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A surrogate-assisted Constrained Optimization evolutionary algorithm by Searching Multiple Kinds of Global and Local Regions

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IEEE TRANSACTIONS ON evolutionary COMPUTATION 2025年第1期29卷 61-75页

作者： Zeng, Yong Cheng, Yuansheng Liu, Jun Huazhong Univ Sci & Technol Sch Naval Architecture & Ocean Engn Wuhan 430074 Peoples R China

This article proposes a surrogate-assisted evolutionary algorithm to tackle expensive inequality-constrained optimization problems through global exploration and local exploitation. The algorithm begins with an exploration stage that involves sampling in three kinds of global regions: 1) the feasible region;2) the better-objective region;and 3) the converging region. Specifically, sampling in the uncertain feasible region mitigates issues caused by inaccurate objective surrogates. In addition, sampling in the uncertain region containing better-objective values than the current best-feasible solution reduces the risk of missing the global optimum due to inaccurate constraint surrogates. Moreover, sampling in the converging region facilitates quick convergence to the global feasible optimum. Following the exploration stage, promising feasible and infeasible solutions are further refined using local surrogate-based search strategies. To address the risk of missing the global optimum resulting from limited local region scope, the regions are adaptively extended if predicted infill points lie on the boundary. If an infill point is determined to showcase a better-objective value after accurate evaluation, a rewarding local search is performed within the local region. This exploration-exploitation process iterates until the computation budget is exhausted. Experimental results demonstrate that the proposed algorithm outperforms the selected state-of-the-art algorithms on the majority of tested problems.

关键词： Statistics Sociology Search problems Training Optimization evolutionary computation Linear programming Differential evolution (DE) expensive constrained optimization global and local search surrogate assisted evolutionary algorithm

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Un-evaluated solutions may be valuable in expensive optimization

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SWARM AND evolutionary COMPUTATION 2025年 94卷

作者： Hao, Hao Zhang, Xiaoqun Zhou, Aimin Shanghai Jiao Tong Univ Inst Nat Sci Shanghai 200240 Peoples R China East China Normal Univ Shanghai Inst AI Educ Shanghai 200062 Peoples R China

Expensive optimization problems (EOPs) are prevalent in real-world applications, where the evaluation of a single solution requires a significant amount of resources. In our study of surrogate-assisted evolutionary algorithms (SAEAs) in EOPs, we discovered an intriguing phenomenon. Because only a limited number of solutions are evaluated in each iteration, relying solely on these evaluated solutions for evolution can lead to reduced disparity in successive populations. This, in turn, hampers the reproduction operators' ability to generate superior solutions, thereby reducing the algorithm's convergence speed. To address this issue, we propose a strategic approach that incorporates high-quality, un-evaluated solutions predicted by surrogate models during the selection phase. This approach aims to improve the distribution of evaluated solutions, thereby generating a superior next generation of solutions. This work details specific implementations of this concept across various reproduction operators and validates its effectiveness using multiple surrogate models. Experimental results demonstrate that the proposed strategy significantly enhances the performance of surrogate-assisted evolutionary algorithms. Compared to mainstream SAEAs and Bayesian optimization algorithms, our approach incorporating the un-evaluated solution strategy shows a marked improvement.

关键词： Expensive optimization Unevaluated solutions surrogate assisted evolutionary algorithm Reproduction operators

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Expensive Optimization via Relation

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IEEE Transactions on evolutionary Computation 2025年

作者： Hao, Hao Zhang, Xiaoqun Zhou, Aimin Shanghai Jiao Tong University Institute of Natural Sciences Shanghai200240 China East China Normal University Shanghai Institute of AI for Education Shanghai200062 China

Expensive optimization problems pose significant challenges to traditional gradient-free optimization due to their costly evaluation overhead. surrogate model-assisted evolutionary optimization, which substitutes expensive evaluation functions with surrogate models, can effectively overcome these challenges. Designing an efficient surrogate model is the key issue in model-assisted evolutionary optimization. In recent years, establishing surrogate models through the relationships between solutions has become a promising modeling strategy, following regression and classification models. However, there has been a notable lack of systematic organization or comprehensive summary of relation models, which has impeded the structured development of this burgeoning research area. This paper seeks to address this gap by viewing relations as a perspective to outline the contextual development of the field, defining a robust framework for researching relation models, and reviewing typical strategies within each framework. Finally, it validates the effectiveness of numerous strategies through experiments. The entire collection of strategies will be open-sourced on GitHub1, facilitating greater participation from the research community in this field of study. © 1997-2012 IEEE.

关键词： expensive optimization relation model surrogate assisted evolutionary algorithm

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A surrogate Model assisted Estimation of Distribution algorithm with Mutil-acquisition Functions for Expensive Optimization

A Surrogate Model Assisted Estimation of Distribution Algori...

