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A novel clustering-based evolutionary algorithm with objective space decomposition for multi/many-objective optimization

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INFORMATION SCIENCES 2024年 677卷

作者： Zheng, Wei Tan, Yanyan Yan, Zeyuan Yang, Mingming Xian Univ Sci & Technol Coll Comp Sci & Technol 58 Yanta Rd Xian 710054 Shaanxi Peoples R China Shandong Normal Univ Sch Informat Sci & Engn Jinan 250358 Shandong Peoples R China Sun Yat Sen Univ Sch Environm Sci & Engn 135 Xingang Xi Rd Guangzhou 510275 Guangdong Peoples R China Chongqing Jiaotong Univ Sch Aeronaut 66 Xuefu Rd Chongqing 400074 Peoples R China

The framework of decomposing a multi -objective optimization problem (MOP) into some MOPs holds considerable promise. However, its advancement is constrained by numerous elements, including the incorrect segmentation of the subspaces and the challenges in balancing convergence and diversity. To address these issues, an objective space Decomposition and Clustering-based Evolutionary Algorithm (DCEA) is proposed in this paper. Specifically, DCEA employs K-means clustering to create an appropriate mating pool for each individual without the necessity to predetermine the number of clusters. Within each mating pool, the proposed adaptive evolutionary operator is applied to produce offspring for balancing the convergence and diversity. To enhance the accuracy of partitioning, a refined environmental selection approach utilizing supplementary weight vectors is developed. Additionally, by utilizing historical clustering data, a straightforward approach to periodically adjust reference vectors for the allocation of computational resources is proposed. In experiments, both MOPs and many-objective optimization problems (MaOPs) are used to test DCEA. A total of 27 MOPs and 30 MaOPs are involved and 16 state-of-the-art algorithms are employed to compare with DCEA. Comprehensive experiments show that DCEA is an effective algorithm for solving both MOPs and MaOPs.

关键词： Decomposition Convergence and diversity Clustering Multi-objective optimization problem many-objective optimization problem

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many-objective Deployment optimization for a Drone-Assisted Camera Network

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IEEE TRANSACTIONS ON NETWORK SCIENCE AND ENGINEERING 2021年第4期8卷 2756-2764页

作者： Cao, Bin Li, Meng Liu, Xin Zhao, Jianwei Cao, Wenxi Lv, Zhihan Hebei Univ Technol State Key Lab Reliabil & Intelligence Elect Equip Tianjin 300130 Peoples R China Hebei Univ Technol Sch Artificial Intelligence Tianjin 300401 Peoples R China Hebei Univ Technol Sch Econ & Management Tianjin 300401 Peoples R China Chinese Acad Sci South China Sea Inst Oceanol Guangdong Key Lab Ocean Remote Sensing Guangzhou 510301 Peoples R China Qingdao Univ Sch Data Sci & Software Engn Qingdao 266071 Peoples R China

Drone-assisted camera networks can be used in many applications. However, different application requirements lead to different deployment scenarios. In this paper, based on a 3D terrain environment represented by triangular mesh data, a many-objective optimization model for the deployment of multiple onboard cameras is constructed. We propose an improved version of the constrained two-archive evolutionary algorithm. A selection operator based on Gaussian process regression is used for enhancement. Additionally, we quantize the polynomial mutation operator. The improved algorithm is applied to optimize drone-assisted camera deployment, and the experimental results show that the improved algorithm is superior to state-of-the-art algorithms.

关键词： Cameras Three-dimensional displays optimization Solid modeling Visualization Drones Gaussian processes Drone-assisted camera network Gaussian process regression many-objective optimization problem quantization of polynomial mutation operator

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A many-objective evolutionary algorithm based on vector angle distance scaling

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JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2021年第5期40卷 10285-10306页

作者： Li, Xin Li, Xiaoli Wang, Kang Beijing Univ Technol Fac Informat Technol Beijing Peoples R China Minist Educ Beijing Key Lab Computat Intelligence & Intellige Engn Res Ctr Digital Community Beijing Peoples R China

In the past two decades, multi-objective evolutionary algorithms (MOEAs) have achieved great success in solving two or three multi-objective optimization problems. As pointed out in some recent studies, however, MOEAs face many difficulties when dealing with many-objective optimization problems(MaOPs) on account of the loss of the selection pressure of the non-dominant candidate solutions toward the Pareto front and the ineffective design of the diversity maintenance mechanism. This paper proposes a many-objective evolutionary algorithm based on vector guidance. In this algorithm, the value of vector angle distance scaling(VADS) is applied to balance convergence and diversity in environmental selection. In addition, tournament selection based on the aggregate fitness value of VADS is applied to generate a high quality offspring population. Besides, we adopt an adaptive strategy to adjust the reference vector dynamically according to the scales of the objective functions. Finally, the performance of the proposed algorithm is compared with five state-of-the-art many-objective evolutionary algorithms on 52 instances of 13 MaOPs with diverse characteristics. Experimental results show that the proposed algorithm performs competitively when dealing many-objective with different types of Pareto front.

