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A surrogate-assisted differential evolution algorithm with a dual-space-driven selection strategy for expensive optimization problems

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COMPLEX & INTELLIGENT SYSTEMS 2025年第5期11卷 1-29页

作者： Liu, Hanqing Ren, Zhigang He, Chenlong Du, Wenhao Xi An Jiao Tong Univ Sch Automat Sci & Engn Xian Peoples R China Shaanxi Univ Sci & Technol Sch Elect & Control Engn Xian Peoples R China

Surrogate-assisted evolutionary algorithms (SAEAs) have shown great potential to solve computationally expensive optimization problems (EOPs). Their two key components, i.e., the optimizer and the surrogate model, both need to select solutions to promote further evolution and to update the model, respectively. However, the corresponding selection strategies are designed independently and mainly consider the predicted fitness of candidate solutions. Consequently, they can hardly complement each other well and are much likely to mislead the population evolution since the surrogate model necessarily has some prediction errors. Directing against this issue, this study proposes a unified dual-space-driven selection (DSDS) strategy and develops a new SAEA by taking differential evolution and radial basis function as the optimizer and the surrogate model, respectively. Besides the predicted fitness in objective space of candidate solutions, DSDS also considers their distribution in decision space by measuring how close they are to the geometric centers of their respective neighborhoods with a new indicator called neighborhood centrality (NC). It tries to select the solutions with good fitness and small NC values under a multi-objective sample selection framework and thus helps the resulting SAEA steadily search in multiple neighborhoods of excellent solutions. The performance of the new SAEA was extensively tested on six commonly used benchmark functions with five different dimensions from 20 to 200 as well as two typical real-word traffic signal optimization cases. Experimental results demonstrate that it possesses more competitive performance and stronger robustness than state-of-the-art SAEAs.

关键词： expensive optimization problem Surrogate-assisted evolutionary algorithm Differential evolution Radial basis function Selection strategy

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A survey on expensive optimization problems using differential evolution

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APPLIED SOFT COMPUTING 2025年 170卷

作者： Ren, Chongle Meng, Zhenyu Fujian Univ Technol Inst Artificial Intelligence Fuzhou Peoples R China

Many real-world problems that require substantial execution time and computational resources for evaluating candidate solutions can be termed expensive optimization problems (EOPs). The major challenge in solving EOPs lies in that evaluating the candidate solutions comes with a high and sometimes even prohibitive cost, thereby presenting notable obstacles for current optimization methods. Differential Evolution (DE), as a branch of evolutionary algorithms, has been widely used to tackle various optimization problems due to its fast convergence speed and powerful search capability. However, the performance of DE may deteriorate rapidly when solving EOPs where the number of function evaluations is limited. Recently, considerable efforts have been dedicated to improving DE-based algorithms for solving EOPs. However, there is a lack of a systematic survey on modifications to DE-based algorithms for tackling EOPs. By collecting and analyzing current DE- based algorithms, this survey presents a comprehensive overview of modifications on DE-based algorithms. The paper divides these modifications into three categories: framework improvement, surrogate-assisted approximation, and parallel and distributed implementation. According to the type of EOPs, existing DE- based algorithms are also classified and analyzed. Lastly, we present current challenges and future directions of employing DE-based algorithms for EOPs. By providing both novice and experienced researchers with a fresh perspective on utilizing DE-based algorithms for tackling EOPs, this survey aims to assist researchers in designing more efficient algorithms for EOPs.

关键词： Differential evolution expensive optimization problem Hybrid techniques Parallel and distributed techniques Surrogate model

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A Multi-Surrogate Assisted Multi-Tasking optimization Algorithm for High-Dimensional expensive problems

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ALGORITHMS 2025年第1期18卷 4-4页

作者： Li, Hongyu Chen, Lei Zhang, Jian Li, Muxi Jiangsu Univ Fac Civil Engn & Mech Zhenjiang 212013 Peoples R China Northwestern Polytech Univ Ocean Inst Taicang 215400 Peoples R China Tianjin Univ Sch Mech Engn Tianjin 300354 Peoples R China

