At last, taking Ti-6Al-4V as an example, a set of satisfactory material parameters is obtained. The calculated results agree with the experimental results well. The identified results show that some parameters involved in the model are poorly identifiable; at the same time, the identifiability analysis method can provide a guide to experiment design.     

Optimization of laminated composites considering different failure criteria

The purpose of the present work is to analyse how different the optimal structures are when different first ply failure criterion are considered in the optimization of laminated composites. Two problems are solved: the minimum weight and the minimum material cost of laminated plates subjected to in-plane loads. The failure criterion is taken into account by means of constraints introduced in the optimization problem. Three different failure criteria are tested independently: maximum stress, Tsai–Wu and the Puck failure criterion (PFC). Emphasis is given to the PFC as it appears to agree better with practical observations. The design variables are the ply orientations, the number of layers and the layer material, and the optimization problem is solved by a genetic algorithm (GA). The results show that optimal structures highly differ when different failure criterion are considered and that none of the failure criteria is always the most or the least conservative when different load conditions are applied.     

Particle swarm optimization approach for multi-objective composite box-beam design

This paper presents a multi-agent search technique to design an optimal composite box-beam helicopter rotor blade. The search technique is called particle swarm optimization (‘inspired by the choreography of a bird flock’). The continuous geometry parameters (cross-sectional dimensions) and discrete ply angles of the box-beams are considered as design variables. The objective of the design problem is to achieve (a) specified stiffness value and (b) maximum elastic coupling. The presence of maximum elastic coupling in the composite box-beam increases the aero-elastic stability of the helicopter rotor blade. The multi-objective design problem is formulated as a combinatorial optimization problem and solved collectively using particle swarm optimization technique. The optimal geometry and ply angles are obtained for a composite box-beam design with ply angle discretizations of 10°, 15° and 45°. The performance and computational efficiency of the proposed particle swarm optimization approach is compared with various genetic algorithm based design approaches. The simulation results clearly show that the particle swarm optimization algorithm provides better solutions in terms of performance and computational time than the genetic algorithm based approaches.     

A surrogate-assisted particle swarm optimization algorithm based on efficient global optimization for expensive black-box problems

Evolutionary algorithms cannot effectively handle computationally expensive problems because of the unaffordable computational cost brought by a large number of fitness evaluations. Therefore, surrogates are widely used to assist evolutionary algorithms in solving these problems. This article proposes an improved surrogate-assisted particle swarm optimization (ISAPSO) algorithm, in which a hybrid particle swarm optimization (PSO) is combined with global and local surrogates. The global surrogate is not only used to predict fitness values for reducing computational burden but also regarded as a global searcher to speed up the global search process of PSO by using an efficient global optimization algorithm, while the local one is constructed for a local search in the neighbourhood of the current optimal solution by finding the predicted optimal solution of the local surrogate. Empirical studies on 10 widely used benchmark problems and a real-world structural design optimization problem of a driving axle show that the ISAPSO algorithm is effective and highly competitive.     

Global optimization of minimum weight truss topology problems with stress,displacement, and local buckling constraints using branch‐and‐bound

We present a convergent continuous branch‐and‐bound algorithm for global optimization of minimum weight truss topology problems with displacement, stress, and local buckling constraints. Valid inequalities which strengthen the problem formulation are derived. The inequalities are generated by solving well‐defined convex optimization problems. Computational results are reported on a large collection of problems taken from the literature. Most of these problems are, for the first time, solved with a proof of global optimality. Copyright © 2004 John Wiley & Sons, Ltd.     

