动态Kriging优化算法求解昂贵约束优化问题

针对昂贵单目标约束优化中真实模型计算费时且现有算法收敛速度慢的问题,提出了动态Krging优化算法以提高计算效率.该算法首先将所有约束条件转换为一个约束函数,然后采用拉丁超立方体采样(LHS)法进行采样,分别建立真实模型目标函数和约束函数的Kriging代理模型,同时结合真实模型对代理模型估计进行误差矫正,采用非支配个体选择、保留和替换机制不断更新样本库和Kriging代理模型.最后将进化最优种群代入真实模型计算其最优值.通过13个标准函数测试表明该算法具有较高的精确度和稳健性,明显减少了真实模型的评价次数.     

基于均值改进控制策略的昂贵约束并行代理优化算法

针对具有黑箱特性的昂贵约束优化问题及工程中计算资源利用率不高问题,提出了新的基于均值改进控制策略的并行代理优化算法.该算法为了减少仿真建模计算负担,选取Kriging近似模型对目标函数和约束函数进行近似估计.在Kriging模型基础上,利用均值改进与新增试验样本间的不等关系构建具有距离特性的控制函数.算法的均值改进控制策略通过控制函数调整最大改进值,实现样本设计空间的多点填充.算法适用范围:1)计算成本主要来自于仿真估计而非优化;2)复杂的工程或商业软件内部无法修改的昂贵仿真问题.数值算例和仿真案例表明:该算法可有效获取近似最优解,减少仿真试验次数的同时弱化均值改进准则的贪婪特性.相比于其他多点填充策略,均值改进控制策略可有效提升算法计算效率.此外,算法获取优化问题近似最优解的稳定性和精度均具有一定优势.     

基于Kriging代理模型的自适应序贯优化方法

提出了一种基于Kriging代理模型的自适应序贯优化算法。首先分析了代理模型使用不当引发的局部收敛问题,然后采用小生境微种群遗传算法求解EI函数来得到校正点,用以更新Kriging模型。这种选择校正点的方法使得优化过程避免陷入局部极值点。通过对4个典型函数优化实例进行实验,并与其他算法的结果作比较,其结果表明,新算法在解的精度、收敛性和收敛速度上表现出很好的性能,并且对所优化的问题没有特殊的要求,具有很强的工程实用价值。     

基于Kriging代理模型的加筋柱壳结构优化

基于Kriging代理模型,研究了加筋柱壳型飞行器舱体结构形状和尺寸优化方法.对加筋柱壳结构建立了三维参数化模型,参数化设计变量包括纵向加强筋数量、尺寸和环向加强筋的位置、尺寸,利用试验设计法选取设计变量采样点,使用有限元静力分析和线性屈曲分析得到采样点的应力、变形、屈曲强度因子等响应值,依据设计变量和响应建立Kriging代理模型,使用优化算法对代理模型进行寻优,获得最优设计结果.整个优化过程在Workbench平台中实现,最优结构比初始模型重量减少了11.91％.加筋柱壳结构优化结果分析表明,所使用优化方法优化效果明显、工作流程清晰、优化效率高,具有较大的工程应用价值.     

基于代理模型的武器装备体系优化算法研究

体系优化是装备体系研究的核心问题,但是基于仿真的武器装备体系优化方法存在寻优效率低、费用高昂的缺陷。本文结合武器装备体系优化问题的特点,提出基于代理模型的武器装备体系优化算法,其中选用Kriging模型作为代理模型,通过均匀设计方法生成初始样本点,运用EI函数进行代理模型更新,采用最速下降法进行迭代优化。示例验证表明,较之仿真方法及多项式响应曲面方法,该算法具有较高的寻优精度和收敛速度,对提高武器装备体系优化的效率具有较高的理论和实用价值。     

基于Kriging代理模型的序列优化

Kriging代理模型通过对某预测点周围的信息加权的线性组合来预估该点的未知信息,因其加权选择由最小化预估值的误差方差来确定而被视为最优的线性无偏估计。本文研究Kriging代理模型的序列优化,提出了一种新的加点规则—DH最大点插值法,并利用遗传算法的全局搜索能力搜索模型迭代的插值点,进而提高了Kriging模型的建模精度。     

异构集成代理辅助多目标粒子群优化算法

针对代理辅助进化算法在减少昂贵适应度评估时难以通过少量样本点构造高质量代理模型的问题,提出异构集成代理辅助多目标粒子群优化算法。该方法通过使用加权平均法将Kriging模型和径向基函数网络模型组合成高精度的异构集成模型,达到增强算法处理不确定性信息能力的目的。基于集成学习的两种代理模型分别应用于全局搜索和局部搜索,在多目标粒子群优化算法框架基础上,新提出的方法为每个目标函数自适应地构造了异构集成模型,利用其模型的非支配解来指导粒子群的更新,得出目标函数的最优解集。实验结果表明,所提方法提高了代理模型的搜索能力,减少了评估次数,并且随着搜索维度的增加,其计算复杂性也具有更好的可扩展性。     

