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Non-dominated sorting on performance indicators for evolutionary many-objective optimization

INFORMATION SCIENCES 2021年 551卷 23-38页

作者： Wang, Hao Sun, Chaoli Zhang, Guochen Fieldsend, Jonathan E. Jin, Yaochu Taiyuan Univ Sci & Technol Sch Elect Informat Engn Taiyuan 030024 Peoples R China Taiyuan Univ Sci & Technol Dept Comp Sci & Technol Taiyuan 030024 Peoples R China Univ Exeter Dept Comp Sci Exeter EX4 4QF Devon England Univ Surrey Dept Comp Sci Guildford GU2 7XH Surrey England

Much attention has been paid to evolutionary multi-objective optimization approaches to efficiently solve real-world engineering problems with multiple conflicting objectives. However, the loss of selection pressure and the non-uniformity in the distribution of the Pareto optimal solutions in the objective space can impede both dominance-based and decomposition-based multi-objective optimizers when solving many-objective problems. In this work, we circumvent this issue by exploiting two performance indicators, and use these in an optimizer's environmental selection via non-dominated sorting. This effectively converts the original many-objective problem into a bi-objective one. Our convergence performance criterion tries to balance the performance of individuals in different parts of the objective space. The angle between solutions on objective space is adopted to measure the diversity of each individual. Using these solutions can be separated into different layers easily, which is often not possible for the original many-objective optimization representation. The performance of the proposed method is evaluated on the DTLZ benchmark problems with up to 30 objectives, and MaF test suite with 10,15, 20 and 30 objectives. The experimental results show that our proposed method is competitive compared to six recently proposed algorithms, especially for solving problems with a large number of objectives. (C) 2020 Elsevier Inc. All rights reserved.

关键词： many-objective optimization problems Performance indicator Non-dominated sorting Environmental selection

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many-objective Evolutionary Algorithm with Adaptive Reference Vector

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INFORMATION SCIENCES 2021年 563卷 70-90页

作者： Zhang, Maoqing Wang, Lei Li, Wuzhao Hu, Bo Li, Dongyang Wu, Qidi Tongji Univ Sch Elect & Informat Engn Shanghai 201804 Peoples R China Jiaxing Vocat Technol Coll Sch Intelligent Mfg Jiaxing 314036 Zhejiang Peoples R China

Convergence is always a major concern for many-objective optimization problems. Over the past few decades, various methods have been designed for measuring the convergence. However, according to our mathematical and empirical analyses, most of these methods are more focused on the convergence, and may neglect the exploration of boundary solutions, resulting in the incomplete Pareto fronts and the poor extent of spread achieved among the obtained non-dominated solutions. Regarding this issue, this paper proposes a many-objective Evolutionary Algorithm with Adaptive Reference Vector (MaOEA-ARV). In MaOEA-ARV, an adaptive reference vector strategy is designed to dynamically adjust the reference vectors according to the current distribution of candidate solutions for ensuring the spread and convergence simultaneously. Additionally, a hierarchical clustering strategy is employed to adaptively partition candidate solutions into multiple clusters for the diversity of candidate solutions. Experimental results on DTLZ, BT, ZDT and WFG test suites with up to 12 objectives demonstrate the effectiveness of MaOEA-ARV. (c) 2021 Elsevier Inc. All rights reserved.

关键词： many-objective optimization problems Convergence Spread Adaptive reference vector strategy Hierarchical clustering strategy

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Multi-objective particle swarm optimization with R2 indicator and adaptive method

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COMPLEX & INTELLIGENT SYSTEMS 2021年第5期7卷 2697-2710页

作者： Gu, Qinghua Jiang, Mengke Jiang, Song Chen, Lu Xian Univ Architecture & Technol Sch Management Xian 710055 Shaanxi Peoples R China Xian Univ Architecture & Technol Xian Key Lab Intelligent Ind Percept Calculat & D Xian 710055 Shaanxi Peoples R China Xian Univ Architecture & Technol Sch Resources Engn Xian 710055 Shaanxi Peoples R China