Surrogate-assisted evolutionary algorithms (SAEAs) are widely used in the field of high-dimensional expensive optimization. However, real-world problems are usually complex and characterized by a variety of features. Therefore, it is very challenging to choose the most appropriate surrogate. It has been shown that multiple surrogates can characterize the fitness landscape more accurately than a single surrogate. In this work, a multi-surrogate-assisted multi-tasking optimization algorithm (MSAMT) is proposed that solves high-dimensional problems by simultaneously optimizing multiple surrogates as related tasks using the generalized multi-factorial evolutionary algorithm. In the MSAMT, all exactly evaluated samples are initially grouped to form a collection of clusters. Subsequently, the search space can be divided into several areas based on the clusters, and surrogates are constructed in each region that are capable of completely describing the entire fitness landscape as a way to improve the exploration capability of the algorithm. Near the current optimal solution, a novel ensemble surrogate is adopted to achieve local search in speeding up the convergence process. In the framework of a multi-tasking optimization algorithm, several surrogates are optimized simultaneously as related tasks. As a result, several optimal solutions spread throughout disjoint regions can be found for real function evaluation. Fourteen 10- to 100-dimensional test functions and a spatial truss design problem were used to compare the proposed approach with several recently proposed SAEAs. The results show that the proposed MSAMT performs better than the comparison algorithms in most test functions and real engineering problems.

关键词： multi-tasking optimization algorithm algorithm design dynamic ensemble of surrogates decision space partition expensive optimization problem

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Graph neural network-assisted evolutionary algorithm for rapid optimization design of shear-wall structures

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ADVANCED ENGINEERING INFORMATICS 2025年 65卷

作者： Fei, Yifan Qin, Sizhong Liao, Wenjie Guan, Hong Lu, Xinzheng Tsinghua Univ Dept Civil Engn Key Lab Civil Engn Safety & Durabil China Educ Minist Beijing 100084 Peoples R China Griffith Univ Sch Engn & Built Environm Gold Coast Campus Brisbane Qld 4222 Australia

When solving expensive optimization problems (EOPs), e.g., optimization design of shear-wall structures, conventional evolutionary algorithms (EAs) face a challenge of elevated costs related to fitness evaluation. On the other hand, surrogate-assisted evolutionary algorithms (SAEAs) can effectively reduce evaluation costs and are therefore widely used. However, when encountering new structure cases to be optimized, existing SAEAs require the effort of establishing datasets and training machine-learning surrogate models from scratch, which significantly lowers their efficiency. To address this issue, a novel graph neural network (GNN)-assisted evolutionary algorithm (GAEA) is proposed, which features a distinct framework and workflow from existing SAEAs. Then, a powerful GNN surrogate model is proposed, which is based on graph representations and exhibits good generalization abilities. After being trained on a large number of cases of the same type, the model can be applied to various new cases of that particular type. By integrating GNN with EA, GAEA can directly use the trained GNN surrogate model for fitness evaluation when dealing with new structure cases. Furthermore, a distance-based evaluation and updating strategy of surrogate models is innovatively proposed, which can efficiently correct the prediction error of GNN without retraining the model. The proposed GAEA is applied to the optimization design of reinforced concrete (RC) shear-wall structures, which is a typical EOP in the field of structural engineering. Numerical experiments show that: 1) for the same number of fitness evaluations, GAEA can achieve 64.4 % to 92.5 % of the optimization outcomes of typical EA or SAEA, respectively, with only 2.8 % to 33.2 % of their computational time;2) for the same optimization duration (10 min, 45 min, and 120 min), GAEA's optimization outcomes are superior to those of typical EA and SAEA, meeting the rapid optimization demands for shear-wall structures in the schem

关键词： Surrogate-assisted evolutionary algorithm Graph neural network optimization design Shear-wall structure expensive optimization problem

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Emulation-based adaptive differential evolution: fast and auto-tunable approach for moderately expensive optimization problems

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COMPLEX & INTELLIGENT SYSTEMS 2024年第3期10卷 3633-3656页

作者： Nishihara, Kei Nakata, Masaya Yokohama Natl Univ Fac Engn 79-1 Tokiwadai Yokohama Kanagawa 2408501 Japan

