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An improved indicator-based two-archive algorithm for many-objective optimization problems

COMPUTING 2024年第5期106卷 1395-1429页

作者： Song, Weida Zhang, Shanxin Ge, Wenlong Wang, Wei Jiangnan Univ Sch Internet Things Engn Wuxi 214122 Jiangsu Peoples R China

The large number of objectives in many-objective optimization problems (MaOPs) has posed significant challenges to the performance of multi-objective evolutionary algorithms (MOEAs) in terms of convergence and diversity. To design a more balanced MOEA, a multiple indicator-based two-archive algorithm named IBTA is proposed to deal with problems with complicated Pareto fronts. Specifically, a two-archive framework is introduced to focus on convergence and diversity separately. In IBTA, we assign different selection principles to the two archives. In the convergence archive, the inverted generational distance with noncontributing solution detection (IGD-NS) indicator is applied to choose the solutions with favorable convergence in each generation. In the diversity archive, we use crowdedness and fitness to select solutions with favorable diversity. To evaluate the performance of IBTA on MaOPs, we compare it with several state-of-the-art MOEAs on various benchmark problems with different Pareto fronts. The experimental results demonstrate that IBTA can deal with multi-objective optimization problems (MOPs)/MaOPs with satisfactory convergence and diversity.

关键词： Evolutionary algorithm Many-objective optimization two-archive algorithm Indicator-based selection

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An ε-domination based two-archive 2 algorithm for many-objective optimization

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Journal of Systems Engineering and Electronics 2022年第1期33卷 156-169页

作者： WU Tianwei AN Siguang HAN Jianqiang SHENTU Nanying College of Mechanical and Electrical Engineering China Jiliang UniversityHangzhou 310018China Key Laboratory of Intelligent Manufacturing Quality Big Data Tracing and Analysis of Zhejiang Province China Jilang UniversityHangzhou 310018China

The two-archive 2 algorithm(two_Arch2) is a manyobjective evolutionary algorithm for balancing the convergence,diversity,and complexity using diversity archive(DA) and convergence archive(CA).However,the individuals in DA are selected based on the traditional Pareto dominance which decreases the selection pressure in the high-dimensional *** traditional algorithm even cannot converge due to the weak selection ***,two_Arch2 adopts DA as the output of the algorithm which is hard to maintain diversity and coverage of the final solutions synchronously and increase the complexity of the *** increase the evolutionary pressure of the algorithm and improve distribution and convergence of the final solutions,an ε-domination based two_Arch2 algorithm(ε-two_Arch2) for many-objective problems(MaOPs) is proposed in this *** ε-two_Arch2,to decrease the computational complexity and speed up the convergence,a novel evolutionary framework with a fast update strategy is proposed;to increase the selection pressure,ε-domination is assigned to update the individuals in DA;to guarantee the uniform distribution of the solution,a boundary protection strategy based on I_(ε+) indicator is designated as two steps selection strategies to update individuals in *** evaluate the performance of the proposed algorithm,a series of benchmark functions with different numbers of objectives is *** results demonstrate that the proposed method is competitive with the state-of-the-art multi-objective evolutionary algorithms and the efficiency of the algorithm is significantly improved compared with two_Arch2.

关键词： many-objective optimization ε-domination boundary protection strategy two-archive algorithm

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A novel two-archive evolutionary algorithm for constrained multi-objective optimization with small feasible regions

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KNOWLEDGE-BASED SYSTEMS 2022年 237卷 107693-107693页

作者： Xia, Mingming Dong, Minggang Guilin Univ Technol Sch Informat Sci & Engn Guilin 541004 Peoples R China Guangxi Key Lab Embedded Technol & Intelligent Sy Guilin 541004 Peoples R China

Constrained multi-objective evolutionary algorithms (CMOEAs) have been extensively studied in recent years. However, the performance of most of traditional CMOEAs is unsatisfied for constrained multi-objective optimization problems (CMOPs) with small feasible regions. Based on the idea of two-archive, this paper proposes a novel two-archive evolutionary algorithm for constrained multi objective optimization with small feasible regions. Specifically, we maintain two archives, named convergence-oriented archive (CA) and diversity-oriented archive (DA). To handle the CMOPs which feasible regions are small and far from the unconstrained Pareto front (PF), a cooperation-based mating selection mechanism is proposed. To strike a balance among convergence, diversity, and feasibility, a high-quality solution selection mechanism is proposed, which can help the CA approach PF from different directions and balance the convergence and diversity. To provide better diversity, a dynamic selection strategy is designed to update DA according to the status of the CA. In addition, in order to make the population evenly distributed in feasible regions, a replacement mechanism of the ideal point is designed. Compared with the four state-of-the-art constrained multi-objective evolutionary optimization algorithms, comprehensive experiments on a series of benchmark problems fully demonstrate the superiority of the proposed algorithm in terms of increment p and hypervolume (HV). (c) 2021 Elsevier B.V. All rights reserved.