结合特征扰动与分配策略的集成辅助多目标优化算法

代理模型利用近似预测代替算法对多目标优化问题的真实评价,大幅减少了算法寻优所需的真实适应度评估次数。为提高代理模型在求解高维问题时的准确性并降低计算开销,提出一种基于特征扰动与分配策略的集成辅助多目标优化算法。将径向基函数网络代理模型与支持向量机回归代理模型作为集成过程中的基模型,降低算法在高维问题上的计算开销。结合特征扰动与基于记忆的影响因子分配策略构建集成代理模型,提高集成准确性。使用集成预测值与不确定信息加权辅助管理集成代理模型,平衡全局搜索与局部探索,增强算法在目标空间中的寻优能力。实验结果表明,该算法在ZDT1~ZDT3和ZDT6测试问题上所得解集的分布性与收敛性相比经典算法更好,并且当决策变量维数增加时,使用集成代理模型相比于Kriging代理模型约减少了90%的适应度评估次数,同时可获得更准确的预测结果。     

结合Kriging和物理规划的多目标代理优化算法

遗传算法处理高耗时且具有黑箱性的工程优化问题效率不足。为了提高工程优化效率，结合Kriging代理优化和物理规划，提出了基于Kriging和物理规划的多目标代理优化算法。在处理多目标问题时，使用物理规划将多目标问题转换成单目标问题，再使用Kriging代理优化对单目标问题进行求解。通过两个多目标数值算例和一个工程实例对提出的算法进行验证。结果表明，提出的算法能够求出符合偏好设置的Pareto最优解，且算法的效率更高。     

Kriging代理模型在对地观测卫星系统优化中的应用

结构优化是对地观测卫星系统(Earth observation satellite system,EOSS)性能提高的关键,但其覆盖性能难以解析计算.为实现EOSS优化,提出了仿真优化的求解思路:构建Kriging代理模型对仿真数据进行拟合,采用代理模型最优和最大化期望提高相结合的机制选择更新点,并定义单位距离的函数改进对更新点进行过滤;提出了改进广义模式搜索算法求解代理模型,搜索步采用遗传算法和序列二次规划算法实现,筛选步采用不完全动态筛选.最后,通过仿真实例和对比实验验证了本文方法的有效性.     

Operation optimization of hydrocracking process based on Kriging surrogate model

Hydrocracking is one of the key technologies in oil refining. It has become a critical secondary processing unit in the refinery for improving the quality of product oil and increasing the light oil volume of production. As such, operation optimization for this process is significant. The basis of operation optimization is the model, and several mechanisms for hydrocracking models have been proposed and studied. However, these models usually require time consuming and exhibit low efficiency especially when applied to optimize operating conditions. In this study, a Kriging surrogate model of hydrocracking is developed based on the mechanism and industrial data. An optimization algorithm is then proposed to optimize operating conditions. The proposed algorithm integrates adaptive step-size global and local search strategy (GLSS) for minimizing the predictor. Simulation results indicate that this optimization strategy integrating GLSS and Kriging surrogate model obtains better revenue of the process production than conventional algorithms such as EGO, DDS, and CAND.     

A study into the potential of GPUs for the efficient construction and evaluation of Kriging models

The surrogate modelling technique known as Kriging, and its various derivatives, requires an optimization process to effectively determine the model’s defining parameters. This optimization typically involves the maximisation of a likelihood function which requires the construction and inversion of a correlation matrix dependent on the selected modelling parameters. The construction of such models in high dimensions and with a large numbers of sample points can, therefore, be considerably expensive. Similarly, once such a model has been constructed the evaluation of the predictor, error and other related design and model improvement criteria can also be costly. The following paper investigates the potential for graphical processing units to be used to accelerate the evaluation of the Kriging likelihood, predictor and error functions. Five different Kriging formulations are considered including, ordinary, universal, non-stationary, gradient-enhanced and multi-fidelity Kriging. Other key contributions include the derivation of the adjoint of the likelihood function for a fully and partially gradient-enhanced Kriging model as well as the presentation of novel schemes to accelerate the likelihood optimization via a mixture of single and double precision calculations and by automatically selecting the best hardware to perform the evaluations on.     

An evolving surrogate model-based differential evolution algorithm

Differential evolution (DE) is a simple and effective approach for solving numerical optimization problems. However, the performance of DE is sensitive to the choice of mutation and crossover strategies and their associated control parameters. Therefore, to achieve optimal performance, a time-consuming parameter tuning process is required. In DE, the use of different mutation and crossover strategies with different parameter settings can be appropriate during different stages of the evolution. Therefore, to achieve optimal performance using DE, various adaptation, self-adaptation, and ensemble techniques have been proposed. Recently, a classification-assisted DE algorithm was proposed to overcome trial and error parameter tuning and efficiently solve computationally expensive problems. In this paper, we present an evolving surrogate model-based differential evolution (ESMDE) method, wherein a surrogate model constructed based on the population members of the current generation is used to assist the DE algorithm in order to generate competitive offspring using the appropriate parameter setting during different stages of the evolution. As the population evolves over generations, the surrogate model also evolves over the iterations and better represents the basin of search by the DE algorithm. The proposed method employs a simple Kriging model to construct the surrogate. The performance of ESMDE is evaluated on a set of 17 bound-constrained problems. The performance of the proposed algorithm is compared to state-of-the-art self-adaptive DE algorithms: the classification-assisted DE algorithm, regression-assisted DE algorithm, and ranking-assisted DE algorithm.     

