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Hypervolume-Guided Decomposition for Parallel expensive multiobjective optimization

IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION 2024年第2期28卷 432-444页

作者： Zhao, Liang Zhang, Qingfu City Univ Hong Kong Dept Comp Sci Hong Kong Peoples R China City Univ Hong Kong Shenzhen Res Inst Shenzhen 518057 Peoples R China

The hypervolume metric is widely used to guide the search in multiobjective optimization. However, in parallel expensive multiobjective optimization, the hypervolume-based multipoint expected improvement (EI) suffers from high computational overhead and scales poorly with the batch size. To address this issue, we integrate hypervolume-based EI with the MOEA/D framework and propose a novel EI, named the expected direction-based hypervolume improvement (DirHV-EI). The DirHV-EI only measures the hypervolume improvement within each axis-parallel box induced by the modified Tchebycheff scalarization. Thus, it has a simple analytical expression that can be easily computed. Theoretical analysis indicates that the maximization of our proposed improvement function can help to maximize both the weighted hypervolume and the Tchebycheff improvement metrics. Using DirHV-EI, we design a decomposition-based Bayesian optimization algorithm for solving expensive multiobjective optimization problems. At each iteration, the MOEA/D is used to maximize the DirHV-EI values with respect to a number of direction vectors in a collaborative manner, and a number of candidate solutions can be obtained. Then, a submodularity-based greedy selection strategy is used to select multiple query points from the candidates. Experimental results on both benchmark instances and real-world problems show that our proposed algorithm is an efficient and effective method for parallel expensive multiobjective optimization.

关键词： Decomposition efficient global optimization (EGO) expected improvement (EI) expensive multiobjective optimization hypervolume

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Grid Classification-Based Surrogate-Assisted Particle Swarm optimization for expensive multiobjective optimization

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IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION 2024年第6期28卷 1867-1881页

作者： Yang, Qi-Te Zhan, Zhi-Hui Liu, Xiao-Fang Li, Jian-Yu Zhang, Jun South China Univ Technol Sch Comp Sci & Engn Guangzhou 510006 Peoples R China Nankai Univ Coll Artificial Intelligence Tianjin 300350 Peoples R China Hanyang Univ Ansan 15588 South Korea

SAEA, mainly including regression-based surrogate-assisted evolutionary algorithms (SAEAs) and classification-based SAEAs, are promising for solving expensive multiobjective optimization problems (EMOPs). Regression-based SAEAs usually use complex regression models to approximate the fitness evaluation, which will suffer from high-training costs to obtain a fine-accuracy surrogate. In contrast, classification-based SAEAs can achieve solution selection via coarse binary relations predicted by classifiers, thus avoiding high requirements in prediction accuracy and training costs. However, most of the binary relations in existing classification-based SAEAs mainly only involve convergence comparison whereas diversity maintenance is neglected. Considering the capacity of the grid technique in maintaining both convergence and diversity, we propose a new classification method called grid classification to discretize the objective space into grids and train a lightweight grid classification-based surrogate (GCS), for which low-training costs are needed. The GCS can evaluate the solution performance in terms of both convergence and diversity simultaneously according to the predicted grid locations, which opens up a new field for follow-up research on classification-based SAEAs. Following this, a GCS-assisted particle swarm optimization algorithm is proposed for tackling EMOPs. Experimental results on widely used benchmark problems (including high-dimensional EMOPs) and a 222-high-dimensional real-world application problem show its competitiveness in terms of both optimization performance and computational cost.

