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Efficient multi-objective CMA-ES algorithm assisted by knowledge-extraction-based variable-fidelity surrogate model

Chinese Journal of Aeronautics 2023年第6期36卷 213-232页

作者： Zengcong LI Kuo TIAN Shu ZHANG Bo WANG State Key Laboratory of Structural Analysis for Industrial Equipment Department of Engineering MechanicsDalian University of TechnologyDalian 116024China

To accelerate the multi-objective optimization for expensive engineering cases, a Knowledge-Extraction-based Variable-Fidelity surrogate-assisted Covariance Matrix Adaptation Evolution Strategy(KE-VFS-CMA-ES) is presented. In the first part, the KE-VFS model is established. Firstly, the optimization is performed using the low-fidelity surrogate model to obtain the Low-Fidelity Non-Dominated Solutions(LF-NDS). Secondly, aiming to obtain the High-Fidelity(HF) sample points located in promising areas, the K-means clustering algorithm and the space-filling strategy are used to extract knowledge from the LF-NDS to the HF space. Finally,the KE-VFS model is established by means of the obtained HF and LF sample points. In the second part, a novel model management based on the Modified Hypervolume Improvement(MHVI) criterion and pre-screening strategy is proposed. In each generation of KE-VFS-CMA-ES, excessive candidate points are firstly generated and then calculated by the MHVI criterion to find out a few potential points, which will be evaluated by the HF model. Through the above two parts,the promising areas can be detected and the potential points can be screened out, which contributes to speeding up the optimization process twofold. Three classic benchmark functions and a time-consuming engineering case of the aerospace integrally stiffened shell are studied, and results illustrate the excellent efficiency, robustness and applicability of KE-VFS-CMA-ES compared with other four known multi-objective optimization algorithms.

关键词： Covariance matrix adaptation evolution strategy Model management Multi-objective optimization surrogate-assisted evolutionary algorithm Variable-fidelity surrogate model

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Elite-driven surrogate-assisted CMA-ES algorithm by improved lower confidence bound method

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ENGINEERING WITH COMPUTERS 2023年第4期39卷 2543-2563页

作者： Li, Zengcong Gao, Tianhe Tian, Kuo Wang, Bo Dalian Univ Technol Dept Engn Mech Key Lab Digital Twin Ind Equipment State Key Lab Struct Anal Ind Equipment Dalian 116024 Peoples R China

To relieve the computational burden and improve the global optimizing ability of Covariance Matrix Adaptation Evolution Strategy (CMA-ES) for real-world expensive problems, an elite-driven surrogate-assisted CMA-ES (ES-CMA-ES) algorithm by the improved Lower Confidence Bound (ILCB) method is proposed in this paper. Firstly, the ILCB method is established by introducing the step size, which captures the trend of exploration and exploitation in CMA-ES, to control the uncertainty term of the ILCB formula adaptively. Next, based on the ILCB method, a novel model management consisting of the efficient pre-screening strategy and the competitive chaotic operator is developed. In each generation of ES-CMA-ES, a large number of candidate points are sampled first, and then a few of them with better ILCB predicted values are screened out by the efficient pre-screening strategy, aiming to enhance the sampling quality and accelerate the optimization convergence. Moreover, the local search is performed on the best-performing screened sample points utilizing the competitive chaotic operator, with the purpose of increasing the diversity of populations in ES-CMA-ES and avoiding being trapped in the local optima. By means of the above procedures of the model management, the elite sample points are finally obtained which will be evaluated by true fitness function in each generation of ES-CMA-ES. To verify the effectiveness of ES-CMA-ES, five known black-box optimization algorithms are employed to make a comparison. Firstly, seven typical numerical examples of 10-dimensional and 20-dimensional benchmark functions are carried out, respectively. Furthermore, a 20-dimensional engineering example of the aerospace variable-stiffness composite shell under combined loadings is studied. Results indicate the outstanding efficiency, global optimizing ability and applicability of the proposed ES-CMA-ES compared to its counterpart algorithms.

关键词： Covariance matrix adaptation evolution strategy surrogate-assisted evolutionary algorithm Lower confidence bound Pre-screening strategy Chaotic operator

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Dexterous workspace optimization for a six degree-of-freedom parallel manipulator based on surrogate-assisted constrained differential evolution

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APPLIED SOFT COMPUTING 2023年 139卷

作者： Pu, Huayan Cheng, Hao Wang, Gang Ma, Jie Zhao, Jinglei Bai, Ruqing Luo, Jun Yi, Jin Chongqing Univ Coll Mech & Vehicle Engn Chongqing 400044 Peoples R China Shanghai Univ Sch Mechatron Engn & Automat Shanghai 200444 Peoples R China