关键词： Constrained multi-objective optimization two-archive algorithm Evolutionary algorithm Convergence Diversity

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A novel two-archive matching-based algorithm for multi- and many-objective optimization

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INFORMATION SCIENCES 2019年 497卷 106-128页

作者： Bao, Chunteng Xu, Lihong Goodman, Erik D. Tongji Univ Coll Elect & Informat Engn Shanghai 201804 Peoples R China Michigan State Univ BEACON Ctr Study Evolut Act E Lansing MI 48824 USA

In evolutionary multi-objective optimization, it is crucial for the evolutionary algorithm to maintain a good balance between convergence and diversity. The recently proposed two_Arch2 algorithm provides a new perspective to solve this problem. However, due to the properties of the mating mechanism and the limitations of the distance-based diversity maintenance scheme, both the computational complexity and the diversity face great challenges as the number of objectives increases. In this paper, we propose an improved two-archive algorithm for both multi- and many-objective optimization, aiming at further promoting the balance between convergence and diversity. In the proposed algorithm, we introduce a decomposition idea into the mating pool of the convergence archive, which increases the number of favorable solutions and reduces the computational complexity. At the same time, we apply a penalty angle-based selection scheme to the diversity archive, which effectively maintains the population diversity. The effectiveness of the proposed algorithm is compared with five state-of-the-art multi-objective evolutionary algorithms on a variety of benchmark problems. The experimental results demonstrate that the proposed algorithm has highly competitive performance on both multi- and many-objective optimization problems in particular, remedying problems of two_Arch2. (C) 2019 Published by Elsevier Inc.

关键词： Evolutionary algorithm Penalty angle Multi-objective optimization Many-objective optimization two-archive algorithm

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A two-archive Harris Hawk Optimization for Solving Many-Objective Optimal Power Flow Problems

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IEEE ACCESS 2023年 11卷 134557-134574页

作者： Khunkitti, Sirote Premrudeepreechacharn, Suttichai Siritaratiwat, Apirat Chiang Mai Univ Fac Engn Dept Elect Engn Chiang Mai 50200 Thailand Khon Kaen Univ Fac Engn Dept Elect Engn Khon Kaen 40002 Thailand

To improve power system operation and management and accomplish modern power system requirements, a new algorithm named two-archive harris hawk optimization (twoArchHHO) is proposed to solve many-objective optimal power flow (MaOOPF) problems in this work. For modern power systems, only single-objective and multiobjective (2-3 objectives) optimal power flow problems (MOOPF) are inadequate. So, the problems become many-objective (more than 3 objectives) optimal power flow problem which is more complicated to be solved. Although several metaheuristic algorithms have been proposed to solve MOOPF problems, very few algorithms have been introduced to solve MaOOPF problems and high-performance algorithms are still required to solve MaOOPF problems which are more complicated. To solve the complicated MaOOPF problems, twoArchHHO is proposed by adding the two-archive concepts of the improved two-archive algorithm into the harris hawk optimization (HHO) in order to enhance the searchability and eventually provide superior solutions. The objective functions considered to be minimized include fuel cost, emission, transmission line loss, and voltage deviation to improve power systems in the economic, environmental, and secure aspects. Several sizes of IEEE standard systems, which are IEEE 30-, 57-, and 118-bus systems, are tested to evaluate the performance of the proposed twoArchHHO. The simulation results comprise Pareto fronts, best-compromised solutions, and hypervolume analysis are generated and compared with results from several algorithms in the literature. The data provided by the experimental trials and the hypervolume performance metric were examined using statistical testing methods. The results indicate that the twoArchHHO obtained better optimal solutions than those of the compared algorithms including its traditional algorithms, especially in large systems. Based on the best-compromised solutions, the twoArchHHO provided one best objective aspect among the compared

关键词： Harris Hawk optimization metaheuristic algorithms many-objective optimal power flow two-archive algorithm

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Balancing Different Optimization Difficulty Between Objectives in Multiobjective Feature Selection

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IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION 2024年第6期28卷 1824-1837页

作者： Song, Zhenshou Wang, Handing Xue, Bing Zhang, Mengjie Xidian Univ Sch Artificial Intelligence Xian 710071 Peoples R China Xidian Univ Collaborat Innovat Ctr Quantum Informat Shaanxi Pr Xian 710071 Peoples R China Victoria Univ Wellington Ctr Data Sci & Artificial Intelligence Wellington 6140 New Zealand Victoria Univ Wellington Sch Engn & Comp Sci Wellington 6140 New Zealand

Multiobjective feature selection (MOFS) aims to find a set of feature subsets that achieves a tradeoff between two objectives, i.e., reducing the number of selected features and improving the classification performance. However, these two objectives might not be always conflicting during the optimization process and have varying difficulties in optimization. Such characteristics pose a great challenge to existing multiobjective evolutionary approaches, which often treat two objectives equally. Specifically, a large number of feature subsets with few features may appear in the population and compete for survival opportunities with promising feature subsets located in not fully explored regions, leading to poor performance. To this end, we propose a two-archive evolutionary feature selection algorithm for MOFS. In the proposed method, all individuals are equally allocated into two independent archives. A two-archive-based solution generation strategy is proposed, where a dynamic dimensionality reduction operator is used to exploit small features subsets while a diversity-based mutation operator is utilized to find feature subsets with better-classification performance. Moreover, a novel environmental selection scheme is proposed, which aims to improve the survival probability of promising feature subsets by providing different selection environments. Experimental results on 23 datasets demonstrate that the proposed algorithm is superior to the other five state-of-the-art algorithms.

