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A multipopulation evolutionary framework with Steffensen's method for dynamic multiobjective optimization problems

MEMETIC COMPUTING 2021年第4期13卷 477-495页

作者： Liu, Tianyu Cao, Lei Wang, Zhu Shanghai Maritime Univ Sch Informat Engn Shanghai Peoples R China Shanghai Maritime Univ Sch Logist Engn Shanghai Peoples R China

dynamic multiobjective optimization problems (DMOPs) require the evolutionary algorithms that can track the moving Pareto-optimal fronts efficiently. This paper presents a dynamic multiobjective evolutionary framework (DMOEF-MS), which adopts a novel multipopulation structure and Steffensen's method to solve DMOPs. In DMOEF-MS, only one population deals with the original DMOP, while the others focus on single-objective problems that are generated by the weighted summation of the original DMOP. Then, Steffensen's method is used to control the evolving process in two ways: prediction and diversity-maintenance. Particularly, the prediction strategy is devised to predict the next promising positions for the individuals that handle single-objective problems, and the diversity-maintenance strategy is used to increase population diversity before the environment changes and reinitialize the multiple populations after the environment changes. This paper gives a comprehensive comparison of DMOEF-MS with some state-of-the-art DMOEAs on 14 DMOPs and the experimental results demonstrate the effectiveness of the proposed algorithm.

关键词： dynamic multiobjective optimization Steffensen's method Multipopulation structure Prediction strategy Diversity-maintenance strategy

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A Framework Based on Historical Evolution Learning for dynamic multiobjective optimization

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IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION 2024年第4期28卷 1127-1140页

作者： Yu, Kunjie Zhang, Dezheng Liang, Jing Qu, Boyang Liu, Mengnan Chen, Ke Yue, Caitong Wang, Ling Zhengzhou Univ Sch Elect & Informat Engn Zhengzhou 450001 Peoples R China Henan Inst Technol Sch Elect Engn & Automat Xinxiang 453003 Peoples R China Zhongyuan Univ Technol Sch Elect & Informat Zhengzhou 450007 Peoples R China Chassis Transmiss Technol Inst State Key Lab Intelligent Agr Power Equipment Luoyang 471000 Peoples R China Tsinghua Univ Dept Automat Beijing 100084 Peoples R China

dynamic multiobjective optimization problems (DMOPs) are widely encountered in real-world applications and have received considerable attention in recent years. During the process of solving DMOPs, tracking the constantly changing Pareto optimal set (POS) quickly is the main task, and numerous methods have been proposed to achieve this task from different perspectives. However, how to improve the evolution of static optimizers via using historical information from past environments gets little attention. In fact, with adequate historical evolution information to learn, the trend of population evolution in the historical environments is promising to guide the future evolution and thus enhance the search ability. Therefore, in this article, a historical evolution learning-based framework is proposed to assist the static optimizers in fully using the historical evolution direction and POSs distribution. Specifically, two new models are designed with a purpose of generating offsprings and environmental selection, respectively. For enhancing the contribution of offsprings, a direction guidance model is developed to guide the offsprings according to the direction tendency of historical evolution. Furthermore, to improve the robustness of static optimizers and avoid the disturbance caused by misleading solutions, a manifold revise model is proposed to produce promising solutions via consulting historical POSs distribution. The proposed framework employs these two models collaboratively, and it is flexible and readily to be embedded into various dynamic response mechanisms and static optimizers in coping with DMOPs. The superiority of the framework has been comprehensively demonstrated by experimental comparison results on a variety of benchmark test problems.

关键词： Statistics Sociology optimization Manifolds Task analysis Robustness Evolutionary computation dynamic multiobjective optimization evolutionary algorithm framework historical learning offspring guidance

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Evolutionary dynamic multiobjective optimization Assisted by a Support Vector Regression Predictor

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IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION 2020年第2期24卷 305-319页

作者： Cao, Leilei Xu, Lihong Goodman, Erik D. Bao, Chunteng Zhu, Shuwei Tongji Univ Dept Control Sci & Engn Shanghai 201804 Peoples R China Michigan State Univ BEACON Ctr Study Evolut Act E Lansing MI 48824 USA

dynamic multiobjective optimization problems (DMOPs) challenge multiobjective evolutionary algorithms (MOEAs) because those problems change rapidly over time. The class of DMOPs whose objective functions change over time steps, in ways that exhibit some hidden patterns has gained much attention. Their predictability indicates that the problem exhibits some correlations between solutions obtained in sequential time periods. Most of the current approaches use linear models or similar strategies to describe the correlations between historical solutions obtained, and predict the new solutions in the following time period as an initial population from which the MOEA can begin searching in order to improve its efficiency. However, nonlinear correlations between historical solutions and current solutions are more common in practice, and a linear model may not be suitable for the nonlinear case. In this paper, we present a support vector regression (SVR)-based predictor to generate the initial population for the MOEA in the new environment. The basic idea of this predictor is to map the historical solutions into a high-dimensional feature space via a nonlinear mapping, and to do linear regression in this space. SVR is used to implement this process. We incorporate this predictor into the MOEA based on decomposition (MOEA/D) to construct a novel algorithm for solving the aforementioned class of DMOPs. Comprehensive experiments have shown the effectiveness and competitiveness of our proposed predictor, comparing with the state-of-the-art methods.

