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A Novel objective Grouping evolutionary algorithm for many-objective Optimization Problems

INTERNATIONAL JOURNAL OF PATTERN RECOGNITION AND ARTIFICIAL INTELLIGENCE 2020年第6期34卷

作者： Guo, Xiaofang Wang, Xiaoli Xian Technol Univ Sch Sci Xuefu Rd Xian Shaanxi Peoples R China Xidian Univ Sch Comp Sci & Technol South Taibai Rd Xian Shaanxi Peoples R China

The thorniest difficulties for multi-objective evolutionary algorithms (MOEAs) handling many-objective optimization problems (MaOPs) are the inefficiency of selection operators and high computational cost. To alleviate such difficulties and simplify the MaOPs, objective reduction algorithms have been proposed to remove the redundant objectives during the search process. However, those algorithms can only be applicable to specific problems with redundant objectives. Worse still, the Pareto solutions obtained by reduced objective set may not be the Pareto solutions of the original MaOPs. In this paper, we present a novel objective grouping evolutionary algorithm (OGEA) for general MaOPs. First, by dividing original objective set into several overlapping lower-dimensional subsets in terms of interdependence correlation information, we aim to separate the MaOPs into a number of sub-problems so that each of them can be able to preserve as much dominance structure in the original objective set as possible. Subsequently, we employ the nondominated sorting genetic algorithm II (NSGA-II) to generate Pareto solutions. Besides, instead of nondominated sorting on the whole population, a novel dual selection mechanism is proposed to choose individuals either having high ranks in subspaces or locating sparse region in the objective space for better proximity and diversity. Finally, we compare the proposed strategy with the other two classical space partition methods on benchmark DTLZ5 (I, M), DTLZ2 and a practical engineering problem. Numerical results show the proposed objective grouping algorithm can preserve more dominance structure in original objective set and achieve better quality of Pareto solutions.

关键词： many-objective evolutionary algorithm objective grouping interdependence relation dual selection mechanism

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many-objective cloud manufacturing service selection and scheduling with an evolutionary algorithm based on adaptive environment selection strategy

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APPLIED SOFT COMPUTING 2021年 112卷

作者： Wang, Tianri Zhang, Pengzhi Liu, Juan Zhang, Minmin Taiyuan Univ Technol Sch Econ & Management Taiyuan 030024 Peoples R China Taiyuan Univ Technol Postgrad Educ Innovat Ctr Big Data Management & A Taiyuan 030024 Peoples R China

Cloud manufacturing service selection and scheduling (CMSSS) problem has obtained wide attentions in recent years. However, most existing methods describe this problem as single-, bi-, or tri-objective models. Little work deals with this problem in four or more objectives simultaneously. This paper investigated CMSSS problem in consideration of the interests of users, cloud platform and service providers. An eight-objective CMSSS optimization model is constructed for the problem. Meanwhile, a many-objective evolutionary algorithm with adaptive environment selection (MaOEA-AES) is designed to address the problem. Specifically, diversity-based population partition technology is used to divide the population into multiple subregions to maintain the population diversity, and an adaptive penalty boundary intersection (APBI) distance is designed to select elitist solutions in different stages of evolutionary process. The proposed algorithm is tested on 2 cases with 5 and 8 objectives in CMSSS problems and each of them has sixteen experimental groups with different problem scales. The experiment results show that MaOEA-AES is competitive to resolve the MaO-CMSSS model compared with eight state-of-the-art evolutionary algorithms in convergence and diversity. (C) 2021 Elsevier B.V. All rights reserved.

关键词： Cloud manufacturing many-objective evolutionary algorithm Manufacturing service scheduling Adaptive penalty boundary intersection

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Improving many-objective evolutionary algorithms by Means of Edge-Rotated Cones 16th

Improving Many-Objective Evolutionary Algorithms by Means of...

