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Modified differential evolution algorithm using a new diversity maintenance strategy for multi-objective optimization problems

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APPLIED INTELLIGENCE 2015年第1期43卷 49-73页

作者： Chen, Bili Lin, Yangbin Zeng, Wenhua Zhang, Defu Si, Yain-Whar Xiamen Univ Software Sch Xiamen 361005 Fujian Peoples R China Xiamen Univ Sch Informat Sci & Engn Xiamen 361005 Fujian Peoples R China Univ Macau Dept Comp & Informat Sci Macau Peoples R China

In this paper, we propose a modified differential evolution (DE) based algorithm for solving multi-objective optimization problems (MOPs). The proposed algorithm, called multi-objective DE with dynamic selection mechanism (DSM), i.e., MODE-DSM, modifies the general DE mutation operation to produce a population at each generation. To determine and evaluate a better spread of the non-dominated solution, a DSM with a new cluster degree measure is developed. The DSM is also used to select diverse non-dominated solutions. The performance of the proposed algorithm is evaluated against seventeen bi-objective and two tri-objective benchmark test problems. The experimental results show that the proposed algorithm achieves better convergence to the Pareto-optimal front as well as better diversity on the final non-dominated solutions than the other five multi-objective evolutionary algorithms (MOEAs). It suggests that the proposed algorithm is promising in dealing with MOPs. The ability of MODE-DSM with small population and the sensitivity of MODE-DSM have also been experimentally investigated in this paper.

关键词： Differential evolution multi-objective optimization problems Non-dominated Pareto-optimal front

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A MODIFIED NON-DOMINATED SORTING GENETIC ALGORITHM WITH FRACTIONAL FACTORIAL DESIGN FOR multi-objective optimization problems

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JOURNAL OF MECHANICS 2010年第2期26卷 143-156页

作者： Liu, J. -L. Lee, T. -F. I Shou Univ Dept Informat Management Kaohsiung 84001 Taiwan

This study develops an intelligent non-dominated sorting genetic algorithm (GA), called INSGA herein, which includes a non-dominated sorting, crowded distance sorting, binary tournament selection, intelligent crossover and non-uniform mutation operators, for solving multi-objective optimization problems (MOOPs). This work adopts Goldberg's notion of non-dominated sorting and Deb's crowded distance sorting in the proposed MOGA to achieve solutions with good diversity-preservation and uniform spread on the approximated Pareto front. In addition, the chromosomes of offspring are generated based on an intelligent crossover operator using a fractional factorial design to select good genes from parents intelligently and achieve the goals of fast convergence and high numerical accuracy. To further improve the fine turning capabilities of the presented MOGA, a non-uniform mutation operator is also applied. A typical mutation approach is to create a random number and then add it to corresponding original value. Performance evaluation of the INSGA is examined by applying it to a variety of unconstrained and constrained multi-objective optimization functions. Moreover, two engineering design problems, which include a two-bar truss design and a welded beam design, are studied by the proposed INSGA. Results include the estimated Pareto-optimal front of non-dominated solutions.

关键词： Intelligent non-dominated sorting genetic algorithm (INSGA) multi-objective optimization problems Fractional factorial design Engineering design problems

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CHARACTERIZATION OF EFFICIENT SOLUTIONS FOR multi-objective optimization problems INVOLVING SEMI-STRONG AND GENERALIZED SEMI-STRONG E-CONVEXITY

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Acta Mathematica Scientia 2008年第1期28卷 7-16页

作者： E.A.Youness Tarek Emam Department of Mathematics Faculty of ScienceTanta UniversityTantaEgypt Department of Mathematics Faculty of Education in SuezSuez Canal UniversitySuezEgypt

The authors of this article are interested in characterization of efficient solutions for special classes of problems. These classes consider semi-strong E-convexity of involved functions. Sufficient and necessary con... 详细信息

关键词： multi-objective optimization problems semi-strong E-convex efficient solutions properly efficient solutions