In the field of expensive optimization, numerous papers have proposed surrogate-assisted evolutionary algorithms (SAEAs) for a few thousand or even hundreds of function evaluations. However, in reality, low-cost simulations suffice for a lot of real-world problems, in which the number of function evaluations is moderately restricted, e.g., to several thousands. In such moderately restricted scenario, SAEAs become unnecessarily time-consuming and tend to struggle with premature convergence. In addition, tuning the SAEA parameters becomes impractical under the restricted budgets of function evaluations-in some cases, inadequate configuration may degrade performance instead. In this context, this paper presents a fast and auto-tunable evolutionary algorithm for solving moderately restricted expensive optimization problems. The presented algorithm is a variant of adaptive differential evolution (DE) algorithms, and is called emulation-based adaptive DE or EBADE. The primary aim of EBADE is to emulate the principle of sample-efficient optimization, such as that in SAEAs, by adaptively tuning the DE parameter configurations. Specifically, similar to Expected Improvement-based sampling, EBADE identifies parameter configurations that may produce expected-to-improve solutions, without using function evaluations. Further, EBADE incepts a multi-population mechanism and assigns a parameter configuration to each subpopulation to estimate the effectiveness of parameter configurations with multiple samples carefully. This subpopulation-based adaptation can help improve the selection accuracy of promising parameter configurations, even when using an expected-to-improve indicator with high uncertainty, by validating with respect to multiple samples. The experimental results demonstrate that EBADE outperforms modern adaptive DEs and is highly competitive compared to SAEAs with a much shorter runtime.

关键词： Adaptation Differential evolution Multi-population expensive optimization problem

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PRETTY: A parallel transgenerational learning-assisted evolutionary algorithm for computationally expensive multi-objective optimization

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INFORMATION SCIENCES 2023年第1期623卷 748-766页

作者： Zou, Mingyin Zhu, Xiaomin Tian, Ye Wang, Ji Chen, Huangke Natl Univ Def Technol Coll Syst Engineer Changsha 410073 Hunan Peoples R China Anhui Univ Inst Phys Sci & Informat Technol Hefei 230601 Anhui Peoples R China

Many real-world optimization problems, called computationally expensive optimization problems, often require a time-consuming fitness evaluation through computer simulation or neural network training. A persistent challenge is to obtain reasonable solutions to these problems quickly. In this study, we design a parallel transgenerational learning-assisted evolutionary algorithm, called PRETTY, to accelerate the search process using three novel mechanisms. First, we fuse the transgenerational learning mechanism with metaheuristic algorithms to reduce unnecessary fitness evaluations. Then, a Hypervolume-Cauchy (HVCauchy) algorithm is proposed to balance population convergence and diversity adaptively. Finally, a parallel-computing framework is proposed to fuse the transgenerational learning mechanism and the HV-Cauchy algorithm into a multipopulation evolutionary algorithm. To verify the performance of the proposed algorithm, empirical experiments are conducted on nine benchmarks and four real-world problems, including feature selection, critical node detection, flocking, and neural network training. In terms of execution time, the experimental results demonstrate that PRETTY has significant advantages over several expensive multi-objective algorithms. Furthermore, PRETTY can maintain population diversity and fast convergence while accelerating the computation. In particular, in tackling real-world problems that require expensive fitness calculations, PRETTY can reduce the execution time by more than five times while ensuring high-quality solutions.(c) 2022 Elsevier Inc. All rights reserved.

关键词： Adaptive convergence judgment expensive optimization problem Multipopulation evolutionary Transgenerational learning

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Evolutionary Computation for expensive optimization:A Survey

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Machine Intelligence Research 2022年第1期19卷 3-23页