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16th International Conference on Parallel Problem Solving from Nature (PPSN)

作者： Wang, Yali Deutz, Andre Back, Thomas Emmerich, Michael Leiden Univ Leiden Inst Adv Comp Sci Niels Bohrweg 1 NL-2333 CA Leiden Netherlands

ISBN: (纸本)9783030581145;9783030581152

Given a point in m-dimensional objective space, any e-ball of a point can be partitioned into the incomparable, the dominated and dominating region. The ratio between the size of the incomparable region, and the dominated (and dominating) region decreases proportionally to 1/2(m-1), i.e., the volume of the Pareto dominating orthant as compared to all other volumes. Due to this reason, it gets increasingly unlikely that dominating points can be found by random, isotropic mutations. As a remedy to stagnation of search in many objective optimization, in this paper, we suggest to enhance the Pareto dominance order by involving an obtuse convex dominance cone in the convergence phase of an evolutionary optimization algorithm. We propose edge-rotated cones as generalizations of Pareto dominance cones for which the opening angle can be controlled by a single parameter only. The approach is integrated in several state-of-the-art multi-objective evolutionary algorithms (MOEAs) and tested on benchmark problems with four, five, six and eight objectives. Computational experiments demonstrate the ability of these edge-rotated cones to improve the performance of MOEAs on many-objective optimization problems.

关键词： Cone order Pareto dominance many-objective evolutionary algorithm

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many-objective emergency aided decision making based on knowledge graph

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APPLIED INTELLIGENCE 2024年第17-18期54卷 7733-7749页

作者： Li, Xiaoxuan Zhao, Tianhao Wen, Jie Cai, Xingjuan Taiyuan Univ Sci & Technol Shanxi Key Lab Big Data Anal & Parallel Comp Taiyuan 030024 Shanxi Peoples R China Nanjing Univ State Key Lab Novel Software Technol Nanjing Peoples R China

After emergencies occur, decision-makers can reference historical cases with similar causes to take similar emergency response measures. However, information about emergencies is usually recorded and stored in textual form, and it is difficult for decision-makers to obtain effective information from large amounts of textual data and make decisions that balance various factors. To address these issues, this paper presents an emergency assisted decision-making model based on a knowledge graph and many-objective optimization. First, we preprocess the information by extracting entities to construct a knowledge graph of emergencies to make the event information more structured and easier to use. A knowledge graph is also used to narrow the range of matching historical events. Second, we construct a many-objective model with four objectives: similarity, diversity, processing time, and resource cost. Finally, combining the model characteristics, we design genetic operations for duplicate location matching and substitution removal strategies to obtain the nonrepetitive VaEA algorithm. This algorithm is used to optimize the model and generate a list of reference cases in the reduced matching range to provide rescue strategy suggestions for the current situation. The experimental results show that the algorithm outperforms the comparison algorithms under all four evaluation metrics. This indicates that the method in this paper can match the higher-quality historical emergency solutions applicable to the current decision-making situation in the case base and provide support for decision-makers to respond reasonably in emergencies.

关键词： Emergency-assisted decision-making Knowledge graph Optimization many-objective evolutionary algorithm

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A new gradient stochastic ranking-based multi-indicator algorithm for many-objective optimization

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SOFT COMPUTING 2019年第21期23卷 10911-10929页

作者： Chen, Ye Yuan, Xiaoping Cang, Xiaohui China Univ Min & Technol Sch Informat & Control Engn Xuzhou 221008 Jiangsu Peoples R China Zhejiang Univ Sch Med Zhejiang Childrens Hosp Div Med Genet & Genom Hangzhou 310058 Zhejiang Peoples R China Zhejiang Univ Sch Med Inst Genet Hangzhou 310058 Zhejiang Peoples R China

In this paper, we propose a gradient stochastic ranking-based multi-indicator algorithm (GSRA) to guide the direction of Pareto front selection pressure. The proposed algorithm primarily aims to enhance the relationship among the different indicators in indicator-based MOEAs. In GSRA, we assigned the Gaussian niche-preservation operation to evaluate the perpendicular distance of every niche member, we also chose two indicators with different biases to balance the convergence and diversity. In environmental selection, we used a two-tier gradient stochastic ranking method to carry out the offspring selection. Seven state-of-the-art EMO algorithms are selected as the peer algorithms to validate GSRA. A series of extensive experiments is conducted on 15 test problems taken from MaF test suites, these functions in the suites are frequently used in many-objective optimization such as DTLZ and WFC problems. The experimental results revealed that the GSRA can achieve both the desired convergence and distribution properties. The solution set obtained by GrEA can achieve a better coverage of the Pareto front than that obtained by other algorithms on most of the tested problems.

