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surrogate-assisted evolutionary algorithms for expensive combinatorial optimization: a survey

COMPLEX & INTELLIGENT SYSTEMS 2024年第4期10卷 5933-5949页

作者： Liu, Shulei Wang, Handing Peng, Wei Yao, Wen Xidian Univ Sch Artificial Intelligence Xian 710071 Shaanxi Peoples R China Chinese Acad Mil Sci Def Innovat Inst Beijing 100071 Peoples R China

As potent approaches for addressing computationally expensive optimization problems, surrogate-assisted evolutionary algorithms (SAEAs) have garnered increasing attention. Prevailing endeavors in evolutionary computation predominantly concentrate on expensive continuous optimization problems, with a notable scarcity of investigations directed toward expensive combinatorial optimization problems (ECOPs). Nevertheless, numerous ECOPs persist in practical applications. The widespread prevalence of such problems starkly contrasts the limited development of relevant research. Motivated by this disparity, this paper conducts a comprehensive survey on SAEAs tailored to address ECOPs. This survey comprises two primary segments. The first segment synthesizes prevalent global, local, hybrid, and learning search strategies, elucidating their respective strengths and weaknesses. Subsequently, the second segment furnishes an overview of surrogate-based evaluation technologies, delving into three pivotal facets: model selection, construction, and management. The paper also discusses several potential future directions for SAEAs with a focus towards expensive combinatorial optimization.

关键词： surrogate-assisted evolutionary algorithms Expensive combinatorial optimization surrogate modeling

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Balancing Between Time Budgets and Costs in surrogate-assisted evolutionary algorithms 18th

Balancing Between Time Budgets and Costs in Surrogate-Assist...

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

作者： Rodriguez, Cedric J. Bosman, Peter A. N. Alderliesten, Tanja Leiden Univ Med Ctr NL-2300 RC Leiden Netherlands Ctr Wiskunde & Informat NL-1090 GB Amsterdam Netherlands

ISBN: (纸本)9783031700675;9783031700682

For many real-world multi-objective optimisation problems, function evaluations are computationally expensive, resulting in a limited budget of function evaluations that can be performed in practice. To tackle such expensive problems, multi-objective surrogate-assisted evolutionary algorithms (SAEAs) have been introduced. Often, the performance of these EAs is measured after a fixed number of function evaluations (typically several hundreds) and complex surrogate models are found to be the best to use. However, when selecting an SAEA for a real-world problem, the surrogate building time, surrogate evaluation time, function evaluation time, and available optimisation time budget should be considered simultaneously. To gain insight into the performance of various surrogate models under different conditions, we evaluate an EA with and without four surrogate models (both complex and simple) for a range of optimisation time budgets and function evaluation times while considering the surrogate building and surrogate evaluation times. We use 55 BBOB-BIOBJ benchmark problems as well as a real-world problem where the fitness function involves a biomechanical simulation. Our results, on both types of problems, indicate that a larger hypervolume can be obtained with SAEAs when a function evaluation takes longer than 0.384 s (on the hardware we used). While we confirm that state-of-the-art complex surrogate models are mostly the best choice if up to several hundred function evaluations can be performed, we also observe that simple surrogate models can still outperform non-surrogate-assisted EAs if several thousand function evaluations can be performed.

关键词： Expensive optimisation surrogate-assisted evolutionary algorithms Real-world problems Biomechanical simulations

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Comparative Study on Different Types of surrogate-assisted evolutionary algorithms for High-Dimensional Expensive Problems

Comparative Study on Different Types of Surrogate-Assisted E...

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

作者： Qiao, Zhuo- Yin Yang, Qiang Gao, Xu-Dong Xu, Peilan Lu, Zhen-Yu School of Artificial Intelligence Nanjing University of Information Science and Technology Nanjing China

ISBN: (纸本)9798350337020

Expensive optimization problems (EOPs) are becoming more and more ubiquitous nowadays. To effectively solve such problems, surrogate-assisted evolutionary algorithms (SAEAs) have been developed. Specifically, a SAEA usually maintains a surrogate model to simulate the real objective function of an EOP. Such a surrogate model is trained based on real-evaluated solutions. Then, it is utilized to evaluate the fitness of individuals in the EA instead of the real expensive fitness evaluation. Though many SAEAs have been designed, they mainly concentrate on dealing with low-dimensional EOPs with fewer than 300 dimensions. Their performance on large-scale EOPs with more than 300 dimensions is unknown. To fill this gap, this paper conducts a comparative study on two types of state-of-the-art SAEAs with a total of four algorithms on four classical EOPs. To make comprehensive comparisons, we range the dimension size from 50 to 1000. As far as we know, this is the first time to assess SAEAs on EOPs with such a wide range of dimension sizes and such high dimensionality. The comparison results show that the optimization performance of the compared four SAEAs on high-dimensional EOPs with more than 500 dimensions is not as satisfactory as their performance on low-dimensional EOPs because of their slow convergence. Therefore, research on large-scale SAEAs for high-dimensional EOPs still deserves intensive attention. © 2023 IEEE.

