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 28 articles )

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  1. Dong, Nan-jiang; Wang, Rui: MEAPCA: a multi-population evolutionary algorithm based on PCA for multi-objective optimization (2020)
  2. Zheng, Wei; Wu, Jianyu; Zhang, Chenghu; Sun, Jianyong: A clustering-based multiobjective evolutionary algorithm for balancing exploration and exploitation (2020)
  3. Liu, Cong; Chen, Qianqian; Chen, Yingxia; Liu, Jie: A fast multiobjective fuzzy clustering with multimeasures combination (2019)
  4. 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)
  5. Jiang, Min; Qiu, Liming; Huang, Zhongqiang; Yen, Gary G.: Dynamic multi-objective estimation of distribution algorithm based on domain adaptation and nonparametric estimation (2018)
  6. Zhou, Chong; Dai, Guangming; Zhang, Cuijun; Li, Xiangping; Ma, Ke: Entropy based evolutionary algorithm with adaptive reference points for many-objective optimization problems (2018)
  7. Kukkonen, Saku; Coello Coello, Carlos A.: Generalized differential evolution for numerical and evolutionary optimization (2017)
  8. Martí, Luis; García, Jesús; Berlanga, Antonio; Molina, José M.: MONEDA: scalable multi-objective optimization with a neural network-based estimation of distribution algorithm (2016)
  9. Li, Ke; Kwong, Sam; Deb, Kalyanmoy: A dual-population paradigm for evolutionary multiobjective optimization (2015)
  10. Zhu, Xiaoshu; Zhang, Jie; Feng, Junhong: Multiobjective particle swarm optimization based on PAM and uniform design (2015)
  11. Alberto, Isolina; Coello Coello, Carlos A.; Mateo, Pedro M.: A comparative study of variation operators used for evolutionary multi-objective optimization (2014)
  12. Giagkiozis, I.; Purshouse, R. C.; Fleming, P. J.: Generalized decomposition and cross entropy methods for many-objective optimization (2014)
  13. Li, Yangyang; Xu, Xia; Li, Peidao; Jiao, Licheng: Improved RM-MEDA with local learning (2014) ioport
  14. Hou, Liqiang; Cai, Yuanli; Zhang, Rongzhi; Li, Jisheng: Evidence theory based multidisciplinary robust optimization for micro Mars entry probe design (2013) ioport
  15. Jiao, L. C.; Wang, Handing; Shang, R. H.; Liu, F.: A co-evolutionary multi-objective optimization algorithm based on direction vectors (2013)
  16. Martí, Luis; García, Jesús; Berlanga, Antonio; Molina, José M.: Multi-objective optimization with an adaptive resonance theory-based estimation of distribution algorithm (2013)
  17. Tan, Yan-yan; Jiao, Yong-chang; Li, Hong; Wang, Xin-kuan: MOEA/D + uniform design: a new version of MOEA/D for optimization problems with many objectives (2013)
  18. Zhou, Aimin; Gao, Feng; Zhang, Guixu: A decomposition based estimation of distribution algorithm for multiobjective traveling salesman problems (2013)
  19. Gong, Mao-Guo; Zhang, Ling-Jun; Ma, Jing-Jing; Jiao, Li-Cheng: Community detection in dynamic social networks based on multiobjective immune algorithm (2012)
  20. Tan, Yan-Yan; Jiao, Yong-Chang; Li, Hong; Wang, Xin-Kuan: A modification to MOEA/D-DE for multiobjective optimization problems with complicated Pareto sets (2012)

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