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Hyper multi-objective evolutionary algorithm for multi-objective optimization problems

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SOFT COMPUTING 2017年第20期21卷 5883-5891页

作者： Guo, Weian Chen, Ming Wang, Lei Wu, Qidi Tongji Univ Sinogerman Coll Appl Sci Shanghai 201804 Peoples R China Tongji Univ Dept Elect & Informat Engn Shanghai 201804 Peoples R China

multi-objective optimization problems (MOPs) are very common in practice. To solve MOPs, many kinds of multi-objective evolutionary algorithms (MOEAs) are proposed. However, different MOEAs have different performances for different MOPs. Therefore, it is a time-consuming task to choose a suitable MOEA for a given problem. To pursue a competitive performance for various kinds of MOPs, in this paper, we propose a framework named hyper multi-objective evolutionary algorithm (HMOEA). In this framework, more than one MOEAs are employed, which is more adaptive to different problems. In HMOEA, the population will be randomly divided into several groups. In each group, a selected MOEA will be implemented. Therefore in the framework, the number of groups is equal to the number of the employed MOEAs. The size of each group, namely the size of sub-population in each group, is adjusted according to the corresponding MOEA's performance. If a MOEA performs well, its corresponding group will have a large size group, which means the MOEA obtains more computational resources. On the contrary, if a MOEA has a poor performance in current generation, its corresponding group will obtain only a few individuals. Although a MOEA does not perform very well in current generation, the framework will not abandon this MOEA, but provide it a group that has predefined small size. The reason is that an involvement of different MOEAs will increase the diversity of algorithms in the hyper framework, which is helpful for HMOEA to avoid local optima and also can help HMOEA be adaptive to different phases in the whole optimization process. To compare MOEAs' performances, coverage rate (CR) metric is used to evaluate the quality of MOEA and therefore decides the size of group for each MOEA. In numerical experiments, ZDT benchmarks are employed to test the proposed hyper framework. Several classic MOEAs are also used in comparisons. According to the comparison results, HMOEA can achieve very competitive

关键词： multi-objective optimization problems Hyper multi-objective evolutionary algorithm Group Coverage rate

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Empirical study on meta-feature characterization for multi-objective optimization problems

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NEURAL COMPUTING & APPLICATIONS 2022年第19期34卷 16255-16273页

作者： Chu, Xianghua Wang, Jiayun Li, Shuxiang Chai, Yujuan Guo, Yuqiu Shenzhen Univ Coll Management Shenzhen Peoples R China Shenzhen Univ Inst Big Data Intelligent Management & Decis Shenzhen Peoples R China Shenzhen Univ Hlth Sci Ctr Sch Biomed Engn Shenzhen Peoples R China Mt Sch York N Yorkshire England

Algorithm recommendation based on meta-learning was studied previously. The research on the meta-features extraction, which is a key for the success of recommendation, is lacking for multi-objective optimization problems (MOPs). This paper proposes four sets of meta-features to characterize MOPs. In addition, the algorithm recommendation model based on meta-learning is extended to the field of multi-objective optimization. To evaluate the efficiency and effectiveness of the extracted meta-features, 29 MOPs benchmark functions with different dimensions and two real-world MOPs are employed for comprehensive comparison. Experimental results show that the proposed meta-features in this paper can fully characterize MOPs and are empirically efficient for algorithm recommendation.

关键词： Meta-feature extraction Meta-learning multi-objective optimization problems Algorithm recommendation

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Hybedrized NSGA-II and MOEA/D with Harmony Search Algorithm to Solve multi-objective optimization problems 22nd

Hybedrized NSGA-II and MOEA/D with Harmony Search Algorithm ...