Parallel manipulators are increasingly applied because of their high stiffness, load capacity, and motion precision. However, the workspace of a parallel manipulator is relatively small compared to that of a serial manipulator. Therefore, appropriate structural designs of parallel manipulators for maximizing the workspace are essential. This paper studies the dexterous workspace maximization problem of a six-degree-of-freedom (DOF) parallel manipulator. First, a constrained optimization model is formulated, in which, the objective is to maximize the dexterous workspace, and the constraints include several kinematic and dynamic indicators, and some general structural limitations. To address the highly constrained, computationally-expensive problem, a surrogate-assisted two-phase constrained differential evolution method is proposed. Its effectiveness and efficiency are verified by the superior performance over two surrogate-free evolutionary methods: differential evolution (DE) and genetic algorithm (GA), and two surrogate-assisted state-of-the-art evolutionary methods: mod-ified constrained expected improvement (CEI) and the lower confidence bounding approach (PCLCB), on ten benchmark functions and the established real-word 6-DOF manipulator design optimization problem. & COPY;2023 Elsevier B.V. All rights reserved.

关键词： Work space optimization Parallel manipulator Constrained optimization surrogate-assisted evolutionary algorithm Differential evolution

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A surrogate-assisted differential evolution for expensive constrained optimization problems involving mixed-integer variables

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INFORMATION SCIENCES 2023年第1期622卷 282-302页

作者： Liu, Yuanhao Yang, Zan Xu, Danyang Qiu, Haobo Gao, Liang Huazhong Univ Sci & Technol Sch Mech Sci & Engn State Key Lab Digital Mfg Equipment & Technol Wuhan 430074 Peoples R China Nanchang Univ Sch Adv Mfg Nanchang 330031 Peoples R China Natl Ctr Technol Innovat Intelligent Design & Nume Wuhan 430074 Peoples R China

Many surrogate-assisted evolutionary algorithms (SAEAs) have been developed for expen-sive constrained optimization problems (ECOPs) with continuous variables. However, there exist some ECOPs that contain mixed-integer variables in real world engineering applica-tions. The mixed-integer variables make the feasible regions of ECOPs exhibit complex dis-joint characteristics, which brings two challenges for the existing methods, i.e., the classical surrogate-assisted pre-screening may easily fall into a local optimum and the population diversity tends to reduce with the influence of integer variables. For tackling these prob-lems, a surrogate-assisted differential evolution for solving ECOPs involving mixed -integer variables (SADE-MI) is proposed. Firstly, the mutation strategy DE/best/2 is used to balance the local and global characteristics of the candidate solutions. Secondly, an adaptive pre-screening operation where the information of the population is effectively employed to construct the distance constraints is designed to avoid excessive exploitation in local regions. Finally, by selecting diversely-located individuals and limiting the number of individuals with the same integer variables, a population diversity maintenance opera-tion is introduced to strengthen global exploration. Experimental studies on some bench-mark problems and engineering optimization cases demonstrate that SADE-MI outperforms other classical algorithms for solving ECOPs with mixed-integer variables.(c) 2022 Elsevier Inc. All rights reserved.

关键词： Adaptive pre-screening operation Differential evolution Expensive constrained optimization problems Mixed-integer Population diversity maintenance operation surrogate-assisted evolutionary algorithm

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ECdo: An Edge Computing Distributed Data-Driven evolutionary Optimization Platform

ECdo: An Edge Computing Distributed Data-Driven Evolutionary...

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2023 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2023

作者： Zeng, Qing-Ye Wei, Feng-Feng Guo, Xiao-Qi Chen, Wei-Neng School of Computer Science and Engineering South China University of Technology State Key Laboratory of Subtropical Building and Urban Science Guangzhou510006 China

ISBN: (纸本)9798350337020

surrogate-assisted evolutionary algorithms (SAEAs) have become a popular method to solve data-driven optimization problems (DOPs), which are common in industry. However, with the development of the Internet of Things, data are collected, processed, and stored in a distributed manner, leading a new optimization paradigm for SAEAs. To make SAEAs adapt to these distributed DOPs, this paper employs the edge computing paradigm to develop a platform that provides technical support for SAEAs with distributed structures, named ECdo. Specifically, the platform utilizes KubeEdge, an open-source edge computing framework, to mount the cluster and combines microservice interface design with the containerization strategy to offer a flexible deployment approach for distributed SAEAs. In addition, an efficient and stable internal communication mechanism is designed for the interaction between distributed components within the platform. To demonstrate the application of ECdo, we take the examples of a class of distributed DOPs, in which the objective and constraints are expensive and need to be approximated by accumulated data. These problems are known as distributed and expensive constrained optimization problems (DECOPs). We implement a distributed SAEA on ECdo to address DECOPs in real-world scenarios. Experiments show that the ECdo can provide the expected implementation for distributed SAEAs with good network tolerance under tough network conditions. © 2023 IEEE.

