An Efficient Reliability-Based Optimization Method Utilizing High-Dimensional Model Representation and Weight-Point Estimation Method

The objective of reliability-based design optimization(RBDO)is to minimize the optimization objective while satisfying the corresponding reliability requirements.However,the nested loop characteristic reduces the efficiency of RBDO algorithm,which hinders their application to high-dimensional engineering problems.To address these issues,this paper proposes an efficient decoupled RBDO method combining high dimensional model representation(HDMR)and the weight-point estimation method(WPEM).First,we decouple the RBDO model using HDMR and WPEM.Second,Lagrange interpolation is used to approximate a univariate function.Finally,based on the results of the first two steps,the original nested loop reliability optimization model is completely transformed into a deterministic design optimization model that can be solved by a series of mature constrained optimization methods without any additional calculations.Two numerical examples of a planar 10-bar structure and an aviation hydraulic piping system with 28 design variables are analyzed to illustrate the performance and practicability of the proposed method.

Multi-Objective Equilibrium Optimizer for Feature Selection in High-Dimensional English Speech Emotion Recognition

Speech emotion recognition(SER)uses acoustic analysis to find features for emotion recognition and examines variations in voice that are caused by emotions.The number of features acquired with acoustic analysis is extremely high,so we introduce a hybrid filter-wrapper feature selection algorithm based on an improved equilibrium optimizer for constructing an emotion recognition system.The proposed algorithm implements multi-objective emotion recognition with the minimum number of selected features and maximum accuracy.First,we use the information gain and Fisher Score to sort the features extracted from signals.Then,we employ a multi-objective ranking method to evaluate these features and assign different importance to them.Features with high rankings have a large probability of being selected.Finally,we propose a repair strategy to address the problem of duplicate solutions in multi-objective feature selection,which can improve the diversity of solutions and avoid falling into local traps.Using random forest and K-nearest neighbor classifiers,four English speech emotion datasets are employed to test the proposed algorithm(MBEO)as well as other multi-objective emotion identification techniques.The results illustrate that it performs well in inverted generational distance,hypervolume,Pareto solutions,and execution time,and MBEO is appropriate for high-dimensional English SER.

Optimal Estimation of High-Dimensional Covariance Matrices with Missing and Noisy Data

The estimation of covariance matrices is very important in many fields, such as statistics. In real applications, data are frequently influenced by high dimensions and noise. However, most relevant studies are based on complete data. This paper studies the optimal estimation of high-dimensional covariance matrices based on missing and noisy sample under the norm. First, the model with sub-Gaussian additive noise is presented. The generalized sample covariance is then modified to define a hard thresholding estimator , and the minimax upper bound is derived. After that, the minimax lower bound is derived, and it is concluded that the estimator presented in this article is rate-optimal. Finally, numerical simulation analysis is performed. The result shows that for missing samples with sub-Gaussian noise, if the true covariance matrix is sparse, the hard thresholding estimator outperforms the traditional estimate method.

Multi-Label Feature Selection Based on Improved Ant Colony Optimization Algorithm with Dynamic Redundancy and Label Dependence

The world produces vast quantities of high-dimensional multi-semantic data.However,extracting valuable information from such a large amount of high-dimensional and multi-label data is undoubtedly arduous and challenging.Feature selection aims to mitigate the adverse impacts of high dimensionality in multi-label data by eliminating redundant and irrelevant features.The ant colony optimization algorithm has demonstrated encouraging outcomes in multi-label feature selection,because of its simplicity,efficiency,and similarity to reinforcement learning.Nevertheless,existing methods do not consider crucial correlation information,such as dynamic redundancy and label correlation.To tackle these concerns,the paper proposes a multi-label feature selection technique based on ant colony optimization algorithm(MFACO),focusing on dynamic redundancy and label correlation.Initially,the dynamic redundancy is assessed between the selected feature subset and potential features.Meanwhile,the ant colony optimization algorithm extracts label correlation from the label set,which is then combined into the heuristic factor as label weights.Experimental results demonstrate that our proposed strategies can effectively enhance the optimal search ability of ant colony,outperforming the other algorithms involved in the paper.