求解约束优化问题的改进布谷鸟搜索算法

为了提高约束优化问题的求解精度和收敛速度,提出求解约束优化问题的改进布谷鸟搜索算法。首先分析了基本布谷鸟搜索算法全局搜索和局部搜索过程中的不足,对其中全局搜索和局部搜索迭代公式进行重新定义,然后以一定概率在最优解附近进行搜索。对12个标准约束优化问题和4个工程约束优化问题进行测试并与多种算法进行对比,实验结果和统计分析表明所提算法在求解约束优化问题上具有较强的优越性。     

铺设角度与铺层顺序对层合板稳定性的影响

以层合板结构的临界屈曲载荷系数最大化为优化目标,基于改进型模拟退火算法对层合板结构铺设角度和铺层顺序进行优化。由于层合板结构的铺层角度是离散变量,模拟退火算法适合求解离散变量的优化问题。利用模拟退火算法优化层合板铺层,在算法内采用并行计算、引入记忆功能同时设置双阈值终止准则,有效地提高了优化过程的收敛速度,同时避免优化过程中出现局部最优解。以临界屈曲载荷系数作为目标函数,选取复合材料层合板的铺设角度顺序为设计变量,采用改进的模拟退火算法得出复合材料层合板的最优铺设角度以及铺层顺序。     

An adaptive metamodel-based global optimization algorithm for black-box type problems

In this article, an adaptive metamodel-based global optimization (AMGO) algorithm is presented to solve unconstrained black-box problems. In the AMGO algorithm, a type of hybrid model composed of kriging and augmented radial basis function (RBF) is used as the surrogate model. The weight factors of hybrid model are adaptively selected in the optimization process. To balance the local and global search, a sub-optimization problem is constructed during each iteration to determine the new iterative points. As numerical experiments, six standard two-dimensional test functions are selected to show the distributions of iterative points. The AMGO algorithm is also tested on seven well-known benchmark optimization problems and contrasted with three representative metamodel-based optimization methods: efficient global optimization (EGO), GutmannRBF and hybrid and adaptive metamodel (HAM). The test results demonstrate the efficiency and robustness of the proposed method. The AMGO algorithm is finally applied to the structural design of the import and export chamber of a cycloid gear pump, achieving satisfactory results.     

Drilling path optimization by the particle swarm optimization algorithm with global convergence characteristics

Drilling path optimization is one of the key problems in holes-machining. This paper presents a new approach to solve the drilling path optimization problem belonging to discrete space, based on the particle swarm optimization (PSO) algorithm. Since the standard PSO algorithm is not guaranteed to be global convergent or local convergent, based on the mathematical model, the algorithm is improved by adopting the method to generate the stop evolution particle once again to obtain the ability of convergence on the global optimization solution. Also, the operators are proposed by establishing the Order Exchange Unit (OEU) and the Order Exchange List (OEL) to satisfy the need of integer coding in drilling path optimization. The experimentations indicate that the improved algorithm has the characteristics of easy realization, fast convergence speed, and better global convergence capability. Hence the new PSO can play a role in solving the problem of drilling path optimization.     

Trends,features, and tests of common and recently introduced global optimization methods

Global optimization techniques have been used extensively due to their capability in handling complex engineering problems. In addition to a number of well known global optimization techniques, many new methods have been introduced recently for various optimal design applications. In this work, a number of representative, well known and recently introduced global optimization techniques are closely examined and compared. The historical development, special features and trends on the development of global optimization algorithms are reviewed. Special attention is devoted to the recent developments of multidisciplinary design optimization algorithms based on effective metamodelling techniques. Commonly used benchmark optimization problems are used as test examples to reveal the pros and cons of these global optimization methods. A new meta-model based global optimization search method, introduced and improved recently by the authors, is also included in the tests and comparison.     

基于遗传算法的复合材料层合板削层结构铺层优化

针对应力变化较大的碳纤维增强复合材料层合板,提出削层结构铺层分级优化模式。通过将结构分解为若干子铺层并对各子铺层的位置、尺寸、铺层数以及铺层顺序进行优化,得到了满足强度和可制造性要求且质量最小的结构设计方案。该模式的第1、2级优化利用参考层对各子铺层位置及尺寸进行优化,第3级优化通过引入3次样条插值参数化方法对各子铺层层数和铺层顺序进行优化。参考层的引入可减少设计变量的数量,3次样条插值参数化方法可解决以铺层角为设计变量时设计变量数目不确定的问题。利用有限元方法对结构进行力学分析计算,并依据Tsai-Wu准则确定结构强度。在第2、3级优化中利用遗传算法对优化问题进行求解。算例计算表明:削层结构铺层分级优化模式结果合理可信。与均匀铺层方法结果比较可知:削层结构可有效减少结构质量。     