关键词： distributed optimization edge computing expensive optimization surrogate-assisted evolutionary algorithm

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Reliability-enhanced surrogate-assisted particle swarm optimization for feature selection and hyperparameter optimization in landslide displacement prediction

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COMPLEX & INTELLIGENT SYSTEMS 2023年第5期9卷 5417-5447页

作者： Wang, Yi Wang, Kanqi Zhang, Maosheng Gu, Tianfeng Zhang, Hui Northwest Univ Sch Informat Sci & Technol Xian 710127 Peoples R China Xi An Jiao Tong Univ Inst Disaster Prevent & Ecol Restorat Xian 710054 Peoples R China Northwest Univ Dept Geol Xian 710127 Peoples R China

Landslides are dangerous disasters that are affected by many factors. Neural networks can be used to fit complex observations and predict landslide displacement. However, hyperparameters have a great impact on neural networks, and each evaluation of a hyperparameter requires the construction of a corresponding model and the evaluation of the accuracy of the hyperparameter on the test set. Thus, the evaluation of hyperparameters requires a large amount of time. In addition, not all features are positive factors for predicting landslide displacement, so it is necessary to remove useless and redundant features through feature selection. Although the accuracy of wrapper-based feature selection is higher, it also requires considerable evaluation time. Therefore, in this paper, reliability-enhanced surrogate-assisted particle swarm optimization (RESAPSO), which uses the surrogate model to reduce the number of evaluations and combines PSO with the powerful global optimization ability to simultaneously search the hyperparameters in the long short-term memory (LSTM) neural network and the feature set for predicting landslide displacement is proposed. Specifically, multiple surrogate models are utilized simultaneously, and a Bayesian evaluation strategy is designed to integrate the predictive fitness of multiple surrogate models. To mitigate the influence of an imprecise surrogate model, an intuitional fuzzy set is used to represent individual information. To balance the exploration and development of the algorithm, intuition-fuzzy multiattribute decision-making is used to select the best and most uncertain individuals from the population for updating the surrogate model. The experiments were carried out in CEC2015 and CEC2017. In the experiment, RESAPSO is compared with several well-known and recently proposed SAEAs and verified for its effectiveness and advancement in terms of accuracy, convergence speed, and stability, with the Friedman test ranking first. For the landslid

关键词： Computationally expensive problems surrogate-assisted evolutionary algorithm Particle swarm optimization Hyperparameter optimization Feature selection

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A surrogate-assisted Partial Optimization for Expensive Constrained Optimization Problems 18th

A Surrogate-Assisted Partial Optimization for Expensive Cons...

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18th International Conference on Parallel Problem Solving from Nature (PPSN)

作者： Nishihara, Kei Nakata, Masaya Yokohama Natl Univ Yokohama Kanagawa 2408501 Japan

ISBN: (纸本)9783031700675;9783031700682

surrogate-assisted evolutionary algorithms (SAEAs) are gradually gaining attention as a method for solving expensive optimization problems with inequality constraints. Most SAEAs construct a surrogate model for each objective/constraint function and then aggregate approximation functions of constraints to estimate the feasibility of unevaluated solutions. However, because of the aggregation, the differences in the scales among constraints are ignored. Constraints with smaller scales do not benefit from constraint handling techniques as much as larger constraints, while the effects of handling constraints with larger scales scatter to the other many constraints. This results in an inefficient constraint optimization. Accordingly, this work proposes a new SAEA that partially optimizes each objective/constraint, namely surrogate-assisted partial optimization (SAPO). Solutions with better values of objective/constraint are selected from the evaluated solutions as the parent solutions and a focused objective/constraint is independently optimized using surrogate models one by one. Experimental results reveal the superiority of SAPO compared to the state-of-the-art SAEAs on a single-objective optimization problem suite with inequality constraints under an expensive optimization scenario.