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IEEE Congress on evolutionary Computation (CEC)

作者： Hao, Hao Wang, Shuai Li, Bingdong Zhou, Aimin East China Normal Univ Shanghai Frontiers Sci Ctr Mol Intelligent Synth Sch Comp Sci & Technol Shanghai Inst AI Educ Shanghai Peoples R China

ISBN: (数字)9781665467087

ISBN: (纸本)9781665467087

The estimation of distribution algorithm (EDA) is an efficient heuristic method for handling black-box optimization problems since the ability for global population distribution modeling and gradient-free searching. However, the trial and error search mechanism relies on a large number of function evaluations, which is a considerable challenge under expensive black-box problems. Therefore, this article presents a surrogate assisted EDA with multi-acquisition functions. Firstly, a variable-width histogram is used as the global distribution model that focuses on promising areas. Next, the evaluated-free local search method improves the quality of new generation solutions. Finally, model management with multiple acquisitions maintains global and local exploration preferences. Several commonly used benchmark functions with 20 and 50 dimensions are adopted to evaluate the proposed algorithm compared with several state-of-the-art surrogate assisted evaluation algorithms (SAEAs) and Bayesian optimization method. In addition, a rover trajectories optimizing problem is used to verify the ability to solve complex problems. The experimental results demonstrate the superiority of the proposed algorithm over these comparison algorithms.

关键词： surrogate assisted evolutionary algorithm Estimation of distribution algorithm Acquisition functions

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Ecodesigning and improving performance of plugin hybrid electric vehicle in rolling terrain through multi-criteria optimisation of powertrain

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PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART D-JOURNAL OF AUTOMOBILE ENGINEERING 2022年第5期236卷 1019-1039页

作者： Bhattacharjee, Debraj Ghosh, Tamal Bhola, Prabha Martinsen, Kristian Dan, Pranab Indian Inst Technol Kharagpur Rajendra Mishra Sch Engn Entrepreneurship Kharagpur 721302 W Bengal India Norwegian Univ Sci & Technol Dept Mfg & Civil Engn IVB Gjovik Norway

This work presents an ecodesigning and operating performance improvement methodology in series-parallel Plugin hybrid electric vehicle (PHEV) in passenger car category, through optimisation of powertrain, considering gradeability overreaching rolling terrain. Designing involves consideration for power of prime movers and the geometric specification governing gear ratio, which is the teeth number. PHEV performance is measured in terms of various output characteristics, such as, fuel economy, emissions, vehicle weight, battery charge, maximum velocity and maximum acceleration etc. and such output indicators comprising both ecodesign and vehicle operating performance attributes, eleven in all, are considered. For optimisation, the design space is generated using NREL, ADVISOR simulator in accordance with Taguchi's method. Multi-criteria optimisation is used to converge the aforesaid output indicators into a single one using TOPSIS, MTOPSIS, Grey Relational Analysis and their surrogate assisted evolutionary algorithm (SAEA) based solutions to select the best from. Such design solutions are tested with UDDS driving cycle for performance analysis;reflecting superiority of SAEA based results. However, best values of output indicators are not from a single solution but are spread over these SAEAs. While, gradability is embedded in the model, its variation as supplemental factor, together with total ownership cost, are included, for extended modelling to ascertain the suitability amongst SAEAs. To extend the test for suitability beyond one driving cycle, also a combined one is formed by integrating two other, namely NEDC and 1015Prius with UDDS. The simulation experiment results from combined driving cycle also indicate preference in favour of MTOPSIS-SAEA model, complying upto 25% gradability for rolling terrain, substantially better than the reference model while also ensuring savings in fuel cost by about 60% over the entire ownership period besides reduction in greenhous

关键词： Plug-in hybrid electric vehicle fuel economy component sizing gradeability multi criteria decision making surrogate assisted evolutionary algorithm

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An adaptive Gaussian process based manifold transfer learning to expensive dynamic multi-objective optimization

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NEUROCOMPUTING 2023年第1期538卷

作者： Zhang, Xi Yu, Guo Jin, Yaochu Qian, Feng East China Univ Sci & Technol Key Lab Smart Mfg Energy Chem Proc Shanghai 200237 Peoples R China Nanjing Tech Univ Inst Intelligent Mfg Nanjing 211816 Peoples R China Bielefeld Univ Fac Technol Chair Nat Inspired Comp & Engn D-33619 Bielefeld Germany Univ Surrey Dept Comp Sci Guildford GU2 7XH England

Expensive dynamic multi-objective optimization problems (EDMOPs) is one kind of DMOPs where the objectives change over time and the function evaluations commonly involve computationally intensive simulations or costly physical experiments. Hence, the key to solve EDMOPs is to quickly and accurately track the time-varying Pareto optimal fronts under the limit of small number of function evaluations, in which how to augment enough training data to build informative surrogate models and manage the mod-els during the search process. To overcome the issue, we propose a transfer learning based surrogate assisted evolutionary algorithm (TrSA-DMOEA) to efficiently solve EDMOPs. Specifically, when a change occurs, we propose a knee point-based manifold transfer learning method based on geodesic flow kernel, which exploits the knowledge from previous high-quality knee solutions to augment the training data for building Gaussian process models, thereby improving the computational complexity and the quality of solutions. Moreover, to efficiently find the optima with limited budget of function evaluations, a novel surrogate-assisted mechanism based on an adaptive acquisition function is introduced, which achieves a balance between convergence and diversity by adaptively adjusting the weights of the angle -penalized distance and average uncertainty at different search stages. By comparing with state-of-the-art algorithms on widely used test problems, the experimental results demonstrate that the proposed method outperforms others and is able to efficiently solve EDMOPs.(c) 2023 Elsevier B.V. All rights reserved.