Multi-objective particle swarm optimization algorithms encounter significant challenges when tackling many-objective optimization problems. This is mainly because of the imbalance between convergence and diversity that occurs when increasing the selection pressure. In this paper, a novel adaptive MOPSO (ANMPSO) algorithm based on R2 contribution and adaptive method is developed to improve the performance of MOPSO. First, a new global best solutions selection mechanism with R2 contribution is introduced to select leaders with better diversity and convergence. Second, to obtain a uniform distribution of particles, an adaptive method is used to guide the flight of particles. Third, a re-initialization strategy is proposed to prevent particles from trapping into local optima. Empirical studies on a large number (64 in total) of problem instances have demonstrated that ANMPSO performs well in terms of inverted generational distance and hyper-volume metrics. Experimental studies on the practical application have also revealed that ANMPSO could effectively solve problems in the real world.

关键词： many-objective optimization problems Multi-objective particle swarm optimization R2 contribution Adaptive strategy

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many-objective evolutionary algorithm based on three-way decision

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EGYPTIAN INFORMATICS JOURNAL 2023年第3期24卷

作者： Cui, Zhihua Li, Bingting Lan, Zhuoxuan Xu, Yubin Taiyuan Univ Sci & Technol Shanxi Key Lab Big Data Anal & Parallel Comp Taiyuan Peoples R China

In recent years, many-objective optimization problems have been widely used. however, with the increase of the number of objectives, the difficulty of solving increases exponentially, and the imbalance between convergence and diversity becomes more serious. In view of the above problems, this paper combines the idea of three-way decision, redesigns the environment selection strategy, and proposes a many-objective optimization algorithm based on three-way decision. Firstly, the distance from the individual to the ideal point is used as an index to measure individual convergence, the minimum distance from the individual to other solutions is used as an indicator to measure individual diversity, and the individuals with good convergence and good diversity are selected separately by combining the thresholds of the three-way decision;and secondly, A dynamic threshold acquisition method is designed to further improve the performance of the algorithm;Finally, it is proved that the algorithm can effectively balance convergence and diversity through tests of different data sets, so as to verify the feasibility and effectiveness of the algorithm & COPY;2023 Production and hosting by Elsevier B.V. on behalf of Faculty of Computers and Information, Cairo University. This is an open access article under the CC BY-NC-ND license (http://***/ licenses/by-nc-nd/4.0/).

关键词： many-objective optimization problems many-objective evolutionary algorithm Three-way decision Convergence Diversity

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Hybrid many-objective particle swarm optimization algorithm for green coal production problem

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INFORMATION SCIENCES 2020年第0期518卷 256-271页

作者： Cui, Zhihua Zhang, Jiangjiang Wu, Di Cai, Xingjuan Wang, Hui Zhang, Wensheng Chen, Jinjun Taiyuan Univ Sci & Technol Complex Syst & Computat Intelligence Lab Taiyuan 030024 Peoples R China Nanchang Inst Technol Sch Informat Engn Nanchang 330099 Peoples R China Chinese Acad Sci Inst Automat State Key Lab Intelligent Control & Management Co Beijing 100190 Peoples R China Swinburne Univ Technol Dept Comp Sci & Software Engn Melbourne Vic 3000 Australia

The key aspect in coal production is realizing safe and efficient mining to maximize the utilization of the resources. A requirement for sustainable economic development is realizing green coal production, which is influenced by factors of coal economic, energy, ecological, coal gangue economic and social benefits. To balance these factors, this paper proposes a many-objective optimization model with five objectives for green coal production. Furthermore, a hybrid many-objective particle swarm optimization (HMaPSO) algorithm is designed to solve the established model. A new offspring of the alternative pool is generated by employing different evolutionary operators. The environmental selection mechanism is adopted to select and store the excellent solutions. Two sets of experiments are performed to verify the effectiveness of the proposed approach: First, the HMaPSO algorithm is tested on the DTLZ functions, and its performance is compared with that of several widely used many-objective algorithms. Second, the HMaPSO algorithm is applied to solve the many-objective green coal production optimization model. The computational results demonstrate the effectiveness of the proposed approach, and the simulation results prove that the designed approach can provide promising choices for decision makers in regional planning. (C) 2020 Elsevier Inc. All rights reserved.