关键词： many-objective evolutionary algorithm Multi-indicator Gaussian niche preservation operation Gradient stochastic ranking

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A NEW HYPERVOLUME-BASED DIFFERENTIAL EVOLUTION algorithm FOR many-objective OPTIMIZATION

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RAIRO-OPERATIONS RESEARCH 2017年第4期51卷 1301-1315页

作者： Liu, Chao Zhao, Qi Yan, Bai Gao, Yang Beijing Univ Technol Coll Econ & Management Beijing 100124 Peoples R China Res Base Beijing Modern Mfg Dev Beijing 100124 Peoples R China Beijing Univ Technol Inst Laser Engn Beijing 100124 Peoples R China

evolutionary algorithms are successfully used for many-objective optimization. However, solutions are prone to become nondominated from each other with the increase in the number of objectives, which reduces the efficiency of Pareto dominance-based algorithms. In this paper, a new hypervolume-based differential evolution algorithm (MODEhv) is proposed for many-objective optimization problems (MaOPs). In MODEhv, a modified differential evolution paradigm with automatic parameter configuration strategy is used to balance exploration and exploitation of the algorithm. Besides, the hypervolume indicator is incorporated for the selection of solutions to be varied and solutions to be kept in archive respectively. Finally, a threshold technique is employed to improve diversity of solutions in archive. MODEhv is investigated on a set of widely used benchmark problems and compared with five state-of-the-art algorithms. The experimental results show the efficiency of MODEhv for solving MaOPs.

关键词： Differential Evolution Hypervolume indicator many-objective optimization many-objective evolutionary algorithm

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many-objective optimization of feature selection based on two-level particle cooperation

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INFORMATION SCIENCES 2020年 532卷 91-109页

作者： Zhou, Yu Kang, Junhao Guo, Hainan Shenzhen Univ Coll Comp Sci & Software Engn Shenzhen Peoples R China Shenzhen Univ Guangdong Lab Artificial Intelligence & Digital E Shenzhen Peoples R China Shenzhen Univ Coll Management Shenzhen Peoples R China

Feature selection (FS) plays a crucial role in classification, which aims to remove redundant and irrelevant data *** However, for high-dimensional FS problems, Pareto optimal solutions are usually sparse, signifying that most of the decision variables are zero. Solving such problems using most existing evolutionary algorithms is difficult. In this paper, we reformulate FS as a many-objective optimization problem comprising three objectives to be minimized. To solve this problem, we proposed a binary particle swarm optimization with a two-level particle cooperation strategy. In the first level, to maintain rapid convergence, randomly generated ordinary particles and strict particles filtered by ReliefF are combined as the initialized particles. In the second level, under the decomposition multiobjective optimization framework, cooperation between particles is conducted during the update process to search for Pareto solutions more efficiently. In addition, a many-objective reset operation is proposed to enable the algorithm to jump out of the local optimum. Experimental studies on 10 real-world benchmark data sets revealed that our proposed algorithm could effectively reduce the number of features and achieve a competitive classification accuracy compared with some state-of-the-art evolutionary FS methods and non-evolutionary approaches. (C) 2020 Elsevier Inc. All rights reserved.

关键词： Feature selection Particle swarm optimization many-objective evolutionary algorithm ReliefF Pareto optimal solutions

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Stochastic Ranking algorithm for many-objective Optimization Based on Multiple Indicators

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IEEE TRANSACTIONS ON evolutionary COMPUTATION 2016年第6期20卷 924-938页

作者： Li, Bingdong Tang, Ke Li, Jinlong Yao, Xin USTC Sch Comp Sci & Technol Univ Sci & Technol China USTC Birmingham Joint Re Hefei 230027 Peoples R China Univ Birmingham Ctr Excellence Res Computat Intelligence & Applic Sch Comp Sci Birmingham B15 2TT W Midlands England