A Bi-population Cooperative Optimization Algorithm Assisted by an Autoencoder for Medium-scale Expensive Problems

This study presents an autoencoder-embedded optimization(AEO)algorithm which involves a bi-population cooperative strategy for medium-scale expensive problems(MEPs).A huge search space can be compressed to an informative lowdimensional space by using an autoencoder as a dimension reduction tool.The search operation conducted in this low space facilitates the population with fast convergence towards the optima.To strike the balance between exploration and exploitation during optimization,two phases of a tailored teaching-learning-based optimization(TTLBO)are adopted to coevolve solutions in a distributed fashion,wherein one is assisted by an autoencoder and the other undergoes a regular evolutionary process.Also,a dynamic size adjustment scheme according to problem dimension and evolutionary progress is proposed to promote information exchange between these two phases and accelerate evolutionary convergence speed.The proposed algorithm is validated by testing benchmark functions with dimensions varying from 50 to 200.As indicated in our experiments,TTLBO is suitable for dealing with medium-scale problems and thus incorporated into the AEO framework as a base optimizer.Compared with the state-of-the-art algorithms for MEPs,AEO shows extraordinarily high efficiency for these challenging problems,t hus opening new directions for various evolutionary algorithms under AEO to tackle MEPs and greatly advancing the field of medium-scale computationally expensive optimization.

Evolutionary Algorithm with Ensemble Classifier Surrogate Model for Expensive Multiobjective Optimization

For many real-world multiobjective optimization problems,the evaluations of the objective functions are computationally expensive.Such problems are usually called expensive multiobjective optimization problems(EMOPs).One type of feasible approaches for EMOPs is to introduce the computationally efficient surrogates for reducing the number of function evaluations.Inspired from ensemble learning,this paper proposes a multiobjective evolutionary algorithm with an ensemble classifier(MOEA-EC)for EMOPs.More specifically,multiple decision tree models are used as an ensemble classifier for the pre-selection,which is be more helpful for further reducing the function evaluations of the solutions than using single inaccurate model.The extensive experimental studies have been conducted to verify the efficiency of MOEA-EC by comparing it with several advanced multiobjective expensive optimization algorithms.The experimental results show that MOEA-EC outperforms the compared algorithms.

A Length-Adaptive Non-Dominated Sorting Genetic Algorithm for Bi-Objective High-Dimensional Feature Selection

As a crucial data preprocessing method in data mining,feature selection(FS)can be regarded as a bi-objective optimization problem that aims to maximize classification accuracy and minimize the number of selected features.Evolutionary computing(EC)is promising for FS owing to its powerful search capability.However,in traditional EC-based methods,feature subsets are represented via a length-fixed individual encoding.It is ineffective for high-dimensional data,because it results in a huge search space and prohibitive training time.This work proposes a length-adaptive non-dominated sorting genetic algorithm(LA-NSGA)with a length-variable individual encoding and a length-adaptive evolution mechanism for bi-objective highdimensional FS.In LA-NSGA,an initialization method based on correlation and redundancy is devised to initialize individuals of diverse lengths,and a Pareto dominance-based length change operator is introduced to guide individuals to explore in promising search space adaptively.Moreover,a dominance-based local search method is employed for further improvement.The experimental results based on 12 high-dimensional gene datasets show that the Pareto front of feature subsets produced by LA-NSGA is superior to those of existing algorithms.

Surrogate-assisted differential evolution using manifold learning-based sampling for highdimensional expensive constrained optimization problems

To address the challenges of high-dimensional constrained optimization problems with expensive simulation models,a Surrogate-Assisted Differential Evolution using Manifold Learning-based Sampling(SADE-MLS)is proposed.In SADE-MLS,differential evolution operators are executed to generate numerous high-dimensional candidate points.To alleviate the curse of dimensionality,a Manifold Learning-based Sampling(MLS)mechanism is developed to explore the high-dimensional design space effectively.In MLS,the intrinsic dimensionality of the candidate points is determined by a maximum likelihood estimator.Then,the candidate points are mapped into a low-dimensional space using the dimensionality reduction technique,which can avoid significant information loss during dimensionality reduction.Thus,Kriging surrogates are constructed in the low-dimensional space to predict the responses of the mapped candidate points.The candidate points with high constrained expected improvement values are selected for global exploration.Moreover,the local search process assisted by radial basis function and differential evolution is performed to exploit the design space efficiently.Several numerical benchmarks are tested to compare SADE-MLS with other algorithms.Finally,SADE-MLS is successfully applied to a solid rocket motor multidisciplinary optimization problem and a re-entry vehicle aerodynamic optimization problem,with the total impulse and lift to drag ratio being increased by 32.7%and 35.5%,respec-tively.The optimization results demonstrate the practicality and effectiveness of the proposed method in real engineering practices.