作者： Jian-Yu Li Zhi-Hui Zhan Jun Zhang School of Computer Science and Engineering South China University of TechnologyGuangzhou 510006China Pazhou Laboratory Guangzhou 510330China Victoria University Melbourne 8001Australia

expensive optimization problem(EOP) widely exists in various significant real-world applications. However, EOP requires expensive or even unaffordable costs for evaluating candidate solutions, which is expensive for the algorithm to find a satisfactory solution. Moreover, due to the fast-growing application demands in the economy and society, such as the emergence of the smart cities, the internet of things, and the big data era, solving EOP more efficiently has become increasingly essential in various fields, which poses great challenges on the problem-solving ability of optimization approach for EOP. Among various optimization approaches, evolutionary computation(EC) is a promising global optimization tool widely used for solving EOP efficiently in the past decades. Given the fruitful advancements of EC for EOP, it is essential to review these advancements in order to synthesize and give previous research experiences and references to aid the development of relevant research fields and real-world applications. Motivated by this, this paper aims to provide a comprehensive survey to show why and how EC can solve EOP efficiently. For this aim, this paper firstly analyzes the total optimization cost of EC in solving EOP. Then, based on the analysis, three promising research directions are pointed out for solving EOP, which are problem approximation and substitution, algorithm design and enhancement, and parallel and distributed computation. Note that, to the best of our knowledge, this paper is the first that outlines the possible directions for efficiently solving EOP by analyzing the total expensive cost. Based on this, existing works are reviewed comprehensively via a taxonomy with four parts, including the above three research directions and the real-world application part. Moreover, some future research directions are also discussed in this paper. It is believed that such a survey can attract attention, encourage discussions, and stimulate new EC research ideas f

关键词： expensive optimization problem evolutionary computation evolutionary algorithm swarm intelligence particle swarm optimization differential evolution

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Model Selecting PSO-FA Hybrid for Complex Function optimization

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INTERNATIONAL JOURNAL OF SWARM INTELLIGENCE RESEARCH 2021年第3期12卷 215-232页

作者： Xiao, Heng Hatanaka, Toshiharu Osaka Univ Osaka Japan Univ Fukuchiyama Fukui Japan

Swarm intelligence is inspired by natural group behavior. It is one of the promising metaheuristics for black-box function optimization. Then plenty of swarm intelligence algorithms such as particle swarm optimization (PSO) and firefly algorithm (FA) have been developed. Since these swarm intelligence models have some common properties and inherent characteristics, model hybridization is expected to adjust a swarm intelligence model for the target problem instead of parameter tuning that needs some trial and error approach. This paper proposes a PSO-FA hybrid algorithm with a model selection strategy. An event-driven trigger based on the personal best update makes each individual do the model selection that focuses on the personal study process. By testing the proposed hybrid algorithm on some benchmark problems and comparing it with a simple PSO, the standard PSO 2011, FA, HFPSO to show how the proposed hybrid swarm averagely performs well in black-box optimization problems.

关键词： expensive optimization problem Firefly Algorithm Hybrid Algorithm Particle Swarm optimization Swarm Intelligence

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A survey of surrogate-assisted evolutionary algorithms for expensive optimization

JOURNAL OF MEMBRANE COMPUTING

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JOURNAL OF MEMBRANE COMPUTING 2024年 1-20页

作者： Liang, Jing Lou, Yahang Yu, Mingyuan Bi, Ying Yu, Kunjie Zhengzhou Univ Sch Elect & Informat Engn Zhengzhou Peoples R China State Key Lab Intelligent Agr Power Equipment Luoyang Peoples R China Henan Inst Technol Sch Elect Engn & Automat Xinxiang 453003 Peoples R China

In practical engineering applications, many problems involve high computational costs in evaluating the objective function during optimization. Traditional optimization algorithms may require a large number of evaluations to find the optimal solution, which leads to large consumption of computational resources. In recent years, surrogate-assisted evolutionary algorithms (SAEAs) have received increasing attention in solving computationally expensive optimization problems (EOPs). This paper provides a review of research on surrogate-assisted evolutionary algorithms. Firstly, it introduces the characteristics and challenges of expensive optimization problems. Secondly, it introduces the framework of SAEAs and the representative single-objective and multi-objective expensive optimization algorithms. Then, it presents methods for surrogate model construction and model management strategy, summarizes relevant literature, and analyzes the characteristics of different methods. Finally, it concludes existing challenges and future research directions in this topic. Through a comprehensive review and analysis of surrogate-assisted evolutionary algorithms, this paper provides essential references and guidance for further research.

关键词： expensive optimization problem Surrogate model Evolutionary algorithm Model management

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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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