关键词： Dynamic multi-objective optimization Transfer learning Gaussian process surrogate assisted evolutionary algorithm

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Investigation of NOx emission under different burner structures with the optimized combustion model

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NEUROCOMPUTING 2022年第0期482卷 224-235页

作者： Yao, Qian Zhang, Yu Wang, Xinjie Tian, Zhou Hu, Guihua Du, Wenli East China Univ Sci & Technol Key Lab Smart Mfg Energy Chem Proc Minist Educ 130 Meilong Rd Shanghai 200237 Peoples R China Shanghai Engn Res Ctr Space Engine Shanghai Inst Space Prop Shanghai 201112 Peoples R China

As restrictions on NOx (nitrogen oxides) emission become increasingly stringent, many efforts have been put into the development of NOx control strategies. The burner structures of the heating furnace can affect NOx formation by the means of changing the flame temperature. To simulate the turbulent combustion process, the Steady Diffusion Flamelet (SDF) model is used and coupled with detailed mechanisms. It is found that some key flamelet parameters of the SDF model will greatly affect the accuracy of the simulation results. In this study, an efficient optimization procedure is proposed to optimize the combustion model parameters with the surrogate assisted evolutionary algorithm K-RVEA. The surrogate model is used to reduce the computational time of the optimization procedure. Using the optimized model parameters, the temperature field and the concentration fields obtained by the simulations are in good agreement with the measurements. Based on this, the investigation of the impact of the length of pilot wall and jet wall on NOx emission is carried out. The results show that the outlet NOx concentration reaches a local minimal value when the length of pilot wall and jet wall are equal. The length of monotonic increasing interval, where the outlet NOx concentration increases when increasing the length of the pilot wall, is 30 mm. If the length of pilot wall is relatively 30 mm longer than that of the jet wall, the outlet NOx concentration will be further reduced. The proposed optimization procedure and obtained results will benefit the improvement of the burner structure of the heating furnace. (C) 2021 Elsevier B.V. All rights reserved.

关键词： Computational fluid dynamics Burner structure surrogate assisted evolutionary algorithm Turbulent combustion NOx

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Regularity model based offspring generation in surrogate-assisted evolutionary algorithms for expensive multi-objective optimization

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SWARM AND evolutionary COMPUTATION 2024年 86卷

作者： Li, Bingdong Lu, Yongfan Qian, Hong Hong, Wenjing Yang, Peng Zhou, Aimin 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 Shanghai Frontiers Sci Ctr Mol Intelligent Synth Shanghai Peoples R China Shenzhen Univ Natl Engn Lab Big Data Syst Comp Technol Shenzhen 518060 Guangdong Peoples R China Southern Univ Sci & Technol Dept Stat & Data Sci Shenzhen 518055 Peoples R China Southern Univ Sci & Technol Dept Comp Sci & Engn Guangdong Prov Key Lab Brain Inspired Intelligent Shenzhen 518055 Peoples R China

evolutionary algorithms face significant challenges when it comes to solving expensive multi -objective optimization problems, which require costly evaluations. One of the most popular approaches to addressing this issue is to use surrogate models, which can replace the expensive real function evaluations with cheaper approximations. However, in many surrogate -assisted evolutionary algorithms (SAEAs), the process of offspring generation has not received sufficient attention. In this paper, we propose a novel framework for expensive multi -objective optimization called RM-SAEA, which utilizes a regularity model (RM) operator to generate offspring more effectively. The regularity model operator is combined with a general genetic algorithm operator to create a heterogeneous offspring generation module that can better approximate the Pareto front. Moreover, to overcome the data deficiency issue in expensive optimization scenarios, we employ a data augmentation strategy while training the regularity model. Finally, we embed three representative SAEAs into the proposed RM-SAEA to demonstrate its efficacy. Experimental results on several benchmark test suites with up to 10 objectives and real -world applications show that RM-SAEA achieves superior overall performance compared to eight state-of-the-art algorithms. By focusing on more effective offspring generation and addressing data deficiencies, our proposed framework is able to generate better approximations of the Pareto front and improve the optimization process in expensive multi -objective optimization scenarios.

关键词： Expensive optimization Multi-objective optimization Regularity model Pareto set learning surrogate assisted evolutionary algorithm

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