Traditional multiobjective evolutionary algorithms face a great challenge when dealing with many objectives. This is due to a high proportion of nondominated solutions in the population and low selection pressure toward the Pareto front. In order to tackle this issue, a series of indicator-based algorithms have been proposed to guide the search process toward the Pareto front. However, a single indicator might be biased and lead the population to converge to a subregion of the Pareto front. In this paper, a multi-indicator-based algorithm is proposed for many-objective optimization problems. The proposed algorithm, namely stochastic ranking-based multi-indicator algorithm (SRA), adopts the stochastic ranking technique to balance the search biases of different indicators. Empirical studies on a large number (39 in total) of problem instances from two well-defined benchmark sets with 5, 10, and 15 objectives demonstrate that SRA performs well in terms of inverted generational distance and hypervolume metrics when compared with state-of-the-art algorithms. Empirical studies also reveal that, in the case a problem requires the algorithm to have strong convergence ability, the performance of SRA can be further improved by incorporating a direction-based archive to store well-converged solutions and maintain diversity.

关键词： Archive method many-objective evolutionary algorithm multi-indicator multiobjective optimization stochastic ranking

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Reference line-based Estimation of Distribution algorithm for many-objective optimization

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KNOWLEDGE-BASED SYSTEMS 2017年 132卷 129-143页

作者： Sun, Yanan Yen, Gary G. Yi, Zhang Sichuan Univ Coll Comp Sci Chengdu 610065 Sichuan Peoples R China Oklahoma State Univ Sch Elect & Comp Engn Stillwater OK 74078 USA

Multi-objective evolutionary algorithms (MOEAs) are preferred in solving multi-objective optimization problems due to their considerable performance giving decision-maker a set of not only convergent but diversified promising solutions. However, the scalability of MOEAs deteriorates in addressing many objective optimization problems which involve more than three conflicting objectives. The principal reason is largely due to the deficiency of the existing genetic operators which cannot generate promising offspring from parents chosen by the Pareto-dominance rule in these MOEAs. Estimation of Distribution algorithms (EDAs) generate offspring with a probabilistic model built from the statistics extracting upon existing solutions to expectedly alleviate the weakness arisen in genetic operators. In this paper, a reference line-based EDA is proposed for effectively solving many-objective optimization problems. Specifically, the estimation model is built based on the reference lines in the decision space to sample solutions with favorable proximity. Then solutions with considerable diversity in Pareto-optimal front are selected. These two phases collectively promote the needed convergence and diversity for the proposed algorithm. To evaluate the performance, extensive experiments are performed against four state-of-the-art many objective evolutionary algorithms and two EDAs over DTLZ and WFG test suites with 5-, 8-, 10-, and 15-objective. Experimental results quantified by the selected performance metrics indicate that the proposed algorithm shows significant competitiveness in tackling many-objective optimization problems. (C) 2017 Elsevier B.V. All rights reserved.

关键词： many-objective evolutionary algorithm evolutionary computation Reference line Estimation of Distribution algorithm

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many-objective Cooperative Co-evolutionary Feature Selection: A Lexicographic Approach 15th

Many-Objective Cooperative Co-evolutionary Feature Selection...

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15th International Work-Conference on Artificial Neural Networks (IWANN)

作者： Gonzalez, Jesus Ortega, Julio Damas, Miguel Martin-Smith, Pedro Univ Granada CITIC Dept Comp Architecture & Technol Granada Spain

ISBN: (纸本)9783030205188;9783030205171

This paper presents a new wrapper method able to optimize simultaneously the parameters of the classifier while the size of the subset of features that better describe the input dataset is also being minimized. The search algorithm used for this purpose is based on a co-evolutionary algorithm optimizing several objectives related with different desirable properties for the final solutions, such as its accuracy, its final number of features, and the generalization ability of the classifier. Since these objectives can be sorted according to their priorities, a lexicographic approach has been applied to handle this many-objective problem, which allows the use of a simple evolutionary algorithm to evolve each one of the different sub-populations.

关键词： many-objective evolutionary algorithm Cooperative co-evolutionary algorithm Lexicographic optimization Feature selection Wrapper approach

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