关键词： surrogate-assisted evolutionary algorithm Constrained Optimization Problem Expensive Optimization Problem Radial Basis Function Network Differential Evolution

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A Kriging-assisted evolutionary algorithm with multiple infill sampling for expensive many-objective optimization

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ENGINEERING APPLICATIONS OF ARTIFICIAL INTELLIGENCE 2024年 135卷

作者： Zhu, Qingling Kang, Gaoli Wu, Xunfeng Lin, Qiuzhen Tang, Huimei Chen, Jianyong Shenzhen Univ Coll Comp Sci & Software Engn Shenzhen Peoples R China

surrogate -assisted evolutionary algorithms (SAEAs) have been extensively used to solve computationally expensive multi -objective optimization problems (MOPs) as they can obtain a set of satisfyingly optimal solutions while remaining within a limited computational budget. Nevertheless, the expensive MOPs with more than three objectives have received little attention, and most existing SAEAs fail to achieve satisfactory results when solving them. Therefore, to fill this research gap, a Kriging-assisted evolutionary algorithm with multiple infill sampling for solving expensive many -objective optimization problems is proposed. In this paper, to balance exploration and exploitation, a new environmental selection operator is proposed, which is composed of three procedures conducted consecutively. In addition, a new multiple infill sampling strategy is proposed to select the most representative solutions for real function evaluations and model updates. Furthermore, to limit the computational costs of constructing/updating the surrogate model, a new archive update strategy is proposed to maneuver the training data set. In experiments, our method is verified on some benchmark problems. The experimental results demonstrate that the proposed algorithm shows promising performance when compared with four state-of-the-art SAEAs for solving expensive many -objective optimization problems.

关键词： surrogate-assisted evolutionary algorithm Kriging model Infill sampling Expensive many-objective optimization

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Accelerating surrogate assisted evolutionary algorithms for expensive multi-objective optimization via explainable machine learning

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SWARM AND evolutionary COMPUTATION 2024年 88卷

作者： Li, Bingdong Yang, Yanting Liu, Dacheng Zhang, Yan Zhou, Aimin Yao, Xin East China Normal Univ Shanghai Inst AI Educ Shanghai 200062 Peoples R China East China Normal Univ Sch Comp Sci & Technol Shanghai 200062 Peoples R China Chinese Acad Sci Aerosp Informat Res Inst Dept Space Microwave Remote Sensing Syst Beijing 100090 Peoples R China Univ Chinese Acad Sci Sch Elect Elect & Commun Engn Beijing 100039 Peoples R China Shanghai Frontiers Sci Ctr Mol Intelligent Synth Shanghai Peoples R China Lingnan Univ Sch Data Sci Hong Kong Peoples R China Univ Birmingham Sch Comp Sci Birmingham England

A series of surrogate-assisted evolutionary algorithms (SAEAs) have been proposed to handle expensive multiobjective optimization problems (EMOPs). However, the surrogate of these SAEAs is underutilized to a large extent, which limits the search efficiency of these algorithms. To be specific, existing algorithms do not sufficiently exploit the estimated solution quality information from the surrogate models during offspring generation. To address this issue, this paper proposes an SAEA framework named EXO-SAEA (EXplanation Operator based surrogate-assisted evolutionary algorithm). First, it divides the current population into two populations according to the a priori knowledge from the surrogate model. Then, for each solution in the first population, EXO-SAEA employs the SHapley Additive exPlanations (SHAP) model to estimate the contribution of each decision variable to the fitness values. After that, the Shapley values are then normalized for the offspring generation of the first population, while the second population uses generic GA operators. Two representative surrogate-assisted evolutionary algorithms are used to instantiate the proposed framework. Experimental results on the synthetic benchmark problems and three real -world problems involving six state -of -the -art algorithms demonstrate the effectiveness of the proposed framework.

关键词： Explainable machine learning Crossover operator Expensive optimization Multi-objective optimization surrogate-assisted evolutionary algorithm

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evolutionary multiobjective optimization assisted by scalarization function approximation for high-dimensional expensive problems

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SWARM AND evolutionary COMPUTATION 2024年 86卷

作者： Horaguchi, Yuma Nishihara, Kei Nakata, Masaya Yokohama Natl Univ Fac Engn Tokiwadai 79-5 Yokohama Kanagawa 2408501 Japan

surrogate -assisted evolutionary algorithms (SAEAs) are a promising approach for solving expensive multiobjective optimization problems, but they often cannot address high -dimensional problems. Although one common approach to overcoming this challenge is to construct reliable surrogates, their accuracy inevitably deteriorates in a high -dimensional search space. Thus, this paper presents a novel SAEA based on scalarization function approximation, which is designed to strengthen its robustness against this deterioration. The proposed algorithm constructs an approximation model for each scalarization function defined in a decompositionbased framework. Each decomposed problem is then solved using multiple independent models trained for its neighbor problems. The intent is to decrease the risk of search performance degradations caused by unreliable approximations and retain the redundancy of the surrogate -assisted search to hedge the risk of over -fitting. Furthermore, each approximation model is adapted to a promising region of its corresponding decomposed problem to reduce the complexity of model fitting given a limited number of training samples. Experimental results show that the proposed algorithm is competitive with state-of-the-art SAEAs adapted for high -dimensional problems.

关键词： surrogate-assisted evolutionary algorithm Multiobjective optimization Scalarization function

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