A State-Migration Particle Swarm Optimizer for Adaptive Latent Factor Analysis of High-Dimensional and Incomplete Data

High-dimensional and incomplete(HDI) matrices are primarily generated in all kinds of big-data-related practical applications. A latent factor analysis(LFA) model is capable of conducting efficient representation learning to an HDI matrix,whose hyper-parameter adaptation can be implemented through a particle swarm optimizer(PSO) to meet scalable requirements.However, conventional PSO is limited by its premature issues,which leads to the accuracy loss of a resultant LFA model. To address this thorny issue, this study merges the information of each particle's state migration into its evolution process following the principle of a generalized momentum method for improving its search ability, thereby building a state-migration particle swarm optimizer(SPSO), whose theoretical convergence is rigorously proved in this study. It is then incorporated into an LFA model for implementing efficient hyper-parameter adaptation without accuracy loss. Experiments on six HDI matrices indicate that an SPSO-incorporated LFA model outperforms state-of-the-art LFA models in terms of prediction accuracy for missing data of an HDI matrix with competitive computational efficiency.Hence, SPSO's use ensures efficient and reliable hyper-parameter adaptation in an LFA model, thus ensuring practicality and accurate representation learning for HDI matrices.

基于代理模型估值不确定度的昂贵多目标优化问题研究

针对代理模型辅助的多目标优化算法中个体不确定度之间相互冲突的问题,本文提出个体每个目标估值不确定的填充准则,同时,为了减少训练模型消耗的计算资源,提出基于非支配排序的样本选择算法。为了验证该算法的可行性,采用DTLZ和WFG测试函数进行测试,得出结果与近些年发表5种具有代表性的同类型算法进行对比,结果说明该算法可以有效的解决昂贵高维高目标优化问题。

三阶段自适应采样和增量克里金辅助的昂贵高维优化算法

代理辅助进化算法已广泛应用于求解代价高昂的多目标优化问题,但大多数由于代理模型的局限性而仅限于解决决策变量低维的问题。为了解决高维的昂贵多目标优化问题,提出了一种基于三阶段自适应采样策略的改进增量克里金辅助的进化算法。该算法使用改进的增量克里金模型来近似每个目标函数,此模型的超参数根据预测的不确定性进行自适应更新,降低计算复杂度的同时保证模型在高维上的准确性;此外,在模型管理方面提出一种三阶段自适应采样的策略,将采样过程分为不同的优化阶段以更有针对性的选择个体,能够首先保证收敛性,提高算法的收敛速度。为了验证算法的有效性,在包含各种特征的两组测试问题DTLZ(deb-thiele-laumanns-zitzler)、MaF(many-objective function)和路径规划实际工程问题上与最新的同类型算法进行实验对比,结果表明该算法在解决决策变量高维的昂贵多目标优化问题上具有较强的竞争力。

带隐藏约束昂贵黑箱问题的自适应代理优化方法

针对带隐藏约束的昂贵黑箱全局优化问题,提出采用自适应转换搜索策略的代理优化方法。在转换搜索子步中采用与已估值点个数相关的标准差在当前最优点附近通过随机扰动生成候选点,以更好地平衡局部搜索和全局搜索。为更好地近似真实黑箱目标函数,采用了自适应组合目标代理模型。在50个测试问题上进行了数值实验,计算结果说明了所提算法的有效性。

基于繁殖策略的求解昂贵约束单目标进化算法

实际工程优化中存在大量约束优化问题,且有一些优化问题目标函数和约束函数的评价非常耗时,导致该类问题无法直接使用传统优化算法求解。为此,为了在评价次数有限的情况下获得较好的可行解,针对昂贵单目标约束优化问题,为评价费时的目标函数和约束函数建立径向基函数(Radial Basis Function,RBF)预测模型,以及根据估值自适应选择个体的繁殖策略,以期能产生较好的可行解。在7个标准测试函数及3个工业测试函数上的测试结果表明,相比于其它现有针对昂贵约束问题的优化方法,本方法无需确保初始种群中必须有可行解,且能在优化目标和约束函数评价次数有限的情况下找到更好的解。

Y公司财务共享服务中心费用报销流程优化研究

随着财务共享服务中心不断发展,如何将区块链技术、大数据技术等新的信息技术应用于业务流程优化,以提高整体运行效率,逐渐成为研究的重点课题。文章以Y公司财务共享服务中心为例,对其费用报销业务流程进行优化。采用OCR光学字符识别技术提取发票中的信息,并自动填充到费用报销单据、触发预算控制,替代原人工填写报销单操作;嵌入智能催批指令,增加超时短信催批功能,对原有费用报销流程进行精简。模拟人工判断,将对费用报销单的审批控制活动嵌入系统,实现费用报销单据的智能自动审批。希望能够为正在实施财务共享服务中心的其他企业提供参考。

两阶段模型协同搜索的昂贵多目标进化优化

近年来,昂贵多目标优化问题的求解获得了越来越多的关注.然而,随着决策空间维度的升高,模型的有效性和准确性很难保证.因此,本文提出了一种两阶段模型协同搜索的昂贵多目标进化优化.在该方法中,每轮种群进化前构建全局模型,以辅助加快对最优解集的搜索.随后,利用搜索到的种群选择其邻域样本训练局部模型,对二者集成辅助算法进行进一步搜索.最后,提出基于不确定度的填充采样策略选点,进行真实评价.为了验证算法的有效性,将本文算法与4个算法分别在DTLZ和MaF测试集以及两个实际问题上进行比较,实验结果表明其具有良好的性能.