关键词： Training Iron Costs optimization Convergence Computational modeling Classification algorithms Evolutionary computation expensive multiobjective optimization grid classification particle swarm optimization (PSO) surrogate-assisted evolutionary algorithm (SAEA)

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An XGBoost-assisted evolutionary algorithm for expensive multiobjective optimization problems

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INFORMATION SCIENCES 2024年 666卷

作者： Mao, Feiqiao Chen, Ming Zhong, Kaihang Zeng, Jiyu Liang, Zhengping Shenzhen Univ Coll Comp Sci & Software Engn Shenzhen 518060 Peoples R China

Many expensive optimization problems exist in various real -world applications. However traditional evolutionary algorithms are inadequate for solving these problems directly. Surrogateassisted evolutionary algorithm (SAEA) can effectively solve expensive optimization problems using computationally inexpensive surrogate models. However, both the Kriging and ensemble models most SAEAs adopted have limited uncertainty of prediction, especially for expensive multiobjective optimization problems (EMOPs). To enhance the optimization performance of SAEA for EMOPs, this paper proposes a new XGBoost-assisted evolutionary algorithm, calling XGBEA. Specifically, XGBoost is used as the surrogate model, and a neighborhood density selection strategy based on a mixed population and archive space (NDS-MPA) is proposed to measure the uncertainties of individuals. XGBoost helps to best fit objective functions with different fitness landscapes. NDS-MPA selects non -dominated individuals with minimal density for re-evaluation, incorporating considerations of convergence, diversity and uncertainty. Experimental results on two well -studied benchmarks demonstrated the superiority of XGBEA over seven state-of-the-art SAEAs.

关键词： XGBoost expensive multiobjective optimization Surrogate-assisted Evolutionary algorithm Infill solutions selection

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Expected Improvement Matrix-Based Infill Criteria for expensive multiobjective optimization

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IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION 2017年第6期21卷 956-975页

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

The existing multiobjective expected improvement (EI) criteria are often computationally expensive because they are calculated using multivariate piecewise integrations, the number of which increases exponentially with the number of objectives. In order to solve this problem, this paper proposes a new approach to develop cheap-to-evaluate multiobjective EI criteria based on the proposed EI matrix (EIM). The elements in the EIM are the single-objective EIs that the studying point has beyond each Pareto front approximation point in each objective. Three multiobjective criteria are developed by combining the elements in the EIM into scalar functions in three different ways. These proposed multiobjective criteria are calculated using only 1-D integrations, whose number increases linearly with respect to the number of objectives. Moreover, all the three criteria are derived in closed form expressions, thus are significantly cheaper to evaluate than the state-of-the-art multiobjective criteria. The efficiencies of the proposed criteria are validated through 12 test problems. Besides the computational advantage, the proposed multiobjective EI criteria also show competitive abilities in approximating the Pareto fronts of the chosen test problems compared against the state-of-the-art multiobjective EI criteria.

关键词： Efficient global optimization ( EGO) expected improvement (EI) expensive multiobjective optimization Kriging model

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Dual-Fuzzy-Classifier-Based Evolutionary Algorithm for expensive multiobjective optimization

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IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION 2023年第6期27卷 1575-1589页

作者： Zhang, Jinyuan He, Linjun Ishibuchi, Hisao Southern Univ Sci & Technol Dept Comp Sci & Engn Guangdong Prov Key Lab Brain Inspired Intelligent Shenzhen 518055 Peoples R China Natl Univ Singapore Dept Elect & Comp Engn Singapore 117575 Singapore

multiobjective evolutionary algorithms (MOEAs) have been widely used to solve multiobjective optimization problems (MOPs). Conventional MOEAs usually require a large number of function evaluations (FEs) for evaluating the quality of solutions. However, only a limited number of FEs are affordable in many real-world optimization problems, where the FEs are computationally or economically expensive. The use of a large number of FEs decreases the effectiveness of MOEAs in solving these problems. This article proposes a dual-fuzzy-classifier-based surrogate model (DFC) and a DFC-based MOEA (DFC-MOEA) framework for expensive optimization problems. The DFC model is used for offspring preselection to choose high-quality offspring solutions and for categorization to divide unevaluated solutions into three categories. In the proposed framework, two fuzzy classifiers are built to predict the quality of each unevaluated solution. To strike a balance between convergence and diversity, one classifier is designed for predicting the dominance relation of unevaluated solutions (i.e., convergence), and another classifier is designed for predicting the crowdedness of unevaluated solutions (i.e., diversity). The integration of the proposed framework in three different types of MOEAs (i.e., a dominance-based MOEA, an indicator-based MOEA, and a decomposition-based MOEA) demonstrates its usefulness in handling expensive optimization problems. Comprehensive experiments on four well-known test suites and several real-world optimization problems demonstrate that the proposed framework is able to improve the performance of MOEAs under a limited number of FEs.