Multi-surrogate-based global optimization using a score-based infill criterion

This paper presents a new global optimization algorithm named MGOSIC to solve unconstrained expensive black-box optimization problems. In MGOSIC, three surrogate models Kriging, Radial Basis Function (RBF), and Quadratic Response Surfaces (QRS) are dynamically constructed, respectively. Additionally, a multi-point infill criterion is proposed to obtain new points in each cycle, where a score-based strategy is presented to mark cheap points generated by Latin hypercube sampling. According to their predictive values from the three surrogate models, the promising cheap points are assigned with different scores. In order to obtain the samples with diversity, a Max-Min approach is proposed to select promising sample points from the cheap point sets with higher scores. Simultaneously, the best solutions predicted by Kriging, RBF, and QRS are also recorded as supplementary samples, respectively. Once MGOSIC gets stuck in a local valley, the estimated mean square error of Kriging will be maximized to explore the sparsely sampled regions. Moreover, the whole optimization algorithm is carried out alternately in the global space and a reduced space. In summary, MGOSIC not only brings a new idea for multi-point sampling, but also builds a reasonable balance between exploitation and exploration. Finally, 19 mathematical benchmark cases and an engineering application of hydrofoil optimization are used to test MGOSIC. Furthermore, seven existing global optimization algorithms are also tested as contrast. The final results show that MGOSIC has high efficiency, strong stability, and better multi-point sampling capability in dealing with expensive black-box optimization problems.

     

GA与PSO解DE与LP问题的效率比较

遗传算法和粒子群算法都具有很强的搜索能力,在最优化问题中有着极其广泛的应用.文章针对常微分方程(DE)近似解和一般线性规划(LP)问题的解利用遗传算法和粒子群算法求解,深入的比较和分析了GA与PSO在这两种优化问题中的效率.在固定其他参数而调整群体数量的基础上比较了GA与PSO在微分方程近似解和LP问题解的优化能力.     

Automatically extracting T–S fuzzy models using cooperative random learning particle swarm optimization

This paper proposes a methodology for automatically extracting T–S fuzzy models from data using particle swarm optimization (PSO). In the proposed method, the structures and parameters of the fuzzy models are encoded into a particle and evolve together so that the optimal structure and parameters can be achieved simultaneously. An improved version of the original PSO algorithm, the cooperative random learning particle swarm optimization (CRPSO), is put forward to enhance the performance of PSO. CRPSO employs several sub-swarms to search the space and the useful information is exchanged among them during the iteration process. Simulation results indicate that CRPSO outperforms the standard PSO algorithm, genetic algorithm (GA) and differential evolution (DE) on the functions optimization and benchmark modeling problems. Moreover, the proposed CRPSO-based method can extract accurate T–S fuzzy model with appropriate number of rules.     

Time-series forecasting using a system of ordinary differential equations

This paper presents a hybrid evolutionary method for identifying a system of ordinary differential equations (ODEs) to predict the small-time scale traffic measurements data. We used the tree-structure based evolutionary algorithm to evolve the architecture and a particle swarm optimization (PSO) algorithm to fine tune the parameters of the additive tree models for the system of ordinary differential equations. We also illustrate some experimental comparisons with genetic programming, gene expression programming and a feedforward neural network optimized using PSO algorithm. Experimental results reveal that the proposed method is feasible and efficient for forecasting the small-scale traffic measurements data.     

Extended Gaussian Kriging for computer experiments in engineering design

Metamodeling or surrogate modeling is becoming increasingly popular for product design optimization in manufacture industries. In this paper, an extended Gaussian Kriging method is proposed to improve the prediction performance of widely used ordinary Kriging in engineering design. Unlike the forgoing approaches, the proposed method places a variance-varying Gaussian prior on the unknown regression coefficients in the mean model of Kriging and makes prediction at untried design points based on the principle of Bayesian maximum a posterior. The achieved regression mean model is adaptive, therefore capable of capturing more effectively the overall trend of computer responses and leading to a more accurate metamodel. Particularly, the regression coefficients in the mean model are estimated by a fast numerical algorithm, making extended Gaussian Kriging implemented roughly as efficient as ordinary Kriging. Experiment results on several examples are presented, showing remarkable improvement in prediction using extended Gaussian Kriging over ordinary Kriging and several other metamodeling methods.