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.

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  1. Anahideh, Hadis; Rosenberger, Jay; Chen, Victoria: High-dimensional black-box optimization under uncertainty (2022)
  2. Karimi-Mamaghan, Maryam; Mohammadi, Mehrdad; Meyer, Patrick; Karimi-Mamaghan, Amir Mohammad; Talbi, El-Ghazali: Machine learning at the service of meta-heuristics for solving combinatorial optimization problems: a state-of-the-art (2022)
  3. Ozaki, Yoshihiko; Tanigaki, Yuki; Watanabe, Shuhei; Nomura, Masahiro; Onishi, Masaki: Multiobjective tree-structured Parzen estimator (2022)
  4. Pour, Pouya Aghaei; Rodemann, Tobias; Hakanen, Jussi; Miettinen, Kaisa: Surrogate assisted interactive multiobjective optimization in energy system design of buildings (2022)
  5. Wang, Wenyu; Akhtar, Taimoor; Shoemaker, Christine A.: Integrating (\varepsilon)-dominance and RBF surrogate optimization for solving computationally expensive many-objective optimization problems (2022)
  6. Belakaria, Syrine; Deshwal, Aryan; Doppa, Janardhan Rao: Output space entropy search framework for multi-objective Bayesian optimization (2021)
  7. Bigeon, Jean; Le Digabel, Sébastien; Salomon, Ludovic: DMulti-MADS: mesh adaptive direct multisearch for bound-constrained blackbox multiobjective optimization (2021)
  8. Korondi, Péter Zénó; Marchi, Mariapia; Parussini, Lucia; Poloni, Carlo: Multi-fidelity design optimisation strategy under uncertainty with limited computational budget (2021)
  9. Lovison, Alberto; Miettinen, Kaisa: On the extension of the \textscdirectalgorithm to multiple objectives (2021)
  10. Ortiz-Martínez, Víctor M.; Martínez-Frutos, Jesús; Hontoria, Eloy; Hernández-Fernández, Francisco J.; Egea, Jose A.: Multiplicity of solutions in model-based multiobjective optimization of wastewater treatment plants (2021)
  11. Prinz, Sebastian; Thomann, Jana; Eichfelder, Gabriele; Boeck, Thomas; Schumacher, Jörg: Expensive multi-objective optimization of electromagnetic mixing in a liquid metal (2021)
  12. Binois, Mickael; Picheny, Victor; Taillandier, Patrick; Habbal, Abderrahmane: The Kalai-Smorodinsky solution for many-objective Bayesian optimization (2020)
  13. Gaudrie, David; Le Riche, Rodolphe; Picheny, Victor; Enaux, Benoît; Herbert, Vincent: Targeting solutions in Bayesian multi-objective optimization: sequential and batch versions (2020)
  14. Han, Ding; Zheng, Jianrong: A Kriging model-based expensive multiobjective optimization algorithm using R2 indicator of expectation improvement (2020)
  15. Ma, Lianbo; Wang, Rui; Chen, Shengminjie; Cheng, Shi; Wang, Xingwei; Lin, Zhiwei; Shi, Yuhui; Huang, Min: A novel many-objective evolutionary algorithm based on transfer matrix with kriging model (2020)
  16. Paulo Paneque Galuzio, Emerson Hochsteiner de Vasconcelos Segundo, Leandro dos Santos Coelho, Viviana Cocco Mariani: MOBOpt - multi-objective Bayesian optimization (2020) not zbMATH
  17. Rojas Gonzalez, Sebastian; Jalali, Hamed; van Nieuwenhuyse, Inneke: A multiobjective stochastic simulation optimization algorithm (2020)
  18. Rojas-Gonzalez, Sebastian; van Nieuwenhuyse, Inneke: A survey on kriging-based infill algorithms for multiobjective simulation optimization (2020)
  19. Wang, Xilu; Jin, Yaochu; Schmitt, Sebastian; Olhofer, Markus: An adaptive Bayesian approach to surrogate-assisted evolutionary multi-objective optimization (2020)
  20. Wauters, Jolan; Keane, Andy; Degroote, Joris: Development of an adaptive infill criterion for constrained multi-objective asynchronous surrogate-based optimization (2020)

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