关键词： Coal production many-objective optimization problems Evolutionary operators Particle swarm optimization (PSO)

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A many-objective evolutionary algorithm based on decomposition with dynamic resource allocation for irregular optimization

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Frontiers of Information Technology & Electronic Engineering 2020年第8期21卷 1171-1190页

作者： Ming-gang DONG Bao LIU Chao JING College of Information Science and Engineering Guilin University of TechnologyGuilin 541004China Guangxi Key Laboratory of Embedded Technology and Intelligent System Guilin 541004China Guangxi Key Laboratory of Trusted Software Guilin University of Electronic&TechnologyGuilin 541004China

The multi-objective optimization problem has been encountered in numerous fields such as high-speed train head shape design,overlapping community detection,power dispatch,and unmanned aerial vehicle *** address such issues,current approaches focus mainly on problems with regular Pareto front rather than solving the irregular Pareto *** this situation,we propose a many-objective evolutionary algorithm based on decomposition with dynamic resource allocation(Ma OEA/D-DRA)for irregular *** proposed algorithm can dynamically allocate computing resources to different search areas according to different shapes of the problem’s Pareto *** evolutionary population and an external archive are used in the search process,and information extracted from the external archive is used to guide the evolutionary population to different search *** evolutionary population evolves with the Tchebycheff approach to decompose a problem into several subproblems,and all the subproblems are optimized in a collaborative *** external archive is updated with the method of rithms using a variety of test problems with irregular Pareto *** results show that the proposed algorithèm out-p￡performs these five algorithms with respect to convergence speed and diversity of population *** comparison with the weighted-sum approach and penalty-based boundary intersection approach,there is an improvement in performance after integration of the Tchebycheff approach into the proposed algorithm.

关键词： many-objective optimization problems Irregular Pareto front External archive Dynamic resource allocation Shift-based density estimation Tchebycheff approach

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Reference-point-based Brain Storm optimization Algorithm for many-objective optimization

Reference-point-based Brain Storm Optimization Algorithm for...

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第32届中国过程控制会议(CPCC2021)

作者： Yali Wu Xiaoxiao Quan Jinjin Qi Yulong Wang School of Automation and Information Engineering Xi'an University of Technology Shaanxi Province Key Laboratory of Complex System Control and Intelligent Information Processing

Brain storm optimization algorithm,as a new type of swarm intelligence optimization algorithm,has attracted the attention of many researchers as soon as it was put ***,it has been applied to various many-objective,multi-modal and practical engineering *** this paper,a brain storm optimization algorithm based on reference points was proposed to solve many-objective optimization ***,a series of reference points are introduced into the target space,and the population is clustered in an adaptive clustering method centered on the reference point poles to guide the evolution of the ***,the idea based on decomposition is combined with the mechanism of brain storm optimization algorithm to solve many-objective optimization ***,a mechanism to update the external archive set based on the strategy of enhanced dominance and weighted boundary intersection is proposed to maintain the convergence and diversity of the *** simulation results on the DTLZ series of test function sets show that the proposed algorithm based on reference points is effective.

关键词： Brain Storm optimization Algorithm Reference Point many-objective optimization problems adaptive cluster

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A hybrid many-objective cuckoo search algorithm

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SOFT COMPUTING 2019年第21期23卷 10681-10697页

作者： Cui, Zhihua Zhang, Maoqing Wang, Hui Cai, Xingjuan Zhang, Wensheng Taiyuan Univ Sci & Technol Complex Syst & Computat Intelligence Lab Taiyuan 030024 Shanxi Peoples R China Tongji Univ Sch Elect & Informat Shanghai 201804 Peoples R China Nanchang Inst Technol Sch Informat Engn Nanchang 330099 Jiangxi Peoples R China Chinese Acad Sci Inst Automat Beijing 100190 Peoples R China

Cuckoo search (CS) is an excellent population-based algorithm and has shown promising performance in dealing with single- and multi-objective optimization problems. However, for many-objective optimization problems (MaOPs), CS cannot be directly employed. So far, few paper have been reported to use CS to solve MaOPs. In this paper, we try to propose a hybrid many-objective cuckoo search (HMaOCS) for MaOPs. In HMaOCS, the standard CS is firstly modified to effectively deal with MaOPs. Then, non-dominated sorting and the strategy of reference points are employed to ensure the convergence and diversity. In order to verify the performance of HMaOCS, DTLZ and WFG benchmark sets are utilized in the experiments. Experimental results show that HMaOCS can achieve promising performance compared with five other well-known many-objective optimization algorithms.

