RM-MEDA: A Regularity Model-Based Multiobjective Estimation of Distribution Algorithm. Under mild conditions, it can be induced from the Karush-Kuhn-Tucker condition that the Pareto set, in the decision space, of a continuous multiobjective optimization problem is a piecewise continuous (m - 1)-D manifold, where m is the number of objectives. Based on this regularity property, we propose a regularity model-based multiobjective estimation of distribution algorithm (RM-MEDA) for continuous multiobjective optimization problems with variable linkages. At each generation, the proposed algorithm models a promising area in the decision space by a probability distribution whose centroid is a (m - 1)-D piecewise continuous manifold. The local principal component analysis algorithm is used for building such a model. New trial solutions are sampled from the model thus built. A nondominated sorting-based selection is used for choosing solutions for the next generation. Systematic experiments have shown that, overall, RM-MEDA outperforms three other state-of-the-art algorithms, namely, GDE3, PCX-NSGA-II, and MIDEA, on a set of test instances with variable linkages. We have demonstrated that, compared with GDE3, RM-MEDA is not sensitive to algorithmic parameters, and has good scalability to the number of decision variables in the case of nonlinear variable linkages. A few shortcomings of RM-MEDA have also been identified and discussed in this paper.

This software is also peer reviewed by journal TOMS.

References in zbMATH (referenced in 35 articles )

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  1. Hansen, Nikolaus; Auger, Anne; Ros, Raymond; Mersmann, Olaf; Tušar, Tea; Brockhoff, Dimo: COCO: a platform for comparing continuous optimizers in a black-box setting (2021)
  2. Dong, Nan-jiang; Wang, Rui: MEAPCA: a multi-population evolutionary algorithm based on PCA for multi-objective optimization (2020)
  3. Wang, Xilu; Jin, Yaochu; Schmitt, Sebastian; Olhofer, Markus: An adaptive Bayesian approach to surrogate-assisted evolutionary multi-objective optimization (2020)
  4. Wu, Yan; Shi, Lulu; Liu, Xiaoxiong: A new dynamic strategy for dynamic multi-objective optimization (2020)
  5. Zhang, Zhechen; Liu, Sanyang; Gao, Weifeng; Xu, Jingwei; Zhu, Shengqi: An enhanced multi-objective evolutionary optimization algorithm with inverse model (2020)
  6. Zheng, Wei; Wu, Jianyu; Zhang, Chenghu; Sun, Jianyong: A clustering-based multiobjective evolutionary algorithm for balancing exploration and exploitation (2020)
  7. Zhou, Aimin; Wang, Yirui; Zhang, Jinyuan: Objective extraction via fuzzy clustering in evolutionary many-objective optimization (2020)
  8. Guerrero-Peña, Elaine; Araújo, Aluízio Fausto Ribeiro: Multi-objective evolutionary algorithm with prediction in the objective space (2019)
  9. Liu, Cong; Chen, Qianqian; Chen, Yingxia; Liu, Jie: A fast multiobjective fuzzy clustering with multimeasures combination (2019)
  10. Wang, Peng; Zhu, Wen; Liu, Haihua; Liao, Bo; Cai, Lijun; Wei, Xiaohui; Ren, Siqi; Yang, Jialiang: A new resource allocation strategy based on the relationship between subproblems for MOEA/D (2019)
  11. Zhou, Yuren; He, Xiaoyu; Xiang, Yi; Cai, Shaowei: A set of new multi- and many-objective test problems for continuous optimization and a comprehensive experimental evaluation (2019)
  12. Jiang, Min; Qiu, Liming; Huang, Zhongqiang; Yen, Gary G.: Dynamic multi-objective estimation of distribution algorithm based on domain adaptation and nonparametric estimation (2018)
  13. Zhou, Chong; Dai, Guangming; Zhang, Cuijun; Li, Xiangping; Ma, Ke: Entropy based evolutionary algorithm with adaptive reference points for many-objective optimization problems (2018)
  14. Kukkonen, Saku; Coello Coello, Carlos A.: Generalized differential evolution for numerical and evolutionary optimization (2017)
  15. Martí, Luis; García, Jesús; Berlanga, Antonio; Molina, José M.: MONEDA: scalable multi-objective optimization with a neural network-based estimation of distribution algorithm (2016)
  16. Li, Ke; Kwong, Sam; Deb, Kalyanmoy: A dual-population paradigm for evolutionary multiobjective optimization (2015)
  17. Zhu, Xiaoshu; Zhang, Jie; Feng, Junhong: Multiobjective particle swarm optimization based on PAM and uniform design (2015)
  18. Alberto, Isolina; Coello Coello, Carlos A.; Mateo, Pedro M.: A comparative study of variation operators used for evolutionary multi-objective optimization (2014)
  19. Giagkiozis, I.; Purshouse, R. C.; Fleming, P. J.: Generalized decomposition and cross entropy methods for many-objective optimization (2014)
  20. Li, Yangyang; Xu, Xia; Li, Peidao; Jiao, Licheng: Improved RM-MEDA with local learning (2014) ioport

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