关键词： Vector angle distance scaling evolutionary algorithm many-objective optimization problem

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A hybridized angle-encouragement-based decomposition approach for many-objective optimization problems

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APPLIED SOFT COMPUTING 2019年 78卷 355-372页

作者： Su, Yuchao Wang, Jia Ma, Lijia Wang, Xiaozhou Lin, Qiuzhen Coello Coello, Carlos A. Chen, Jianyong Shenzhen Univ Coll Comp Sci & Software Engn Shenzhen Peoples R China IPN Dept Comp Sci CINVESTAV Mexico City 07360 DF Mexico

Due to the large objective space when handling many-objective optimization problems (MaOPs), it is a challenging work for multi-objective evolutionary algorithms (MOEAs) to balance convergence and diversity during the search process. Although a number of decomposition-based MOEAs have been designed for the above purpose, some difficulties are still encountered for tackling some difficult MaOPs. As inspired by the existing decomposition approaches, a new Hybridized Angle-Encouragement-based (HAE) decomposition approach is proposed in this paper, which is embedded into a general framework of decomposition-based MOEAs, called MOEA/D-HAE. Two classes of decomposition approaches, i.e., the angle-based decomposition and the proposed encouragement-based boundary intersection decomposition, are sequentially used in HAE. The first one selects appropriate solutions for association in the feasible region of each subproblem, which is expected to well maintain the diversity of associated solutions. The second one acts as a supplement for the angle-based one under the case that no solution is located in the feasible region of subproblem, which aims to ensure the convergence and explore the boundaries. By this way, HAE can effectively combine their advantages, which helps to appropriately balance convergence and diversity in evolutionary search. To study the effectiveness of HAE, two series of well-known test MaOPs (WFG and DTLZ ) are used. The experimental results validate the advantages of HAE when compared to other classic decomposition approaches and also confirm the superiority of MOEA/D-HAE over seven recently proposed many-objective evolutionary algorithms. (C) 2019 Elsevier B.V. All rights reserved.

关键词： many-objective optimization problem Angle-based decomposition Encouragement-based decomposition

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Multi-objective optimization of Satellite-ground time synchronization Scheduling problem

Multi-objective Optimization of Satellite-ground time synchr...

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IEEE Congress on Evolutionary Computation (IEEE CEC)

作者： Wang, Zhaohui Zhang, Zhongshan Chen, Yingwu Natl Univ Def Technol Coll Syst Engn Changsha Hunan Peoples R China

ISBN: (纸本)9781728121536

The task planning of satellite-ground time synchronization (SGTSTP) in global navigation satellite system is a complex many-objective ground station scheduling problem. In this paper, we first provide a mathematical formulation of the over-subscribed problem and compare with traditional scheduling problems likes job-shop scheduling problem (JSP) and satellite range scheduling problems (SRSP). In application of the Beidou Navigation System of China, with the limit of ground resource and visible time between satellites and antennas, it is no doubt a difficult problem to solve, besides, there are several objectives for SGTSTP. To solve this SGTSTP problem with efficiency and effectiveness, we propose a solving method based on decomposition-and-integration (DI), and transform SGTSTP from many-objective optimization problem (MaOPs) into a multi-objective optimization problem (MOP), to make it suitable for a multi-objective evolutionary algorithm (MOEA). Meanwhile, evolutionary many-objective optimization algorithm (EMOA) is used for original objectives as comparison. We embed the DI method into two classes of evolutionary algorithm frameworks. DI-MOEA works on a transformed two-objective version of the SGTSTP while DI-EMOA deals with the original four-objective SGTSTP problem. Computational results on two well-designed instances show that the DI-MOEA achieves worse convergence and diversity but better objective value and computational efficiency compared to the DI-EMOA.