异构集成代理辅助的区间多模态粒子群优化算法

现实生活中的很多黑盒优化问题可归为高计算代价的多模态优化问题(Multimodal optimization problem,MMOP),即昂贵多模态优化问题(Expensive MMOP,EMMOP).在处理该类问题时,决策者希望以尽量少的计算代价(即尽量少的真实函数评价次数)找到多个高质量的最优解.然而,已有代理辅助的进化优化算法(Surrogate-assisted evolutionary algorithm,SAEA)很少考虑问题的多模态属性,运行一次仅可获得问题的一个最优解.鉴于此,研究一种异构集成代理辅助的区间多模态粒子群优化(Interval multimodal particle swarm optimization algorithm assisted by heterogeneous ensemble surrogate,IMPSO-HES)算法.首先,借助异构集成的思想构建一个由多个基础代理模型组成的模型池;随后,依据待评价粒子与已发现模态之间的匹配关系,从模型池中自主选择部分基础代理模型进行集成,并使用集成后的代理模型预测该粒子的适应值.进一步,为节约代理模型管理的代价,设计一种增量式的代理模型管理策略;为减少代理模型预测误差对算法性能的影响,首次将区间排序关系引入到进化过程中.将所提算法与当前流行的5种代理辅助进化优化算法和7种最先进的多模态优化算法进行对比,在20个测试函数和1个建筑节能实际问题上的实验结果表明,所提算法可以在较少计算代价下获得问题的多个高竞争最优解.

双阶段填充采样辅助的昂贵多目标优化

针对代理模型引导多目标优化算法,求解决策变量数量增多的昂贵多目标优化问题时,搜索效率较低的问题,提出一种双阶段填充采样辅助的昂贵多目标优化算法。第一阶段,利用一组方向向量引导产生靠近真实最优解集的样本,加快模型引导算法搜索;第二阶段,由代理模型估计获得估值误差,融合个体与样本之间相似性、个体估值收敛性,选择个体用于真实评价后填充样本集,实现模型性能的提升。在100维和200维的多目标基准测试问题上的实验结果表明,所提算法在同等有限资源内获得了比其它算法更为显著的优势。

自适应模型选用辅助的多种群进化算法

代理模型辅助的进化算法是求解目标函数评价昂贵优化问题的有效方法.在这类算法中,算法的搜索策略和填充采样策略是在有限评价次数下获得优化问题较好解的重要因素.为此,本文使用多种群搜索策略用于平衡种群搜索的多样性和收敛性,同时基于个体和训练样本之间目标函数值的距离自适应选择模型进行个体的目标函数值估计,以提高估值的准确度.为了验证算法的有效性,在CEC2005测试函数以及扩频雷达Polly编码优化设计问题上进行测试,并和现有求解昂贵优化问题的算法进行了结果对比.实验结果表明本文提出的算法在目标函数评价次数有限的情况下能够获得昂贵优化问题的较好解.

基于参考向量关联估计的离线多目标优化算法

很多实际工程和科学问题都是计算费时的多目标优化问题,这类问题中每个候选解的评价往往都非常费时,因此仅允许使用少量真实评价。论文采用离线数据驱动的进化算法求解计算费时多目标优化问题,以期节省优化时间。论文通过训练代理模型来估计候选解的收敛性,采用最近邻样本估计候选解与参考向量的关联关系,减少了使用目标估值计算候选解与参考向量夹角大小所产生的误差累积。使用DTLZ测试集验证论文算法的有效性,论文算法与离线数据驱动的优化算法MS-RV以及三个经典在线数据驱动优化算法进行对比,实验结果表明论文提出的算法在保证性能的前提下,可以减少使用真实的评价次数。

双模型驱动的多偏好策略自适应差分演化算法

为增强代理模型辅助进化算法对高维昂贵优化问题的求解性能,提出了一种双模型驱动的多偏好策略自适应差分演化算法。该算法基于全局和局部两种代理建模方法,有机融合了3种具有不同寻优偏好的进化策略。每次迭代,通过利用优化过程中最优解在线更迭反馈信息,以序贯方式自适应调整不同进化策略调用频次,以高效平衡算法的全局勘探和局部开采。为促进种群内个体间优秀信息共享,设计了一种精英个体驱动的差分扰动策略,以增量潜在优解区域的最优样本先验。通过处理26个不同规模的高维基准测试问题,结果表明,所提算法的收敛性能和优化效率较4种先进的同类型算法在至少17个测试问题上绝对占优。