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 17 articles )

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  1. Kukkonen, Saku; Coello Coello, Carlos A.: Generalized differential evolution for numerical and evolutionary optimization (2017)
  2. Alberto, Isolina; Coello Coello, Carlos A.; Mateo, Pedro M.: A comparative study of variation operators used for evolutionary multi-objective optimization (2014)
  3. Li, Yangyang; Xu, Xia; Li, Peidao; Jiao, Licheng: Improved RM-MEDA with local learning (2014)
  4. Jiao, L.C.; Wang, Handing; Shang, R.H.; Liu, F.: A co-evolutionary multi-objective optimization algorithm based on direction vectors (2013)
  5. Martí, Luis; García, Jesús; Berlanga, Antonio; Molina, José M.: Multi-objective optimization with an adaptive resonance theory-based estimation of distribution algorithm (2013)
  6. 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)
  7. Zhou, Aimin; Gao, Feng; Zhang, Guixu: A decomposition based estimation of distribution algorithm for multiobjective traveling salesman problems (2013)
  8. Gong, Mao-Guo; Zhang, Ling-Jun; Ma, Jing-Jing; Jiao, Li-Cheng: Community detection in dynamic social networks based on multiobjective immune algorithm (2012)
  9. 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)
  10. Martí, Luis; García, Jesús; Berlanga, Antonio; Coello Coello, Carlos A.; Molina, José M.: MB-GNG: Addressing drawbacks in multi-objective optimization estimation of distribution algorithms (2011)
  11. Shim, Vui Ann; Tan, Kay Chen; Chia, Jun Yong; Chong, Jin Kiat: Evolutionary algorithms for solving multi-objective travelling salesman problem (2011)
  12. Sindhya, Karthik; Ruuska, Sauli; Haanpää, Tomi; Miettinen, Kaisa: A new hybrid mutation operator for multiobjective optimization with differential evolution (2011)
  13. Wang, Feng; Lin, Zhiyi; Yang, Cheng; Li, Yuanxiang: Using selfish gene theory to construct mutual information and entropy based clusters for bivariate optimizations (2011)
  14. Ahn, Chang Wook; Kim, Eungyeong; Kim, Hyun-Tae; Lim, Dong-Hyun; An, Jinung: A hybrid multiobjective evolutionary algorithm: Striking a balance with local search (2010)
  15. Wang, Yu; Li, Bin; Weise, Thomas: Estimation of distribution and differential evolution cooperation for large scale economic load dispatch optimization of power systems (2010)
  16. Zhang, Qingfu; Zhou, Aimin; Jin, Yaochu: RM-MEDA: A regularity model-based multiobjective estimation of distribution algorithm. (2008)
  17. Zhang, Q.; Zhou, A.; Jin, Y.: Errata to ”RM-MEDA: A regularity model-based multiobjective estimation of distribution algorithm” [Feb 08 41-63]. (2008)