关键词： evolutionary algorithms Expensive Optimization Problems Large-Scale Optimization surrogate Models surrogate-assisted evolutionary algorithms

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Rapid Multi-Objective Antenna Synthesis via Deep Neural Network surrogate-Driven evolutionary Optimization

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IEEE JOURNAL ON MULTISCALE AND MULTIPHYSICS COMPUTATIONAL TECHNIQUES 2025年 10卷 151-159页

作者： Singh, Praveen Panda, Soumyashree S. Dash, Jogesh C. Riscob, Bright Pathak, Surya K. Hegde, Ravi S. Indian Inst Technol Gandhinagar Dept Elect Engn Gandhinagar 382355 India Pandit Deendayal Energy Univ Dept Informat & Comp Technol Gandhinagar 382007 India Natl Inst Technol Rourkela Dept Elect & Commun Engn Rourkela 769008 India Inst Plasma Res Ahmadabad 382428 India

Antenna synthesis is becoming increasingly challenging with tight requirements for C-SWAP (cost, size, weight and power) reduction while maintaining stringent electromagnetic performance specifications. While machine learning approaches are increasingly being explored for antenna synthesis, they are still not capable of handling large shape sets with diverse responses. We propose a branched deep convolutional neural network architecture that can serve as a drop-in replacement for a full-wave simulator (it can predict the full spectral response of reflection co-efficient, input impedance and radiation pattern). We show the utility of such models in surrogate-assisted evolutionary optimization for antenna synthesis with arbitrary specification of targeted response. Specifically, we consider the large shape set defined by the set of 16-vertexes polygonal patch antennas and consider antenna synthesis by specifying independent constraints on return loss, radiation pattern and gain. In contrast to online surrogates, our approach is an offline surrogate that is objective-agnostic;trained once, it can be used over multiple optimizations whereby the model training costs become amortized across multiple synthesis requests. Our approach outperforms evolutionary optimizations relying on full-wave solver-based fitness estimation. Specifically, we report the design, fabrication and experimental characterization of three polygon-shaped patch antennas, each fulfilling different objectives (narrow band, dual-band & wide-band). The reported methodology enables rapid synthesis (in seconds), produces verifiable sound designs and is promising for furthering data-driven design methodologies for electromagnetic wave device synthesis.

关键词： Optimization Antennas Training Antenna radiation patterns Patch antennas Shape Encoding Electromagnetics Costs Geometry Antenna synthesis deep learning differential evolution multi-objective optimization offline surrogate models patch antenna surrogate-assisted evolutionary algorithms

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surrogate-assisted differential evolution: A survey

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SWARM AND evolutionary COMPUTATION 2025年 94卷

作者： Yu, Laiqi Meng, Zhenyu Kong, Lingping Snasel, Vaclav Pan, Jeng-Shyang Fujian Univ Technol Inst Artificial Intelligence Fuzhou Peoples R China VSB Tech Univ Ostrava Fac Elect Engn & Comp Sci Ostrava Czech Republic Nanjing Univ Informat Sci & Technol Sch Artificial Intelligence Nanjing Peoples R China

Expensive Optimization Problems (EOPs) area pressing challenge in real-world applications because they require high-quality solutions under tight computational budgets. To tackle this, numerous surrogate-assisted evolutionary algorithms (SAEAs) have been proposed that combine evolutionary algorithms (EAs) with surrogate models. Recently, researchers have conducted systematic surveys on SAEAs to better showcase their potential in solving EOPs. However, most of these efforts have focused on surrogate models, while largely overlooking EAs. This imbalance poses a challenge to the long-term development of SAEAs. Among various SAEAs, surrogate-assisted Differential Evolution (SADE) is widely favored by researchers due to the competitive performance of DE in evolutionary Computation. It has been broadly applied across diverse engineering and scientific domains. Nevertheless, there is still no work that systematically investigates the progress of SADE. To balance the research direction of SAEAs and fill the gap, this paper provides a comprehensive survey of SADE. Its contributions are summarized as follows: This paper first introduces the general optimization framework of SAEAs and briefly reviews the research directions and advances of its key components. Next, a comprehensive survey of SADE is conducted, covering commonly used surrogate models and DE algorithms. It also examines how existing SADE algorithms use DE, performance evaluation methods, and real-world applications. Finally, future challenges and potential research directions are discussed. We hope this work will draw attention to EAs and inspire further research to advance related fields.

