HypE swMATH ID: 19794 Software Authors: Bader, J., Zitzler, E. Description: HypE: an algorithm for fast hypervolume-based many-objective optimization. In the field of evolutionary multi-criterion optimization, the hypervolume indicator is the only single set quality measure that is known to be strictly monotonic with regard to Pareto dominance: whenever a Pareto set approximation entirely dominates another one, then the indicator value of the dominant set will also be better. This property is of high interest and relevance for problems involving a large number of objective functions. However, the high computational effort required for hypervolume calculation has so far prevented the full exploitation of this indicator’s potential; current hypervolume-based search algorithms are limited to problems with only a few objectives. This paper addresses this issue and proposes a fast search algorithm that uses Monte Carlo simulation to approximate the exact hypervolume values. The main idea is not that the actual indicator values are important, but rather that the rankings of solutions induced by the hypervolume indicator. In detail, we present HypE, a hypervolume estimation algorithm for multi-objective optimization, by which the accuracy of the estimates and the available computing resources can be traded off; thereby, not only do many-objective problems become feasible with hypervolume-based search, but also the runtime can be flexibly adapted. Moreover, we show how the same principle can be used to statistically compare the outcomes of different multi-objective optimizers with respect to the hypervolume—so far, statistical testing has been restricted to scenarios with few objectives. The experimental results indicate that HypE is highly effective for many-objective problems in comparison to existing multi-objective evolutionary algorithms. HypE is available for download at http://www.tik.ee.ethz.ch/sop/download/supplementary/hype/ Homepage: http://www.mitpressjournals.org/doi/10.1162/EVCO_a_00009#.WQbq3KP5zu4 Related Software: MOEA/D; SPEA2; SMS-EMOA; NBI; PlatEMO; weightedHypervolume; RM-MEDA; ParEGO; MOMBI; MSOPS-II; jMetal; PISA; SMPSO; MOPSO; PAES; EGO; GDE3; Borg; irace; KEEL Cited in: 83 Publications all top 5 Cited by 276 Authors 3 Guerreiro, Andreia P. 3 Jiao, Licheng 3 Wang, Rui 3 Yang, Shengxiang 3 Zheng, Jinhua 2 Berlanga, Antonio 2 Bringmann, Karl 2 Dai, Cai 2 Fernandes, Islame F. C. 2 Fleming, Peter John 2 Friedrich, Tobias 2 Goldbarg, Elizabeth Ferreira Gouvêa 2 Goldbarg, Marco César 2 Gong, Maoguo 2 Huang, Peiqiu 2 Jin, Yaochu 2 Li, Jie 2 Li, Miqing 2 Li, Xia 2 Liefooghe, Arnaud 2 Lin, Qiuzhen 2 Maia, Silvia M. D. M. 2 Martí, Luis 2 Molina, José Manuel 2 Paquete, Luís F. 2 Purshouse, Robin C. 2 Sun, Jianyong 2 Tan, Kay Chen 2 Zhou, Yuren 2 Zou, Juan 1 Abdollahpouri, Alireza 1 Akkan, Can 1 Ali, Musrrat 1 Allmendinger, Richard W. 1 Auger, Anne 1 Bader, Johannes 1 Bai, Hui 1 Bao, Chunteng 1 Barán, Benjamin 1 Basseur, Matthieu 1 Bect, Julien 1 Bian, Kun 1 Bilge, Ümit 1 Binois, Mickaël 1 Brizuela, Carlos A. 1 Brockhoff, Dimo 1 Cai, Lijun 1 Cai, Shaowei 1 Cao, Yongtao 1 Chabane, Brahim 1 Chan, Felix T. S. 1 Chen, Huangke 1 Chen, Lei 1 Chen, Minrong 1 Chen, Zefeng 1 Chen, Zehua 1 Cheng, Ran 1 Cheung, Yiuming 1 Creighton, Douglas 1 Deb, Kalyanmoy 1 Derbel, Bilel 1 Dong, Zhiming 1 Du, Wei 1 Emperador, José María 1 Ermis, Gülcin 1 Fan, Rui 1 Feliot, Paul 1 Feng, Jie 1 Feng, Jiqiang 1 Fieldsend, Jonathan E. 1 Figueira, José Rui 1 Fonseca, Carlos M. 1 Fu, Liuwei 1 Galván, Blas 1 Gao, Liang 1 Gao, Weifeng 1 Gao, Yang 1 Ghodsi, Siamak 1 Giagkiozis, Ioannis 1 Gomes, Ricardo J. 1 Gong, Dunwei 1 Goodman, Erik D. 1 Greiner, David 1 Guo, Weian 1 Guo, Zhaoxia 1 Habbal, Abderrahmane 1 Hale, Joshua Q. 1 Han, Ding 1 Hanoun, Samer 1 Hao, Jin-Kao 1 Hayashida, Tomohiro 1 He, Fazhi 1 He, Xiaoguang 1 He, Xiaoyu 1 Hikoyama, Kazuhisa 1 Hu, Bo 1 Huang, Xiongwen 1 Humeau, Jérémie 1 Hyndman, Rob J. 1 Igel, Christian ...and 176 more Authors all top 5 Cited in 26 Serials 32 Information Sciences 8 Computers & Operations Research 6 European Journal of Operational Research 4 Journal of Global Optimization 4 Mathematical Problems in Engineering 3 Artificial Intelligence 3 International Journal of Systems Science. Principles and Applications of Systems and Integration 2 Theoretical Computer Science 2 Annals of Operations Research 1 Computers & Mathematics with Applications 1 Applied Mathematics and Computation 1 Journal of Statistical Planning and Inference 1 Mathematics and Computers in Simulation 1 Computational Optimization and Applications 1 Applied Mathematics. Series B (English Edition) 1 Annals of Mathematics and Artificial Intelligence 1 INFORMS Journal on Computing 1 Soft Computing 1 Discrete Dynamics in Nature and Society 1 International Journal of Applied Mathematics and Computer Science 1 Optimization and Engineering 1 RAIRO. Operations Research 1 Archives of Computational Methods in Engineering 1 Journal of Machine Learning Research (JMLR) 1 Computational Intelligence 1 Journal of Control Science and Engineering all top 5 Cited in 8 Fields 80 Operations research, mathematical programming (90-XX) 24 Computer science (68-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Statistics (62-XX) 3 Numerical analysis (65-XX) 2 Combinatorics (05-XX) 1 Mechanics of deformable solids (74-XX) 1 Systems theory; control (93-XX) Citations by Year