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 43 articles )

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  1. Mariappan, Ragunathan; Rajan, Vaibhav: Deep collective matrix factorization for augmented multi-view learning (2019)
  2. Bradford, Eric; Schweidtmann, Artur M.; Lapkin, Alexei: Efficient multiobjective optimization employing Gaussian processes, spectral sampling and a genetic algorithm (2018)
  3. Horn, Daniel; Demircioğlu, Aydın; Bischl, Bernd; Glasmachers, Tobias; Weihs, Claus: A comparative study on large scale kernelized support vector machines (2018)
  4. 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
  5. 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)
  6. Davins-Valldaura, Joan; Moussaoui, Saïd; Pita-Gil, Guillermo; Plestan, Franck: ParEGO extensions for multi-objective optimization of expensive evaluation functions (2017)
  7. Feliot, Paul; Bect, Julien; Vazquez, Emmanuel: A Bayesian approach to constrained single- and multi-objective optimization (2017)
  8. Steponavičė, Ingrida; Hyndman, Rob J.; Smith-Miles, Kate; Villanova, Laura: Dynamic algorithm selection for Pareto optimal set approximation (2017)
  9. Ye Tian, Ran Cheng, Xingyi Zhang, Yaochu Jin: PlatEMO: A MATLAB Platform for Evolutionary Multi-Objective Optimization (2017) arXiv
  10. Zhan, Dawei; Qian, Jiachang; Cheng, Yuansheng: Pseudo expected improvement criterion for parallel EGO algorithm (2017)
  11. Akhtar, Taimoor; Shoemaker, Christine A.: Multi objective optimization of computationally expensive multi-modal functions with RBF surrogates and multi-rule selection (2016)
  12. Emmerich, Michael; Yang, Kaifeng; Deutz, André; Wang, Hao; Fonseca, Carlos M.: A multicriteria generalization of Bayesian global optimization (2016)
  13. Martínez-Frutos, Jesús; Herrero-Pérez, David: Kriging-based infill sampling criterion for constraint handling in multi-objective optimization (2016)
  14. Steponavičė, Ingrida; Shirazi-Manesh, Mojdeh; Hyndman, Rob J.; Smith-Miles, Kate; Villanova, Laura: On sampling methods for costly multi-objective black-box optimization (2016)
  15. Svenson, Joshua; Santner, Thomas: Multiobjective optimization of expensive-to-evaluate deterministic computer simulator models (2016)
  16. Binois, M.; Ginsbourger, D.; Roustant, O.: Quantifying uncertainty on Pareto fronts with Gaussian process conditional simulations (2015)
  17. Mlakar, Miha; Petelin, Dejan; Tušar, Tea; Filipič, Bogdan: GP-DEMO: differential evolution for multiobjective optimization based on Gaussian process models (2015)
  18. Picheny, Victor: Multiobjective optimization using Gaussian process emulators via stepwise uncertainty reduction (2015)
  19. Rakshit, Pratyusha; Konar, Amit: Differential evolution for noisy multiobjective optimization (2015)
  20. Couckuyt, Ivo; Deschrijver, Dirk; Dhaene, Tom: Fast calculation of multiobjective probability of improvement and expected improvement criteria for Pareto optimization (2014)

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