关键词： Cuckoo search many-objective optimization problems Non-dominated sorting Reference points

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A many-objective population extremal optimization algorithm with an adaptive hybrid mutation operation

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INFORMATION SCIENCES 2019年 498卷 62-90页

作者： Chen, Min-Rong Zeng, Guo-Qiang Lu, Kang-Di South China Normal Univ Sch Comp Sci Guangzhou 510631 Guangdong Peoples R China Wenzhou Univ Natl Local Joint Engn Lab Digitalize Elect Design Wenzhou 325035 Peoples R China Donghua Univ Dept Automat Coll Informat Sci & Technol Shanghai 201620 Peoples R China

many-objective optimization problems abbreviated as MaOPs with more than three objectives have attracted increasing interests due to their widely existing in a variety of real world applications. This paper presents a novel many-objective population extremal optimization called MaOPEO-HM algorithm for MaOPs by introducing a reference set based many-objective optimization mechanism into a recently developed population extremal optimization framework and designing an adaptive hybrid mutation operation for updating the population. Despite of the successful applications of extremal optimization in different kinds of numerical and engineering optimization problems, it has never been explored to the many-objective optimization domain so far. Because most of the existing many-objective evolutionary algorithms are usually guided by a single mutation operation, which has insufficient ability to exploit the search space of MaOPs and will get stuck at any local efficient front, it is the first attempt to design a novel hybrid mutation scheme in MaOPEO-HM algorithm by combining the advantages of polynomial mutation operator and multi-non-uniform mutation operator effectively. The experiment results for DTLZ test problems with 3, 5, 8, 10, and 15 objectives and WFG test problems with 3, 5, and 8 objectives have demonstrated the superiority of the proposed MaOPEO-HM to five state-of-the-art decomposition-based many-objective evolutionary algorithms including NSGA-III, RVEA, EFR-RR, theta-DEA, and MOEA/DD and two non-decomposition-based algorithms in-cluding GrEA and Two_Arch2. Furthermore, the great ability of the designed adaptive hybrid mutation operation incorporated into many-objective population extremal optimization (MaOPEO) has also been illustrated by comparing MaOPEO-HM and two MaOPEO algorithms only based on traditional multi-non-uniform mutation or polynomial mutation for DTLZ problems. (C) 2019 Elsevier Inc. All rights reserved.

关键词： many-objective optimization problems many-objective evolutionary algorithms many-objective population extremal optimization Adaptive hybrid mutation operation

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An integrated algorithm for multi-agent fault-tolerant scheduling based on MOEA

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FUTURE GENERATION COMPUTER SYSTEMS-THE INTERNATIONAL JOURNAL OF ESCIENCE 2019年 94卷 51-61页

作者： Wu, Binghong Hao, Kuangrong Cai, Xin Wang, Tong Donghua Univ Minist Educ Engn Res Ctr Digitized Text & Apparel Technol Shanghai Peoples R China Donghua Univ Coll Informat Sci & Technol Shanghai PR Peoples R China

With the increasing functionality of multi-agent systems, fault tolerance has become an essential requirement, especially for workflow with interdependencies among tasks. In this paper, we propose a scheme that combines a novel intrinsic-plasticity-inspired rescheduling execution model (IPIREM) with an improved NSGA-III with knee points. The IPIREM provides a relatively stable evaluation without any estimation of the failure distribution when transient failures happen. Based on the evaluation result of IPIREM, the multi-objective optimization problem is solved by use of an improved NSGA-III, which accelerates convergence and promotes diversity. Finally, experimental results show that the proposed algorithm is effective in enhancing efficiency of the workflow. (C) 2018 Elsevier B.V. All rights reserved.

关键词： Fault-tolerant Intrinsic-plasticity-inspired rescheduling execution model many-objective optimization problems NSGA-III Knee point Multi-agent systems

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