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22nd International Conference on Neural Information Processing (ICONIP)

作者： Abu Doush, Iyad Bataineh, Mohammad Qasem Yarmouk Univ Dept Comp Sci Irbid Jordan

ISBN: (纸本)9783319265322;9783319265315

A multi-objective optimization problem is an area concerned an optimization problem involving more than one objective function to be optimized simultaneously. Several techniques have been proposed to solve multi-objective optimization problems. The two most famous algorithms are: NSGA-II and MOEA/D. Harmony Search is relatively a new heuristic evolutionary algorithm that has successfully proven to solve single objective optimization problems. In this paper, we hybridized two well-known multi-objective optimization evolutionary algorithms: NSGA-II and MOEA/D with Harmony Search. We studied the efficiency of the proposed novel algorithms to solve multi-objective optimization problems. To evaluate our work, we used well-known datasets: ZDT, DTLZ and CEC2009. We evaluate the algorithm performance using Inverted Generational Distance (IGD). The results showed that the proposed algorithms outperform in solving problems with multiple local fronts in terms of IGD as compared to the original ones (i.e., NSGA-II and MOEA/D).

关键词： multi-objective optimization problems Harmony search algorithm multi-objective optimization evolutionary algorithms

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A Strength Pareto Gravitational Search Algorithm for multi-objective optimization problems

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INTERNATIONAL JOURNAL OF PATTERN RECOGNITION AND ARTIFICIAL INTELLIGENCE 2015年第6期29卷 1559010-1559010页

作者： Yuan, Xiaohui Chen, Zhihuan Yuan, Yanbin Huang, Yuehua Zhang, Xiaopan Huazhong Univ Sci & Technol Sch Hydropower & Informat Engn Wuhan 430074 Peoples R China Wuhan Univ Technol Sch Resource & Environm Engn Wuhan 430070 Peoples R China China Three Gorges Univ Coll Elect Engn & New Energy Yichang 443002 Peoples R China

A novel strength Pareto gravitational search algorithm (SPGSA) is proposed to solve multi-objective optimization problems. This SPGSA algorithm utilizes the strength Pareto concept to assign the fitness values for agents and uses a fine-grained elitism selection mechanism to keep the population diversity. Furthermore, the recombination operators are modeled in this approach to decrease the possibility of trapping in local optima. Experiments are conducted on a series of benchmark problems that are characterized by difficulties in local optimality, non-uniformity, and nonconvexity. The results show that the proposed SPGSA algorithm performs better in comparison with other related works. On the other hand, the effectiveness of two subtle means added to the GSA are verified, i.e. the fine-grained elitism selection and the use of SBX and PMO operators. Simulation results show that these measures not only improve the convergence ability of original GSA, but also preserve the population diversity adequately, which enables the SPGSA algorithm to have an excellent ability that keeps a desirable balance between the exploitation and exploration so as to accelerate the convergence speed to the true Pareto-optimal front.

关键词： Gravitational search algorithm strength Pareto multi-objective optimization problems recombination operator fine-grained elitism selection

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A modified differential evolution algorithm for multi-objective optimization problems

A modified differential evolution algorithm for multi-object...

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Chinese Conference on Pattern Recognition/1st CJK Joint Workshop on Pattern Recognition

作者： Tang Ke-zong Sun Ting-kai Yang Jing-yu Gao Shang Nanjing Univ Sci & Technol Sch Comp Sci & Technol Nanjing 210094 Peoples R China Jiangsu Univ Sci & Technol Schl Comp Sci & Engn Zhenjiang 212003 Peoples R China

ISBN: (纸本)9781424441990

Differential Evolutionary (DE) is a simple, fast and robust evolutionary algorithm for multi-objective optimization problems (MOPs). This paper is to introduce a modified differential evolutionary algorithm (MDE) to solve MOPs. There are some different points between MDE and traditional DE: individual mutation and its selection strategy;M DE allows infeasible solutions of population to participate in mutation process, and mutation strategy of individuals adapt to a modified updating scheme of particle velocity in PSO. The fast nondominated sorting and ranking selection scheme of NSGA-II proposed by Deb is incorporated into individual's selection process. We finally obtain a set of global optimal solutions (gbest). Simulated experiments show that the obtained solutions present good uniformity of diversity, and they are close to the true frontier of Pareto. Also, the convergence of solutions obtained is satisfactory.