关键词： optimization Iron Linear programming Convergence Evolutionary computation Computational modeling Training expensive multiobjective optimization fuzzy classifiers multiobjective evolutionary algorithms (MOEAs) surrogate-based evolutionary algorithms

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A Batched expensive multiobjective optimization Based on Constrained Decomposition with Grids

A Batched Expensive Multiobjective Optimization Based on Con...

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IEEE Symposium Series on Computational Intelligence (SSCI)

作者： Zhang, Feng Cai, Xinye Fan, Zhun Nanjing Univ Aeronaut & Astronaut Coll Comp Sci & Technol Nanjing 210016 Jiangsu Peoples R China Shantou Univ Sch Engn Dept Elect Engn Shantou Guangdong Peoples R China

ISBN: (纸本)9781728124858

A batched constrained decomposition with grids (BCDG) is proposed for expensive multiobjective optimization problems. In this algorithm, each objective function is approximated by a Gaussian process model and CDG-MOEA is used to optimize a candidate population. Finally, we use Hypervolume Indicator to select some better points from the candidate population for evaluation. In the process of CDG-MOEA optimizing candidate solutions and using Hypervolume Indicator to select candidate solutions for evaluation, we use Gaussian process lower confidence bound criteria to consider the uncertainty of Gaussian process prediction. Experimental study on some special test problems shows that BCDG can effectively solve some special expensive multiobjective optimization problems.

关键词： expensive multiobjective optimization constrained decomposition with grids lower confidence bound criteria gaussian process model hypervolume

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Conjugate Surrogate for expensive multiobjective optimization

Conjugate Surrogate for Expensive Multiobjective Optimizatio...

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2023 IEEE Symposium Series on Computational Intelligence, SSCI 2023

作者： Yang, Qi-Te Luo, Liu-Yue Xu, Xin-Xin Chen, Chun-Hua Wang, Hua Zhang, Jun Zhan, Zhi-Hui School of Computer Science and Engineering South China University of Technology Guangzhou510006 China College of Artificial Intelligence Nankai University Tianjin300350 China School of Computer Science and Technology Ocean University of China Qingdao266100 China School of Software Engineering South China University of Technology Guangzhou510006 China Institute for Sustainable Industries and Liveable Cities Victoria University MelbourneVIC 8001 Australia Hanyang University Ansan15588 Korea Republic of

ISBN: (纸本)9781665430654

The Kriging surrogate (KS) has been widely used in surrogate-assisted multiobjective evolutionary algorithms (SAMOEAs) for solving expensive multiobjective optimization problems (EMOPs). Typically, when tackling an M-objective EMOP, a KS consists of M Kriging models, in which each model is used to approximate one objective function to replace the expensive fitness evaluation. Since such a KS is only efficient in solving low-dimensional EMOPs, the dimension reduction method has been adopted to construct the reduction surrogate (RS) to reduce training costs. However, both KS and RS can only approximate the mapping from variables to different objectives (i.e., objective function) but ignore the potential relationship between objectives. For practical applications, it is necessary to take into account the mapping between different objectives for the reliability of the surrogate. Therefore, we for the first time propose the concept of the conjugate surrogate (CS) and construct a simple CS to realize the approximated mapping from objectives to objectives. Different from KS or RS, all models in CS are conjugate symbiosis. In collaboration with RS, CS can not only benefit the light training cost, but also improve the convergence speed. Compared with five state-of-the-art SAMOEAs, the CS-assisted algorithm shows its effectiveness and competitiveness in solving EMOPs. © 2023 IEEE.

