ParEGO swMATH ID: 10968 Software Authors: Knowles, Joshua; Hughes, Evan J. Description: Multiobjective optimization on a budget of 250 evaluations. In engineering and other ‘real-world’ applications, multiobjective optimization problems must frequently be tackled on a tight evaluation budget – tens or hundreds of function evaluations, rather than thousands. In this paper, we investigate two algorithms that use advanced initialization and search strategies to operate better under these conditions. The first algorithm, Bin_MSOPS, uses a binary search tree to divide up the decision space, and tries to sample from the largest empty regions near ‘fit’ solutions. The second algorithm, ParEGO, begins with solutions in a latin hypercube and updates a Gaussian processes surrogate model of the search landscape after every function evaluation, which it uses to estimate the solution of largest expected improvement. The two algorithms are tested using a benchmark suite of nine functions of two and three objectives – on a budget of only 250 function evaluations each, in total. Results indicate that the two algorithms search the space in very different ways and this can be used to understand performance differences. Both algorithms perform well but ParEGO comes out on top in seven of the nine test cases after 100 function evaluations, and on six after the first 250 evaluations. Homepage: http://link.springer.com/chapter/10.1007/978-3-540-31880-4_13 Keywords: multiobjective optimization; expensive black-box functions; ParEGO; DACE; Bin_MSOPS; landscape approximation; response surfaces; test suites Related Software: EGO; MOEA/D; SPEA2; DACE; HypE; Spearmint; PAES; SMS-EMOA; Hyperopt; PlatEMO; NBI; weightedHypervolume; MLMSRBF; MultiGLODS; GitHub; GPareto; SPACE; PISA; jMetal; DiceOptim Cited in: 61 Publications all top 5 Cited by 177 Authors 3 Picheny, Victor 2 Akhtar, Taimoor 2 Binois, Mickaël 2 Coello Coello, Carlos A. 2 Couckuyt, Ivo 2 Deutz, André H. 2 Dhaene, Tom 2 Emmerich, Michael T. M. 2 Eskandari, Hamidreza 2 Geiger, Christopher D. 2 Goel, Tushar 2 Hyndman, Rob J. 2 Lovison, Alberto 2 Martínez-Frutos, Jesús 2 Miettinen, Kaisa M. 2 Rojas-Gonzalez, Sebastian 2 Shoemaker, Christine A. 2 Smith-Miles, Kate A. 2 Steponavičė, Ingrida 2 Van Nieuwenhuyse, Inneke 2 Vazquez, Emmanuel 2 Villanova, Laura 2 Zhan, Dawei 2 Žilinskas, Antanas 1 Alba, Enrique 1 Anahideh, Hadis 1 Auger, Anne 1 Bäck, Thomas H. W. 1 Bader, Johannes 1 Bect, Julien 1 Belakaria, Syrine 1 Benetto, E. 1 Bigeon, Jean 1 Bilionis, Ilias 1 Bischl, Bernd 1 Boeck, Thomas 1 Bradford, Eric 1 Brockhoff, Dimo 1 Bureerat, Sujin 1 Buxton, Bernard F. 1 Byrne, Emma 1 Calvin, James M. 1 Capitanescu, Florin 1 Charalampakis, Aristotelis E. 1 Chen, Shengminjie 1 Chen, Victoria C. P. 1 Cheng, Shi 1 Cheng, Yuansheng 1 Clarkson, P. John 1 Corney, David 1 Davins-Valldaura, Joan 1 Degroote, Joris 1 Demircioğlu, Aydin 1 Deschrijver, Dirk 1 Deshwal, Aryan 1 Doppa, Janardhan Rao 1 Durillo, Juan J. 1 Egea, Jose A. 1 Eichfelder, Gabriele 1 Enaux, Benoit 1 Feliot, Paul 1 Filipič, Bogdan 1 Fonseca, Carlos M. 1 Gao, Liang 1 Gaudrie, David 1 Ginsbourger, David 1 Glasmachers, Tobias 1 Gorissen, Dirk 1 Habbal, Abderrahmane 1 Haftka, Raphael T. 1 Hakanen, Jussi 1 Han, Ding 1 Han, Xu 1 Herbert, Vincent 1 Hernández-Fernández, Francisco J. 1 Herrero-Pérez, David 1 Hontoria, Eloy 1 Horn, Daniel R. 1 Huang, Min 1 Hughes, Evan J. 1 Jaeggi, D. M. 1 Jakobsson, Stefan 1 Jalali, Hamed 1 Jiang, Chen 1 Jiang, Chen 1 Jin, Yaochu 1 Kaliszewski, Ignacy 1 Karimi-Mamaghan, Amir Mohammad 1 Karimi-Mamaghan, Maryam 1 Keane, Andy J. 1 Kipouros, Timoleon 1 Klinkenberg, Jan-Willem 1 Knowles, Joshua D. 1 Konar, Amit 1 Korondi, Péter Zénó 1 Kristensen, Jesper Torp 1 Kunakote, Tawatchai 1 Laermans, Eric 1 Lapkin, Alexei 1 Le Digabel, Sébastien ...and 77 more Authors all top 5 Cited in 21 Serials 17 Journal of Global Optimization 6 European Journal of Operational Research 5 Optimization and Engineering 3 Journal of Heuristics 2 Computer Methods in Applied Mechanics and Engineering 2 Information Sciences 2 International Journal for Numerical Methods in Engineering 2 Computers & Operations Research 2 The Journal of Artificial Intelligence Research (JAIR) 2 Mathematical Problems in Engineering 1 Artificial Intelligence 1 Journal of Optimization Theory and Applications 1 Theoretical Computer Science 1 Machine Learning 1 Computational Statistics and Data Analysis 1 Computational Optimization and Applications 1 Annals of Mathematics and Artificial Intelligence 1 Journal of Machine Learning Research (JMLR) 1 Advances in Data Analysis and Classification. ADAC 1 Optimization Letters 1 Statistics and Computing all top 5 Cited in 9 Fields 49 Operations research, mathematical programming (90-XX) 10 Computer science (68-XX) 9 Statistics (62-XX) 6 Numerical analysis (65-XX) 4 Mechanics of deformable solids (74-XX) 2 Fluid mechanics (76-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Probability theory and stochastic processes (60-XX) 1 Biology and other natural sciences (92-XX) Citations by Year