weightedHypervolume swMATH ID: 31878 Software Authors: Johannes Bader, Dimo Brockhoff, Eckart Zitzler Description: Weighted Hypervolume Indicator: Implementation of hypervolume indicators for different weight distribution functions. Using the hypervolume of the dominated portion of the objective space as a measure for the quality of Pareto set approximations has received more and more attention in recent years. So far, the hypervolume indicator is the only measure known in the literature on evolutionary multiobjective optimization that possesses the following two properties. On the one hand, it is sensitive to any type of improvements, i.e., whenever an approximation set A dominates another approximation set B, then the measure yields a strictly better quality value for the former than for the latter set. On the other hand, the hypervolume measure guarantees that any approximation set A that achieves the maximally possible quality value for a particular problem contains all Pareto-optimal objective vectors. With the recently proposed approach of a weighted hypervolume indicator, these properties are not removed by simultaneously be able to incorporate various user preferences. According to [zbt2007a], three different hypervolume based indicators have been developed incorporating the following preferences: Focus on extreme points, Focus on the extremes of the second objective plus one additional extreme point for the first objective, Focus on a given reference point. Homepage: http://people.ee.ethz.ch/~sop/download/supplementary/weightedHypervolume/?page=weightedHypervolume Related Software: HypE; SMS-EMOA; NBI; SPEA2; ParEGO; MOEA/D; CPLEX; SPOT; irace; jMetal; EGO; Gurobi; Paramils; FPBH.jl; Julia; FEASPUMP; GitHub; MONEDA; RM-MEDA; fminsearch Cited in: 29 Publications all top 5 Cited by 75 Authors 4 Charkhgard, Hadi 2 Berlanga, Antonio 2 Guerreiro, Andreia P. 2 Hyndman, Rob J. 2 López-Ibáñez, Manuel 2 Martí, Luis 2 Molina, José Manuel 2 Pal, Aritra 2 Smith-Miles, Kate A. 2 Steponavičė, Ingrida 2 Villanova, Laura 1 Araya, Ignacio J. 1 Asouti, Varvara G. 1 Audet, Charles 1 Auger, Anne 1 Bader, Johannes 1 Berghammer, Rudolf 1 Bigeon, Jean 1 Boland, Natashia L. 1 Brockhoff, Dimo 1 Cao, Yongtao 1 Cartier, Dominique 1 Chen, Lei 1 Cheung, Yiuming 1 Dai, Rui 1 Dauzère-Pérès, Stéphane 1 Diaz, Juan Esteban 1 Dolgui, Alexandre B. 1 Engelbrecht, Andries Petrus 1 Eremeev, Anton Valentinovich 1 Figueira, José Rui 1 Fleming, Peter John 1 Fonseca, Carlos M. 1 Friedrich, Tobias 1 García-León, Andrés Alberto 1 Giagkiozis, Ioannis 1 Giannakoglou, Kyriakos C. 1 Gutjahr, Walter J. 1 Hale, Joshua Q. 1 Helbig, Mardé 1 Jiao, Licheng 1 Kampolis, Ioannis C. 1 Kaucic, Massimiliano 1 Le Digabel, Sébastien 1 Liu, Hailin 1 Liu, Jiangdi 1 Liu, Ruochen 1 Manquinho, Vasco M. 1 Mati, Yazid 1 Moyano, Mauricio 1 Neumann, Frank 1 Nicosia, Giuseppe 1 Purshouse, Robin C. 1 Reiter, Peter 1 Ren, Rui 1 Robinson, Timothy J. 1 Rojas-Gonzalez, Sebastian 1 Romano, Vittorio 1 Salomon, Ludovic 1 Sanchez, Cristobal 1 Savelsbergh, Martin W. P. 1 Shirazi-Manesh, Mojdeh 1 Sigaev, V. S. 1 Smucker, Byran J. 1 Stracquadanio, Giovanni 1 Stützle, Thomas G. 1 Tan, Kay Chen 1 Tang, Weisen 1 Trompoukis, Xenofon S. 1 Van Nieuwenhuyse, Inneke 1 Wang, Rui 1 Zhou, Enlu 1 Zhou, Runan 1 Zhu, Helin 1 Zitzler, Eckart all top 5 Cited in 13 Serials 6 Computers & Operations Research 6 European Journal of Operational Research 3 Information Sciences 2 Theoretical Computer Science 2 Journal of Global Optimization 2 INFORMS Journal on Computing 1 Computer Methods in Applied Mechanics and Engineering 1 Journal of Computational Physics 1 Journal of Statistical Planning and Inference 1 Automation and Remote Control 1 Annals of Mathematics and Artificial Intelligence 1 CEJOR. Central European Journal of Operations Research 1 Mathematical Programming Computation all top 5 Cited in 8 Fields 27 Operations research, mathematical programming (90-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Computer science (68-XX) 2 Statistics (62-XX) 2 Numerical analysis (65-XX) 1 Fluid mechanics (76-XX) 1 Optics, electromagnetic theory (78-XX) 1 Systems theory; control (93-XX) Citations by Year