关键词： Expensive optimization problems surrogate-assisted evolutionary algorithms surrogate-assisted differential evolution

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surrogate-assisted Differential Evolution with multiple sampling mechanisms for high-dimensional expensive problems

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INFORMATION SCIENCES 2025年 687卷

作者： Yu, Laiqi Meng, Zhenyu Fujian Univ Technol Inst Artificial Intelligence Fuzhou Peoples R China

Recently, surrogate-assisted evolutionary algorithms (SAEAs) have been widely employed in solving Expensive Optimization Problems (EOPs) due to their efficiency in obtaining satisfactory solutions with limited resources. By leveraging historical data to construct surrogate models for approximation, SAEAs can significantly reduce the number of expensive fitness evaluations for EOPs. A hierarchical SAEA optimization framework based on evolutionary sampling methods has achieved remarkable success in High-dimensional EOPs (HEOPs), which can effectively balance the exploration and exploitation capabilities. However, the majority of existing hierarchical SAEAs focus on either switching between different sampling strategies or enhancing a single sampling strategy, potentially overlooking the potential to improve multiple sampling strategies simultaneously. In this paper, we propose a surrogate-assisted Differential Evolution with Multiple Sampling Mechanisms (SADE-MSM) to tackle HEOPs, incorporating three sampling strategies with different mechanisms. The contributions of SADE-MSM are summarized as follows: 1) A centroid sampling method is applied before iterative optimization to enhance the early exploration ability;2) An improved global prescreening sampling strategy is introduced to balance the exploration and exploitation capabilities;3) A local search sampling with the adaptive optimal region strategy is proposed, significantly improving the exploitation ability. To validate the performance of SADEMSM, we compared it with the state-of-the-art SAEAs on benchmark problems with dimensions ranging from 30 to 500. Experimental results demonstrate that SADE-MSM has a significant performance superiority.

关键词： evolutionary sampling High-dimensional expensive optimization surrogate-assisted evolutionary algorithms

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Efficient Optimization of High-Quality Microwave Metasurface Absorbers Using a Random Forest-assisted Improved Estimation of Distribution Algorithm

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ADVANCED MATERIALS TECHNOLOGIES 2025年第0期

作者： Liu, Si-Xing Tao, Shi-Fei Wu, Fan Wang, Hao Nanjing Univ Sci & Technol Sch Elect & Opt Engn Nanjing 210094 Peoples R China Tianjin Univ Sch Sci Tianjin 300072 Peoples R China

The design of microwave metasurface absorbers (MMAs) is complicated because numerous design parameters require high-performance optimization algorithms. In this article, a random forest-assisted improved estimation of distribution algorithm (RFIEDA) is proposed. RFIEDA aims to obtain a high-quality MMA design with a limited number of exact expensive evaluations, where the geometric parameters and MMA unit patterns are both optimized. To address the mixed variable nature of geometric parameters and MMA unit patterns, a coding method is presented to transform geometric parameters into binary sequences, effectively making them discrete like MMA unit patterns. A random forest (RF) model is employed to establish a mapping between design variables and the objective function. Improved estimation of distribution algorithm (IEDA) is used to globally search for the combination of MMA unit patterns and geometric parameters, which cooperated with RF to accelerate the convergence speed. Moreover, a model management strategy is introduced to identify candidate solutions from the individuals generated by the IEDA for the exact expensive evaluations. The performance of RFIEDA is demonstrated by a broadband MMA and a triple-band MMA.

关键词： machine learning microwave metasurface absorbers random forest surrogate-assisted evolutionary algorithms

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NeuroLGP-SM: A surrogate-assisted Neuroevolution Approach Using Linear Genetic Programming 7th

NeuroLGP-SM: A Surrogate-Assisted Neuroevolution Approach Us...

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7th International Conference on Optimization and Learning

作者： Stapleton, Fergal Cody-Kenny, Brendan Galvan, Edgar Maynooth Univ Hamilton Inst CS Dept Naturally Inspired Comp Res Grp Maynooth Kildare Ireland Sema Baltimore MD USA