关键词： Decomposition dynamic multiobjective optimization multiobjective evolutionary algorithm (MOEA) nonlinear mapping predictor support vector regression (SVR)

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A prediction strategy based on special points and multiregion knee points for evolutionary dynamic multiobjective optimization

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APPLIED INTELLIGENCE 2020年第12期50卷 4357-4377页

作者： Wei, Lixin Guo, Zeyin Fan, Rui Sun, Hao Zhao, Zhiwei Yanshan Univ Inst Elect Engn Qinhuangdao 066004 Hebei Peoples R China Yanshan Univ Minist Educ Intelligent Control Syst & Intelligen Engn Res Ctr Qinhuangdao 066004 Hebei Peoples R China Tangshan Univ Dept Comp Sci & Technol Tangshan 063000 Hebei Peoples R China

dynamic multiobjective optimization problems exist widely in the real word and require the optimization algorithms to track the Pareto front (PF) over time. A prediction strategy based on special points and multi-region knee points (MRKPs) is proposed for solving dynamic multiobjective optimization problems. Whenever a change is detected, the prediction strategy reacts effectively to the change by generating four subpopulations based on four strategies. The first subpopulation is created by selecting the representative individuals using a special point strategy. The second subpopulation consists of a solution set using a multiregion knee point strategy. The third subpopulation is introduced to the nondominated set by a convergence strategy. The fourth subpopulation comprises diverse individuals from an adaptive diversity maintenance strategy. The four subpopulations merge into a new population to accurately predict the location and distribution of the PF after an environmental change. MRKP is compared with four popular evolutionary algorithms on standard instances with different changing dynamics. Finally, MRKP provides better results than other competitors in terms of Inverted Generational Distance and Hypervolume metrics. The results reveal that MRKP can quickly adapt to changing environments and provide good tracking ability when dealing with dynamic multiobjective optimization problems.

关键词： Evolutionary algorithm dynamic multiobjective optimization Special point Knee point

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A prediction method based on fractional order displacement for dynamic multiobjective optimization

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ISA TRANSACTIONS 2022年 130卷 163-176页

作者： Li, Guoping Liu, Yanmin Deng, Xicai Guizhou Univ Sch Math & Stat Guiyang 550025 Guizhou Peoples R China Hunan Inst Technol Sch Sci Hengyang 421002 Hunan Peoples R China Zunyi Normal Univ Sch Math Zunyi 563006 Guizhou Peoples R China Guizhou Normal Coll Dept Math & Comp Guiyang 550018 Guizhou Peoples R China

Prediction-based methods have become more popular for solving dynamic multiobjective optimization problems. However, most of these proposed methods only use the optimal solutions in the previous two or three environments to predict the new optimal solutions after a change. Doing so neglects information from earlier in the history, which may reduce the accuracy of the prediction method. Conversely, if all history information is utilized for prediction, it will incur exorbitant computing costs, and it is not necessary because it is not all old optimal solutions correlate strongly with predicted solutions. Therefore, a novel prediction method based on fractional displacement (FDPM) is proposed. In this method, the previous optimal solutions that have a certain degree of correlation with the new solutions after a change are identified using the proposed prediction model, the parameters of which are obtained by training a certain length of previous optimal solution series. Then, these identified solutions are used to predict the optimal solutions in the new environment. This can balance the accuracy and computation cost of the prediction method. The performance of the proposed method is compared with five chosen state-of-the-art algorithms over fourteen benchmark problems covering diverse properties, and the results demonstrate that the proposed method is superior to the other selected algorithms. (c) 2022 ISA. Published by Elsevier Ltd. All rights reserved.