关键词： Evolutionary Computation expensive multiobjective optimization Kriging Surrogate-assisted

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expensive multiobjective Evolutionary optimization Assisted by Dominance Prediction

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IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION 2022年第1期26卷 159-173页

作者： Yuan, Yuan Banzhaf, Wolfgang Michigan State Univ Dept Comp Sci & Engn E Lansing MI 48824 USA Michigan State Univ BEACON Ctr Study Evolut Act E Lansing MI 48824 USA

We propose a new surrogate-assisted evolutionary algorithm for expensive multiobjective optimization. Two classification-based surrogate models are used, which can predict the Pareto dominance relation and theta-dominance relation between two solutions, respectively. To make such surrogates as accurate as possible, we formulate dominance prediction as an imbalanced classification problem and address this problem using deep learning techniques. Furthermore, to integrate the surrogates based on dominance prediction with multiobjective evolutionary optimization, we develop a two-stage preselection strategy. This strategy aims to select a promising solution to be evaluated among those produced by genetic operations, taking proper account of the balance between convergence and diversity. We conduct an empirical study on a number of well-known multiobjective and many-objective benchmark problems, over a relatively small number of function evaluations. Our experimental results demonstrate the superiority of the proposed algorithm compared with several representative surrogate-assisted algorithms.

关键词： Deep neural networks expensive multiobjective optimization many-objective optimization metamodeling surrogate-assisted evolutionary computation

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Evolutionary Algorithm with Ensemble Classifier Surrogate Model for expensive multiobjective optimization

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Transactions of Nanjing University of Aeronautics and Astronautics 2020年第S01期37卷 76-87页

作者： LAN Tian College of Computer Science and Technology Nanjing University of Aeronautics and AstronauticsNanjing 211106P.R.China

For many real-world multiobjective optimization problems,the evaluations of the objective functions are computationally *** 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 *** from ensemble learning,this paper proposes a multiobjective evolutionary algorithm with an ensemble classifier(MOEA-EC)for *** 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 *** extensive experimental studies have been conducted to verify the efficiency of MOEA-EC by comparing it with several advanced multiobjective expensive optimization *** experimental results show that MOEA-EC outperforms the compared algorithms.

关键词： multiobjective evolutionary algorithm expensive multiobjective optimization ensemble classifier surrogate model

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High-Dimensional expensive optimization by Classification-based multiobjective Evolutionary Algorithm with Dimensionality Reduction 62

High-Dimensional Expensive Optimization by Classification-ba...

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62nd Annual Conference of the Society-of-Instrument-and-Control-Engineers (SICE)

作者： Horaguchi, Yuma Nakata, Masaya Yokohama Natl Univ Fac Engn Kanagawa Japan

ISBN: (纸本)9784907764807

Surrogate-assisted multiobjective evolutionary algorithms (SAMOEAs) are a promising approach for solving expensive multiobjective optimization problems (EMOPs), wherein the number of function evaluations is extremely restricted due to expensive-to-evaluate objective functions. However, most SAEAs are not well-scaled to high-dimensional problems because the accuracy of surrogate models degrades as the problem dimension increases. This paper proposes a dimensionality reduction-based SAEA, which involves the following two strategies to address high-dimensional EMOPs. First, mapping high-dimensional training samples to a low-dimensional space in building surrogate models can boost the accuracy of surrogate models. Second, compared to approximation-based surrogate models, reliable classification-based models can be obtained under a few training samples. Accordingly, the proposed algorithm is designed to integrate a dimensionality reduction technique into an existing classification-based SAEA, MCEA/D. It builds classification models in low-dimensional spaces and then utilizes these models to estimate good solutions without expensive function evaluations. Experimental results statistically confirm that the proposed algorithm derives state-of-the-art performance in many experimental cases.

关键词： Surrogate-assisted evolutionary computation expensive multiobjective optimization dimensionality reduction classification

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