关键词： Feature extraction Optimization Sociology Classification algorithms Search problems Task analysis Training Classification feature selection (FS) multiobjective optimization two-archive algorithm

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TA-ABC: two-archive Artificial Bee Colony for Multi-objective Software Module Clustering Problem

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JOURNAL OF INTELLIGENT SYSTEMS 2018年第4期27卷 619-641页

作者： Amarjeet Chhabra, Jitender Kumar NIT Kurukshetra Dept Comp Engn Kurukshetra Haryana India

Multi-objective software module clustering problem (M-SMCP) aims to automatically produce clustering solutions that optimize multiple conflicting clustering criteria simultaneously. Multi-objective evolutionary algorithms (MOEAs) have been a most appropriate alternate for solving M-SMCPs. Recently, it has been observed that the performance of MOEAs based on Pareto dominance selection technique degrades with multi-objective optimization problem having more than three objective functions. To alleviate this issue for M-SMCPs containing more than three objective functions, we propose a two-archive based artificial bee colony (TA-ABC) algorithm. For this contribution, a two-archive concept has been incorporated in the TA-ABC algorithm. Additionally, an improved indicator-based selection method is used instead of Pareto dominance selection technique. To validate the performance of TA-ABC, an empirical study is conducted with two well-known M-SMCPs, i.e. equal-size cluster approach and maximizing cluster approach, each containing five objective functions. The clustering result produced by TA-ABC is compared with existing genetic based two-archive algorithm (TAA) and non-dominated sorting genetic algorithm II (NSGA-II) over seven un-weighted and 10 weighted practical problems. The comparison results show that the proposed TA-ABC outperforms significantly TAA and NSGA-II in terms of modularization quality, coupling, cohesion, Pareto optimality, inverted generational distance, hypervolume, and spread performance metrics.

关键词： Artificial bee colony multi-objective optimization software module clustering two-archive algorithm

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Using Modified Determinantal Point Process Sampling to Update Population

Using Modified Determinantal Point Process Sampling to Updat...

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

作者： Li, Tengfei Li, Jinlong Univ Sci & Technol China Sch Comp Sci & Technol Hefei Anhui Peoples R China

ISBN: (纸本)9781509060177

Many-objective optimization problems (MaOPs) have posed a great challenge to the traditional Pareto-based multi-objective evolutionary algorithms (MOEAs) to balance convergence and diversity. To deal with this issue, we propose a Modified Determinantal Point Process Sampling (MDPPS) to select representatives from population. In order to evaluate the performance of our MDPPS, we plugged MDPPS into the two archive algorithm in which the convergence archive and the diversity archive are updated by our MDPPS. Finally, the new two archive algorithm named TADPP is compared with five state-of-the-art algorithms on a variety of benchmark problems with different numbers of objectives. Experimental results demonstrate that TADPP is highly competitive on both convergence enhancement and diversity maintenance.

关键词： Convergence diversity evolutionary algorithm many-objective optimization two-archive algorithm determinantal point processes

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An improved assisted evolutionary algorithm for data-driven mixed integer optimization based on two_Arch

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COMPUTERS & INDUSTRIAL ENGINEERING 2021年 159卷 107463-107463页

作者： Gu, Qinghua Wang, Danna Jiang, Song Xiong, Naixue Jin, Yu Xian Univ Architecture & Technol Sch Management Xian 710055 Shaanxi Peoples R China Xian Univ Architecture & Technol Sch Resources Engn Xian 710055 Shaanxi Peoples R China

Most of the existing data-driven surrogate-assisted optimization algorithms are developed to solve continuous optimization problems, but there are many problems in reality belong to combinatorial optimization/discrete optimization problems, especially (subdivided into) mixed-integer optimization problems. However, there are few researches based on online data-driven mixed-integer linear programming. Therefore, in this work, we solve a kind of expensive data-driven constrained multi-objective mixed-integer optimization problem, the objectives and constraints are derived based on a large number of calculations. In order to solve this kind of problem, we proposed the use of a random forest classifier (RF) as a surrogate model to approximate the objective and constraints. At the same time, to balance the convergence, diversity, and complexity of the objective, this paper proposes a new improvement strategy that combines the surrogate-assisted model and the two_Arch method, which assigns different selection principles to the two files, and a dual structure multi-objective maintenance program based on Hypervolume district size (HD) indicators. To further improve the accuracy and performance of the model, this paper also adopts a new crossover operator. To verify the effectiveness of the algorithm, tests are carried out on ten benchmark problems of multi-objective knapsack, and comprehensive comparison with several well-known algorithms is carried out. Experimental results show that the improved algorithm is effective in solving data-driven multi-objective mixed-integer optimization problems.

关键词： Data-driven optimization Expensive constrained multi-objective mixed-integer optimization problem Surrogate model two-archive algorithm Differential evolution strategy

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