ISBN: (纸本)9783031779404;9783031779411

evolutionary algorithms are increasingly recognised as a viable computational approach for the automated optimisation of deep neural networks (DNNs) within artificial intelligence. This method extends to the training of DNNs, an approach known as neuroevolution. However, neuroevolution is an inherently resource-intensive process, with certain studies reporting the consumption of thousands of GPU days for refining and training a single DNN network. To address the computational challenges associated with neuroevolution while still attaining good DNN accuracy, surrogate models emerge as a pragmatic solution. Despite their potential, the integration of surrogate models into neuroevolution is still in its early stages, hindered by factors such as the effective use of high-dimensional data and the representation employed in neuroevolution. In this context, we address these challenges by employing a suitable representation based on Linear Genetic Programming, denoted as NeuroLGP, and leveraging Kriging Partial Least Squares. The amalgamation of these two techniques culminates in our proposed methodology known as the NeuroLGP-surrogate Model (NeuroLGP-SM). For comparison purposes, we also code and use a baseline approach incorporating a repair mechanism, a common practice in neuroevolution. Notably, the baseline approach surpasses the renowned VGG-16 model in accuracy. Given the computational intensity inherent in DNN operations, a singular run is typically the norm. To evaluate the efficacy of our proposed approach, we conducted 96 independent runs spanning a duration of 4weeks. Significantly, our methodologies consistently outperform the baseline, with the SM model demonstrating superior accuracy or comparable results to the NeuroLGP approach. Noteworthy is the additional advantage that the SM approach exhibits a 25% reduction in computational requirements, further emphasising its efficiency for neuroevolution.

关键词： Neuroevolution Linear Genetic Programming surrogate-assisted evolutionary algorithms

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A surrogate-assisted differential evolution for high-dimensional expensive constrained optimization problems with mixed-integer variables

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EXPERT SYSTEMS WITH APPLICATIONS 2025年 272卷

作者： Liu, Yuanhao Yang, Zan Jiang, Chen Xu, Danyang Qiu, Haobo Gao, Liang Huazhong Univ Sci & Technol Sch Mech Sci & Engn State Key Lab Intelligent Mfg Equipment & Technol Wuhan 430074 Peoples R China Tellhow Sci Tech Co Ltd Nanchang 330031 Peoples R China Nanchang Univ Jiangxi Prov Key Lab Light Alloy Nanchang 330031 Peoples R China Natl Ctr Technol Innovat Intelligent Design & Nume Wuhan 430074 Peoples R China

Recently, surrogate-assisted evolutionary algorithms (SAEAs) received a lot of attention due to their excellent performance in handling expensive constrained optimization problems (ECOPs). However, most of them can only be used for solving problems that are low-dimensional and with only continuous variables. Therefore, a surrogate-assisted differential evolution for high-dimensional ECOPs with mixed-integer variables (SADE-HDMI) is proposed in this paper. Firstly, a Multiple Local Extremum based Sampling (MLES) method is designed, in which two sampling strategies focusing on constraints and objective functions are utilized alternatively based on iterative information, so that the feasible region and high-quality feasible solutions can be efficiently located. Secondly, a Diverse Population Generation Operation for Mixed-Integer Variables (DPMI) is devised to avoid the population from falling into a local optimal region, where the diversity of the population is maintained by selecting solutions with more diversity and limiting the number of solutions with the same integer variables in the population. Convergence and diversity can be well balanced under the help of these two operations. Finally, the performance of SADE-HDMI is validated on fifteen benchmarks and a real-world optimization problem. The optimization results demonstrate that SADE-HDMI can locate feasible solutions with 100% probability on these 16 problems, and it is superior to or similar to other three state-of-the-art algorithms on 15 out of 16 problems.

关键词： Differential evolution Expensive constrained optimization problems surrogate-assisted evolutionary algorithms High-dimensional Mixed-integer Multiple local extremum-based sampling

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evolutionary Programming for High-Dimensional Constrained Expensive Black-Box Optimization Using Radial Basis Functions

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IEEE TRANSACTIONS ON evolutionary COMPUTATION 2014年第3期18卷 326-347页

作者： Regis, Rommel G. St Josephs Univ Dept Math Philadelphia PA 19131 USA

This paper develops a surrogate-assisted evolutionary programming (EP) algorithm for constrained expensive black-box optimization that can be used for high-dimensional problems with many black-box inequality constraints. The proposed method does not use a penalty function and it builds surrogates for the objective and constraint functions. Each parent generates a large number of trial offspring in each generation. Then, the surrogate functions are used to identify the trial offspring that are predicted to be feasible with the best predicted objective function values or those with the minimum number of predicted constraint violations. The objective and constraint functions are then evaluated only on the most promising trial offspring from each parent, and the method proceeds in the same way as in a standard EP. In the numerical experiments, the type of surrogate used to model the objective and each of the constraint functions is a cubic radial basis function (RBF) augmented by a linear polynomial. The resulting RBF-assisted EP is applied to 18 benchmark problems and to an automotive problem with 124 decision variables and 68 black-box inequality constraints. The proposed method is much better than a traditional EP, a surrogate-assisted penalty-based EP, stochastic ranking evolution strategy, scatter search, and CMODE, and it is competitive with ConstrLMSRBF on the problems used.

关键词： Black-box optimization constrained optimization evolutionary programming high-dimensional optimization radial basis functions surrogate-assisted evolutionary algorithms

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