关键词： many-objective optimization problem multi-objective optimization evolutionary algorithm job-shop scheduling ground station scheduling

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Review of the Research Landscape of Multi-Criteria Evaluation and Benchmarking Processes for many-objective optimization Methods: Coherent Taxonomy, Challenges and Recommended Solution

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INTERNATIONAL JOURNAL OF INFORMATION TECHNOLOGY & DECISION MAKING 2020年第6期19卷 1619-1693页

作者： Mohammed, R. T. Yaakob, R. Zaidan, A. A. Sharef, N. M. Abdullah, R. H. Zaidan, B. B. Dawood, K. A. Univ Pendidikan Sultan Idris UPSI Comp Dept Tanjung Malim Malaysia Univ Putra Malaysia UPM Fac Comp Sci & Informat Technol Seri Kembangan Selangor Malaysia

Evaluation and benchmarking of many-objective optimization (MaOO) methods are complicated. The rapid development of new optimization algorithms for solving problems with many objectives has increased the necessity of developing performance indicators or metrics for evaluating the performance quality and comparing the competing optimization algorithms fairly. Further investigations are required to highlight the limitations of how criteria/metrics are determined and the consistency of the procedures with the evaluation and benchmarking processes of MaOO. A review is conducted in this study to map the research landscape of multi-criteria evaluation and benchmarking processes for MaOO into a coherent taxonomy. Then contentious and challenging issues related to evaluation are highlighted, and the performance of optimization algorithms for MaOO is benchmarked. The methodological aspects of the evaluation and selection of MaOO algorithms are presented as the recommended solution on the basis of four distinct and successive phases. First, in the determination phase, the evaluation criteria of MaOO are collected, classified and grouped for testing experts' consensus on the most suitable criteria. Second, the identification phase involves the process of establishing a decision matrix via a crossover of the 'evaluation criteria' and MaOO', and the level of importance of each selective criteria and sub-criteria from phase one is computed to identify its weight value by using the best-worst method (BWM). Third, the development phase involves the creation of a decision matrix for MaOO selection on the basis of the integrated BWM and VIKOR method. Last, the validation phase involves the validation of the proposed solution.

关键词： Evaluation fuzzy Delphi many-objective optimization many-objective optimization problem multi-criteria decision making (MCDM)

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Entropy based evolutionary algorithm with adaptive reference points for many-objective optimization problems

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INFORMATION SCIENCES 2018年 465卷 232-247页

作者： Zhou, Chong Dai, Guangming Zhang, Cuijun Li, Xiangping Ma, Ke China Univ Geosci Sch Comp Wuhan 430074 Hubei Peoples R China Hebei GEO Univ Sch Informat Engn Shijiazhuang 050031 Hebei Peoples R China China Univ Geosci Hubei Key Lab Intelligent Geoinformat Proc Wuhan 430074 Hubei Peoples R China

many-objective optimization problems (MaOPs) have attracted more and more attention due to its challenges for multi-objective evolutionary algorithms. Reference points or weight vectors based evolutionary algorithms have been developed successfully for solving MaOPs. However, these algorithms do not solve efficiently the MaOPs with irregular Pareto fronts, such as disconnected, degenerate, and inverted. Although some algorithms with adaptive weight vectors or reference points are designed to handle the problems with irregular shapes of Pareto fronts, they still exist some drawbacks. These adaptive algorithms do not obtain good performance in solving regular problem. For solving regular and irregular Pareto fronts of the problems, a novel entropy based evolutionary algorithm with adaptive reference points, named EARPEA, is proposed to solve regular and irregular many-objective optimization problems. Entropy computed based on reference points and a learning period are employed to control adaptation of the reference points. In addition, in order to maintain diversity of the reference points, a reference point adaptation method based on cosine similarity is designed in the adjusting reference point phase. The proposed algorithm is empirically compared with eight state-of-the-art many-objective evolutionary algorithms on 72 instances of 18 benchmark problems. The comparative results demonstrate that the overall performance of the proposed algorithm is superior to the counterparts on MaOPs with regular and irregular Pareto fronts. (C) 2018 Elsevier Inc. All rights reserved.

关键词： many-objective optimization problem Evolutionary algorithm Entropy Adaptive reference points Irregular and regular Pareto front

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Effectiveness of NSGA-II with Linearly Scheduled Pareto-Partial Dominance for Practical many-Objecitve Nurse Scheduling 7

Effectiveness of NSGA-II with Linearly Scheduled Pareto-Part...