关键词： dynamic multiobjective optimization Prediction method Fractional order derivative

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Transfer Learning-Based dynamic multiobjective optimization Algorithms

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IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION 2018年第4期22卷 501-514页

作者： Jiang, Min Huang, Zhongqiang Qiu, Liming Huang, Wenzhen Yen, Gary G. Xiamen Univ Dept Cognit Sci & Technol Xiamen 361005 Peoples R China Xiamen Univ Fujian Key Lab Machine Intelligence & Robot Xiamen 361005 Peoples R China Oklahoma State Univ Sch Elect & Comp Engn Stillwater OK 74078 USA Sangfor Technol Inst Innovat Res Shenzhen 518071 Peoples R China Chinese Acad Sci Inst Automat Beijing 100190 Peoples R China

One of the major distinguishing features of the dynamic multiobjective optimization problems (DMOPs) is that optimization objectives will change over time, thus tracking the varying Pareto-optimal front becomes a challenge. One of the promising solutions is reusing "experiences" to construct a prediction model via statistical machine learning approaches. However, most existing methods neglect the nonindependent and identically distributed nature of data to construct the prediction model. In this paper, we propose an algorithmic framework, called transfer learning-based dynamic multiobjective evolutionary algorithm (EA), which integrates transfer learning and population-based EAs to solve the DMOPs. This approach exploits the transfer learning technique as a tool to generate an effective initial population pool via reusing past experience to speed up the evolutionary process, and at the same time any population-based multiobjective algorithms can benefit from this integration without any extensive modifications. To verify this idea, we incorporate the proposed approach into the development of three well-known EAs, non-dominated sorting genetic algorithm II, multiobjective particle swarm optimization, and the regularity model-based multiobjective estimation of distribution algorithm. We employ 12 benchmark functions to test these algorithms as well as compare them with some chosen state-of-the-art designs. The experimental results confirm the effectiveness of the proposed design for DMOPs.

关键词： Dimensionality reduction domain adaption dynamic multiobjective optimization evolutionary algorithm (EA) transfer learning

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Novel Prediction Strategies for dynamic multiobjective optimization

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IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION 2020年第2期24卷 260-274页

作者： Zhang, Qingyang Yang, Shengxiang Jiang, Shouyong Wang, Ronggui Li, Xiaoli Jiangsu Normal Univ Sch Comp Sci & Technol Xuzhou Jiangsu Peoples R China De Montfort Univ Sch Comp Sci & Informat Leicester LE1 9BH Leics England Southern Univ Sci & Technol Dept Comp Sci & Engn Shenzhen 518055 Peoples R China Univ Lincoln Sch Comp Sci Lincoln LN6 7TS England Hefei Univ Technol Sch Comp & Informat Hefei 230009 Peoples R China Beijing Univ Technol Fac Informat Technol Beijing 100124 Peoples R China

This paper proposes a new prediction-based dynamic multiobjective optimization (PBDMO) method, which combines a new prediction-based reaction mechanism and a popular regularity model-based multiobjective estimation of distribution algorithm (RM-MEDA) for solving dynamic multiobjective optimization problems. Whenever a change is detected, PBDMO reacts effectively to it by generating three subpopulations based on different strategies. The first subpopulation is created by moving nondominated individuals using a simple linear prediction model with different step sizes. The second subpopulation consists of some individuals generated by a novel sampling strategy to improve population convergence as well as distribution. The third subpopulation comprises some individuals generated using a shrinking strategy based on the probability distribution of variables. These subpopulations are tailored to form a population for the new environment. The experimental results carried out on a variety of bi- and three-objective benchmark functions demonstrate that the proposed technique has competitive performance compared with some state-of-the-art algorithms.

关键词： Heuristic algorithms Sociology Statistics Prediction algorithms optimization Optical fibers Convergence dynamic multiobjective optimization nondominated sorting prediction-based reaction probability distribution

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Learning to Guide Particle Search for dynamic multiobjective optimization

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IEEE TRANSACTIONS ON CYBERNETICS 2024年第9期54卷 5529-5542页

作者： Song, Wei Liu, Shaocong Wang, Xinjie Guo, Yinan Yang, Shengxiang Jin, Yaochu Jiangnan Univ Sch Artificial Intelligence & Comp Sci Jiangsu Prov Engn Lab Pattern Recognit & Computat Wuxi 214122 Peoples R China East China Univ Sci & Technol Key Lab Smart Mfg Energy Chem Proc Minist Educ Shanghai 200237 Peoples R China China Univ Min & Technol Sch Informat & Control Engn Xuzhou 221116 Peoples R China De Montfort Univ Inst Artificial Intelligence Sch Comp Sci & Informat Leicester LE1 9BH England Westlake Univ Sch Engn Trustworth & Gen Artificial Intelligence Lab Hangzhou 331712 Peoples R China

dynamic multiobjective optimization problems (DMOPs) are characterized by multiple objectives that change over time in varying environments. More specifically, environmental changes can be described as various dynamics. However, it is difficult for existing dynamic multiobjective algorithms (DMOAs) to handle DMOPs due to their inability to learn in different environments to guide the search. Besides, solving DMOPs is typically an online task, requiring low computational cost of a DMOA. To address the above challenges, we propose a particle search guidance network (PSGN), capable of directing individuals' search actions, including learning target selection and acceleration coefficient control. PSGN can learn the actions that should be taken in each environment through rewarding or punishing the network by reinforcement learning. Thus, PSGN is capable of tackling DMOPs of various dynamics. Additionally, we efficiently adjust PSGN hidden nodes and update the output weights in an incremental learning way, enabling PSGN to direct particle search at a low computational cost. We compare the proposed PSGN with seven state-of-the-art algorithms, and the excellent performance of PSGN verifies that it can handle DMOPs of various dynamics in a computationally very efficient way.