Ply level uncertainty effects on failure curves and optimal design of laminated composites using directional bat algorithm

The present study investigates the effect of both ply level material uncertainty and ply angle uncertainty on the failure envelope, strength characteristics and design of laminated composite. Multiple failure envelopes and distributions of the strength parameters are obtained for Tsai-Wu and maximum stress criteria using Monte Carlo simulation. A newly developed directional bat algorithm (dBA) is then used to perform the constrained design optimization of laminated composite for the first time while considering uncertainty effects. The effect of ply level uncertainty on failure envelopes and the corresponding optimal design of laminated composite structures is thus quantified.     

A global optimization algorithm for simulation-based problems via the extended DIRECT scheme

This article presents a global optimization algorithm via the extension of the DIviding RECTangles (DIRECT) scheme to handle problems with computationally expensive simulations efficiently. The new optimization strategy improves the regular partition scheme of DIRECT to a flexible irregular partition scheme in order to utilize information from irregular points. The metamodelling technique is introduced to work with the flexible partition scheme to speed up the convergence, which is meaningful for simulation-based problems. Comparative results on eight representative benchmark problems and an engineering application with some existing global optimization algorithms indicate that the proposed global optimization strategy is promising for simulation-based problems in terms of efficiency and accuracy.     

An evolutionary algorithm for global optimization based on self-organizing maps

In this article, a new population-based algorithm for real-parameter global optimization is presented, which is denoted as self-organizing centroids optimization (SOC-opt). The proposed method uses a stochastic approach which is based on the sequential learning paradigm for self-organizing maps (SOMs). A modified version of the SOM is proposed where each cell contains an individual, which performs a search for a locally optimal solution and it is affected by the search for a global optimum. The movement of the individuals in the search space is based on a discrete-time dynamic filter, and various choices of this filter are possible to obtain different dynamics of the centroids. In this way, a general framework is defined where well-known algorithms represent a particular case. The proposed algorithm is validated through a set of problems, which include non-separable problems, and compared with state-of-the-art algorithms for global optimization.     

不确定条件下复合材料结构的全局灵敏度分析

基于不确定条件下结构的全局灵敏度分析理论,研究了输入变量的不确定性对复合材料结构输出响应量方差和失效概率的影响。考虑材料力学性能、铺设角、铺层厚度及加载载荷的不确定性,利用基于方差和基于失效概率的全局灵敏度分析方法,对复合材料结构输出位移和强度比的不确定性来源进行分析,得到输入变量的全局灵敏度排序结果。对复合材料工字梁结构进行算例分析,验证了所得排序结果的有效性,为工程实际中复合材料结构稳定性优化设计提供了一定的指导。     

基于粒子群与聚类的多目标优化算法

针对粒子群优化算法容易陷入局部最优的问题,提出了一种基于粒子群优化与分解聚类方法相结合的多目标优化算法。算法基于参考向量分解的方法,通过聚类优选粒子策略来更新全局最优解。首先,通过每条均匀分布的参考向量对粒子进行聚类操作,来促进粒子的多样性。从每个聚类中选择一个具有最小聚合函数适应度值的粒子,以平衡收敛性和多样性。动态更新全局最优解和个体最优解,引导种群均匀分布在帕累托前沿附近。通过仿真实验,与4种粒子群多目标优化算法进行对比。实验结果表明,提出的算法在27个选定的基准测试问题中获得了20个反世代距离(IGD)最优值。     

基于退火算法的物流配送网的求优研究

模拟退火算法是一种启发式算法,是受到加热紧缩的退火过程所启发而提出来一种求解组合优化问题的一种逼近算法。算法要优于传统的贪婪算法,避免了陷入局部最优的可能,从而达到全局最优解。在物流配送网络中经常为有一些寻求最短路径等问题出现,为了能够达到最短、最优、最经济等,需要进行物流配送路径寻优。文中采用模拟退火算法进行一个示例的验证,效果证明可行。