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7th International Conference on Control, Decision and Information Technologies (CoDIT)

作者： Ohki, Makoto Tottori Univ Fac Engn 1014 Koyama Minami Tottori 6800945 Japan

ISBN: (纸本)9781728159539

This paper describes an application of NSGA-II as one of Multi-objective Evolutionary Algorithms (MOEAs) to a many-objective Nurse Scheduling in an actual hospitals in Japan and its effectiveness. Although many techniques for the actual nurse scheduling have been poposed, they are based on the culture of work styles in Europe or in the US, and then they are not fitted for creating a nurse work schedule in Japan. The nurse scheduling problem has many objectives, twelve objectives specially in the problem shown in this paper. Such an optimization problem having many objectives is generally called a many-objective optimization problem (MaOP), and it is considered that MOEAs such as NSGA-II are not effective. Although MOEA/D and NSGA-III, which are one of MaOEA, are known as effective algorithms for MaOPs, these algorithms, for example, require an so many number of scalarization vectors or appropriate reference set, they are not always easy to apply to real world problems. The MaOEAs are also very sensitive techniques to the vectors or reference set. On the other hand, although it has been pointed out that MOEAs are not suitable for MaOP in verification reports with several benchmarks, there is no fact that MOEAs have been applied to real-world MaOPs and their effectiveness has been denied. Therefore, this paper tries to apply NSGA-II, one of MOEAs, to the practical nurse scheduling problem without omitting or reducing all the objectives, and verify its effectiveness.

关键词： nurse scheduling multi-objective evolutionary algorithm many-objective optimization problem NSGA-II

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Nadir point estimation for many-objective optimization problems based on emphasized critical regions

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SOFT COMPUTING 2017年第9期21卷 2283-2295页

作者： Wang, Handing He, Shan Yao, Xin Xidian Univ Key Lab Intelligent Percept & Image Understanding Int Res Ctr Intelligent Percept & Computat Minist Educ Xian 710071 Peoples R China Univ Surrey Dept Comp Sci Guildford GU2 7XH Surrey England Univ Birmingham Sch Comp Sci CERCIA Birmingham B15 2TT W Midlands England

Nadir points play an important role in many-objective optimization problems, which describe the ranges of their Pareto fronts. Using nadir points as references, decision makers may obtain their preference information for many-objective optimization problems. As the number of objectives increases, nadir point estimation becomes a more difficult task. In this paper, we propose a novel nadir point estimation method based on emphasized critical regions for many-objective optimization problems. It maintains the non-dominated solutions near extreme points and critical regions after an individual number assignment to different critical regions. Furthermore, it eliminates similar individuals by a novel self-adaptive -clearing strategy. Our approach has been shown to perform better on many-objective optimization problems (between 10 objectives and 35 objectives) than two other state-of-the-art nadir point estimation approaches.

关键词： Multi-objective evolutionary algorithm Nadir point Critical region many-objective optimization problem Decision making

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An Improved Visualization Approach in many-objective optimization

An Improved Visualization Approach in Many-Objective Optimiz...

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IEEE Congress on Evolutionary Computation (CEC) held as part of IEEE World Congress on Computational Intelligence (IEEE WCCI)

作者： He, Zhenan Yen, Gary G. Sichuan Univ Coll Comp Sci Chengdu Sichuan Peoples R China Oklahoma State Univ Sch Elect & Comp Engn Stillwater OK 74078 USA

ISBN: (纸本)9781509006229

In a high-dimensional objective space, visualization of population in an approximate Pareto front is crucial to decision making process. By directly observing the performance of each solution, the trade-off between objectives, and distribution of approximate front, the decision maker can effectively decide which solution should be chosen from. Furthermore, visualization throughout the evolution process can also be exploited in designing effective many-objective evolutionary algorithms. Recently, a new visualization approach was developed by constructing a mapping from a high dimensional objective space into a two dimensional polar coordinate system, where a group of predefined direction vectors divide the whole space into a number of sub regions and each individual is associated with one weight vector. This method can be scalable to any dimensions, and simultaneously deal with a large number of individuals and multiple Pareto fronts for the purpose of visual comparison. It faithfully preserves shape, location, range, and distribution of Pareto front. However, distributions of Pareto front within each subregion and relations between different sub regions cannot be observed by this method. In this paper, in order to overcome this deficiency, we incorporate a modified multi-dimensional scaling (MDS) approach into this method. Experimental results show that the modified MDS is a suitable complementary to the existing method. Furthermore, the new design combined with existing visualization approach provides a comprehensive mean to visualize all important information in a many-objective optimization problem.

关键词： visualization many-objective optimization problem multi-dimensional scaling

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