关键词： Heuristic algorithms Statistics Sociology optimization Prediction algorithms Optical fibers Costs dynamic multiobjective optimization incremental learning neural network particle swarm optimization reinforcement learning

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A domain adaptation learning strategy for dynamic multiobjective optimization

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INFORMATION SCIENCES 2022年 606卷 328-349页

作者： Chen, Guoyu Guo, Yinan Huang, Mingyi Gong, Dunwei Yu, Zekuan China Univ Min & Technol Sch Informat & Control Engn Xuzhou 221116 Jiangsu Peoples R China China Univ Min & Technol Beijing Sch Mech Elect & Informat Engn Beijing 100083 Peoples R China Fudan Univ Acad Engn & Technol Shanghai 200433 Peoples R China Fudan Univ Huashan Hosp Ctr Shanghai Intelligent Imaging Crit Brain Dis E Shanghai 200040 Peoples R China

dynamic multiobjective optimization problems (DMOPs) require the robust tracking of Pareto-optima varying over time. Previous transfer learning-based problem solvers consume the most time on complex training of transfer model or applying a plenty of evaluations to find transferred individuals, decreasing computational efficiency. To address this issue, a domain adaptation learning strategy based dynamic multiobjective evolutionary algorithm is proposed in this paper. The mapping matrix learned by subspace distribution alignment (SDA) is utilized to transform the search space between last and current environments for promoting efficient knowledge transfer. Especially, the process of constructing mapping is derived from the simpler calculation, saving computational cost. Based on this model, transferred individuals are generated from a part of historical optima at last time. Additionally, an increment information is defined as the difference between center points of POSs in past two environments, and employed to produce a noise obeying uniform distribution. After adding it on a temporary population consisting of transferred individuals and the rest historical optima, an initial population with good diversity under new environment is formed. Experimental results on 12 benchmark functions indicate that the proposed method outperforms the other six state-of-the-art comparative ones, achieving the promising performance in solving DMOPs. (C) 2022 Elsevier Inc. All rights reserved.

关键词： dynamic multiobjective optimization Domain adaptation Increment information

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Domain Generalization-Based dynamic multiobjective optimization: A Case Study on Disassembly Line Balancing

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IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION 2023年第6期27卷 1851-1865页

作者： Fang, Yilin Liu, Fubo Li, Miqing Cui, Hao Wuhan Univ Technol Sch Informat Engn Wuhan 430070 Peoples R China Univ Birmingham Sch Comp Sci Birmingham B15 2TT England

The objective of disassembly lines is to disassemble end-of-life products in a remanufacturing field. The disassembly line balancing problem (DLBP) considers how to allocate disassembly operations to operators on the disassembly line to optimize predetermined goals, such as cycle time. In practice, various environmental uncertainties (e.g., uncertain product quality) exist in the disassembly line. These uncertainties entail DLBP essentially a dynamic multiobjective optimization problem (DMOP). This study presents a dynamic DLBP (D-DLB) to model the effect of environmental uncertainties on the assignment of disassembly operations. Furthermore, a prediction-based dynamic optimization algorithm, termed domain generalization-based dynamic multiobjective evolutionary algorithm (DG-DMOEA), combining meta-learning with multiobjective optimization, is proposed to solve D-DLB. In DG-DMOEA, a meta-learning algorithm is employed to learn the parameters of a solution-generative model from the Pareto-optimal sets (POSs) in all historical environments. Subsequently, the solution-generative model is applied to generate a high-quality initial population that can assist multiobjective optimization algorithms in finding the POS in the new environment faster. Since no information in the new environment is required, learning can begin before the new environment arrives, significantly reducing computational time. Moreover, different solution-generative models can be designed for different DMOPs. Therefore, DG-DMOEA can thoroughly combine real-world problem properties to represent knowledge. The experimental results show that, compared with state-of-the-art methods, DG-DMOEA can considerably improve the quality of solutions and significantly enhance the ability to react quickly to environmental changes.

关键词： optimization Heuristic algorithms Prediction algorithms Uncertainty Predictive models Statistics Sociology Disassembly line balancing domain generalization dynamic multiobjective optimization dynamic optimization algorithm (DOA) meta-learning

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