RM-MEDA swMATH ID: 8554 Software Authors: Qingfu Zhang; Aimin Zhou; Yaochu Jin Description: 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. Homepage: http://dl.acm.org/citation.cfm?id=2221857 Related Software: MOEA/D; SPEA2; HypE; SMS-EMOA; PlatEMO; GDE3; MOPED; jMetal; MOPSO; MSOPS-II; NBI; PISA; apcluster; APCluster; weightedHypervolume; MONEDA; PAES; SSA; MOMPA; ALO Cited in: 31 Documents all top 5 Cited by 109 Authors 3 Berlanga, Antonio 3 Coello Coello, Carlos A. 3 Martí, Luis 3 Molina, José Manuel 3 Tan, Yanyan 2 Jiao, Licheng 2 Jiao, Yongchang 2 Li, Hong 2 Wang, Xin-Kuan 2 Zhou, Aimin 1 Ahn, Changwook 1 Alberto, Isolina 1 An, Jinung 1 Araújo, Aluizio Fausto Ribeiro 1 Auger, Anne 1 Brockhoff, Dimo 1 Cai, Lijun 1 Cai, Shaowei 1 Chen, Qianqian 1 Chen, Yingxia 1 Chia, Jun Yong 1 Chong, Jin Kiat 1 Dai, Guangming 1 Deb, Kalyanmoy 1 Feng, Junhong 1 Fleming, Peter John 1 Gao, Feng 1 Gao, Weifeng 1 Gao, Ziyou 1 Giagkiozis, Ioannis 1 Gong, Maoguo 1 Guerrero-Peña, Elaine 1 Hansen, Nikolaus 1 He, Xiaoyu 1 Hu, Ziyu 1 Huang, Peiqiu 1 Huang, Zhongqiang 1 Ji, Hao 1 Jia, Bin 1 Jiang, Min 1 Jin, Yaochu 1 Khodadadi, Nima 1 Kim, Eungyeong 1 Kim, Hyuntae 1 Kong, Xiangyong 1 Kukkonen, Saku 1 Kwong, Sam 1 Li, Fei 1 Li, Ke 1 Li, Xiangping 1 Liao, Bo 1 Lim, Donghyun 1 Liu, Cong 1 Liu, Fang 1 Liu, Haihua 1 Liu, Jianchang 1 Liu, Jie 1 Liu, Sanyang 1 Liu, Xiaoxiong 1 Ma, Jingjing 1 Ma, Ke 1 Ma, Xuemin 1 Mateo, Pedro M. 1 Meng, Lili 1 Mersmann, Olaf 1 Mirjalili, Seyed Mohammad 1 Mirjalili, SeyedAli 1 Olhofer, Markus 1 Purshouse, Robin C. 1 Qiu, Liming 1 Ren, Siqi 1 Ros, Raymond 1 Schmitt, Sebastian 1 Shang, Ronghua 1 Shang, Xiaoting 1 Shi, Lulu 1 Shim, Vui Ann 1 Tan, Kay Chen 1 Tušar, Tea 1 Wang, Handing 1 Wang, Liying 1 Wang, Peng 1 Wang, Xilu 1 Wang, Yirui 1 Wei, Lixin 1 Wei, Xiaohui 1 Wu, Yan 1 Xiang, Yi 1 Xu, Jingwei 1 Yan, Zeyuan 1 Yang, Jialiang 1 Yang, Jingming 1 Yang, Kai 1 Yen, Gary G. 1 Zhang, Cuijun 1 Zhang, Guixu 1 Zhang, Huaxiang 1 Zhang, Jie 1 Zhang, Jinyuan 1 Zhang, Lingjun ...and 9 more Authors all top 5 Cited in 16 Serials 14 Information Sciences 2 Mathematical Problems in Engineering 1 Artificial Intelligence 1 Computers & Mathematics with Applications 1 Computer Methods in Applied Mechanics and Engineering 1 Operations Research Letters 1 Journal of Computer Science and Technology 1 Computers & Operations Research 1 Mathematical and Computer Modelling 1 Journal of Global Optimization 1 Applied Mathematical Modelling 1 European Journal of Operational Research 1 Annals of Mathematics and Artificial Intelligence 1 Optimization Methods & Software 1 Flexible Services and Manufacturing Journal 1 International Journal of Systems Science. Principles and Applications of Systems and Integration all top 5 Cited in 7 Fields 28 Operations research, mathematical programming (90-XX) 9 Computer science (68-XX) 3 Numerical analysis (65-XX) 2 Statistics (62-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Information and communication theory, circuits (94-XX) Citations by Year