关键词： Differential evolution multi-objective optimization problems Pareto-optimal solution

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Sparse large-scale multi-objective optimization algorithm based on impact factor assistance

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ENGINEERING APPLICATIONS OF ARTIFICIAL INTELLIGENCE 2025年 151卷

作者： Hu, Ziyu Nie, Xuetao Sun, Hao Wei, Lixin Zhang, Jinlu Wang, Cong Yanshan Univ Sch Elect Engn Qinhuangdao 066004 Hebei Peoples R China Yanshan Univ Key Lab Ind Comp Control Engn Hebei Prov Qinhuangdao 066004 Hebei Peoples R China

In the real world, there exists a special category of multi-objective optimization problems with more than 1000 decision variables. However, only a few decision variables play a crucial role in optimizing the objective functions. Such problems are defined as sparse large-scale multi-objective optimization problems (SLSMOPs). Due to the difficulty in effectively identifying the non-zero positions of decision variables, traditional evolutionary optimization algorithms suffer from slow convergence speed and poor convergence effect, which means it is unable to efficiently obtain the Pareto optimal solution set. To address this challenge, the Impact Factor Assisted Algorithm (IFA) is proposed, which adopts a novel initial population strategy to generate sparse populations. Meanwhile, the impact factor of each decision variable is calculated, serving as a key basis for measuring the importance of each decision variable. During the algorithm's operation, the impact factors are iteratively updated to rationally group decision variables and guide population evolution. This approach can accurately identify the positions of non-zero decision variables. The experimental results on eight benchmark and real-world problems indicate that the algorithm outperforms several existing sparse large-scale multi-objective optimization algorithms (SLSMOEAs).

关键词： Evolutionary algorithm Impact factor Decision variable grouping multi-objective optimization problems Sparse large-scale optimization Instance selection

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An improved multi-objective particle swarm optimization algorithm for the design of foundation pit of rail transit upper cover project

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SCIENTIFIC REPORTS 2025年第1期15卷 1-25页

作者： Shao, Jinyan Lu, Yuan Sun, Yi Zhao, Lei Beijing Jiaotong Univ TOD Inst Beijing 100044 Peoples R China Beijing Jiao Tong Univ Sch Architecture & Design Beijing 100044 Peoples R China China Architecture Design & Res Inst Co Ltd Shanghai Branch Shanghai Peoples R China Beijing Urban Construct Design & Dev Grp Co Ltd Beijing 100037 Peoples R China

In this study, a multi-objective particle swarm optimization (MOIPSO) algorithm is proposed to address complex optimization problems, including real-world engineering challenges. The algorithm retains the basic convergence mechanism of particle swarm optimization (PSO) as its core, while innovatively combining the fast non-dominated sorting technique to effectively evaluate and approximate the Pareto optimal solution set. To enhance the diversity and generalization of the solution set, the crowding distance mechanism is introduced, ensuring a good balance between multiple optimization objectives and a wider coverage of the solution space. Additionally, an acceleration factor based on trigonometric functions and an adaptive Gaussian mutation strategy are incorporated, improving the exploration ability of the particles in the search space and facilitating their movement towards the global optimal solution more effectively. The performance of the algorithm is verified using the multi-modal multi-objective benchmark function set provided by CEC2020, and comparisons are made with five advanced multi-objective metaheuristics. The MOIPSO algorithm is also applied to solve the design problem of rail transit upper cover foundation pit, further demonstrating the practical effectiveness of the proposed algorithm. The results show that MOIPSO not only performs well in multi-objective function testing but also proves highly competitive in solving real-world engineering problems. Note that the source codes of MOGWO are publicly available at https://***/matlabcentral/fileexchange/177404-moipso-optimization-engineering-problem.

关键词： multi-objective optimization problems Particle swarm optimization multi-objective particle swarm optimization (MOIPSO) Rail transit upper cover foundation pit

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