ParEGO

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.


References in zbMATH (referenced in 58 articles )

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  1. Lovison, Alberto; Miettinen, Kaisa: On the extension of the \textscdirectalgorithm to multiple objectives (2021)
  2. Binois, Mickael; Picheny, Victor; Taillandier, Patrick; Habbal, Abderrahmane: The Kalai-Smorodinsky solution for many-objective Bayesian optimization (2020)
  3. Gaudrie, David; Le Riche, Rodolphe; Picheny, Victor; Enaux, Benoît; Herbert, Vincent: Targeting solutions in Bayesian multi-objective optimization: sequential and batch versions (2020)
  4. Han, Ding; Zheng, Jianrong: A Kriging model-based expensive multiobjective optimization algorithm using R2 indicator of expectation improvement (2020)
  5. 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)
  6. Paulo Paneque Galuzio, Emerson Hochsteiner de Vasconcelos Segundo, Leandro dos Santos Coelho, Viviana Cocco Mariani: MOBOpt - multi-objective Bayesian optimization (2020) not zbMATH
  7. Rojas Gonzalez, Sebastian; Jalali, Hamed; van Nieuwenhuyse, Inneke: A multiobjective stochastic simulation optimization algorithm (2020)
  8. Rojas-Gonzalez, Sebastian; van Nieuwenhuyse, Inneke: A survey on kriging-based infill algorithms for multiobjective simulation optimization (2020)
  9. Wang, Xilu; Jin, Yaochu; Schmitt, Sebastian; Olhofer, Markus: An adaptive Bayesian approach to surrogate-assisted evolutionary multi-objective optimization (2020)
  10. Wauters, Jolan; Keane, Andy; Degroote, Joris: Development of an adaptive infill criterion for constrained multi-objective asynchronous surrogate-based optimization (2020)
  11. Zhan, Dawei; Xing, Huanlai: Expected improvement for expensive optimization: a review (2020)
  12. Mariappan, Ragunathan; Rajan, Vaibhav: Deep collective matrix factorization for augmented multi-view learning (2019)
  13. Yang, Zan; Qiu, Haobo; Gao, Liang; Jiang, Chen; Zhang, Jinhao: Two-layer adaptive surrogate-assisted evolutionary algorithm for high-dimensional computationally expensive problems (2019)
  14. Zhigljavsky, Anatoly; Žilinskas, Antanas: Selection of a covariance function for a Gaussian random field aimed for modeling global optimization problems (2019)
  15. Žilinskas, Antanas; Calvin, James: Bi-objective decision making in global optimization based on statistical models (2019)
  16. Bradford, Eric; Schweidtmann, Artur M.; Lapkin, Alexei: Efficient multiobjective optimization employing Gaussian processes, spectral sampling and a genetic algorithm (2018)
  17. Horn, Daniel; Demircioğlu, Aydın; Bischl, Bernd; Glasmachers, Tobias; Weihs, Claus: A comparative study on large scale kernelized support vector machines (2018)
  18. Bernd Bischl, Jakob Richter, Jakob Bossek, Daniel Horn, Janek Thomas, Michel Lang: mlrMBO: A Modular Framework for Model-Based Optimization of Expensive Black-Box Functions (2017) arXiv
  19. Capitanescu, F.; Marvuglia, A.; Benetto, E.; Ahmadi, A.; Tiruta-Barna, L.: Linear programming-based directed local search for expensive multi-objective optimization problems: application to drinking water production plants (2017)
  20. Davins-Valldaura, Joan; Moussaoui, Saïd; Pita-Gil, Guillermo; Plestan, Franck: ParEGO extensions for multi-objective optimization of expensive evaluation functions (2017)

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