A1 Journal article (refereed)
Treed Gaussian Process Regression for Solving Offline Data-Driven Continuous Multiobjective Optimization Problems (2023)

Mazumdar, A., López-Ibáñez, M., Chugh, T., Hakanen, J., & Miettinen, K. (2023). Treed Gaussian Process Regression for Solving Offline Data-Driven Continuous Multiobjective Optimization Problems. Evolutionary Computation, 31(4), 375-399. https://doi.org/10.1162/evco_a_00329

JYU authors or editors

Publication details

All authors or editors: Mazumdar, Atanu; López-Ibáñez, Manuel; Chugh, Tinkle; Hakanen, Jussi; Miettinen, Kaisa

Journal or series: Evolutionary Computation

ISSN: 1063-6560

eISSN: 1530-9304

Publication year: 2023

Publication date: 28/04/2023

Volume: 31

Issue number: 4

Pages range: 375-399

Publisher: MIT Press

Publication country: United States

Publication language: English

DOI: https://doi.org/10.1162/evco_a_00329

Publication open access: Openly available

Publication channel open access: Partially open access channel

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/87648

Abstract

For offline data-driven multiobjective optimization problems (MOPs), no new data is available during the optimization process. Approximation models (or surrogates) are first built using the provided offline data and an optimizer, e.g. a multiobjective evolutionary algorithm, can then be utilized to find Pareto optimal solutions to the problem with surrogates as objective functions. In contrast to online data-driven MOPs, these surrogates cannot be updated with new data and, hence, the approximation accuracy cannot be improved by considering new data during the optimization process. Gaussian process regression (GPR) models are widely used as surrogates because of their ability to provide uncertainty information. However, building GPRs becomes computationally expensive when the size of the dataset is large. Using sparse GPRs reduces the computational cost of building the surrogates. However, sparse GPRs are not tailored to solve offline data-driven MOPs, where good accuracy of the surrogates is needed near Pareto optimal solutions. Treed GPR (TGPR-MO) surrogates for offline data-driven MOPs with continuous decision variables are proposed in this paper. The proposed surrogates first split the decision space into subregions using regression trees and build GPRs sequentially in regions close to Pareto optimal solutions in the decision space to accurately approximate tradeoffs between the objective functions. TGPR-MO surrogates are computationally inexpensive because GPRs are built only in a smaller region of the decision space utilizing a subset of the data. The TGPR-MO surrogates were tested on distance-based visualizable problems with various data sizes, sampling strategies, numbers of objective functions, and decision variables. Experimental results showed that the TGPR-MO surrogates are computationally cheaper and can handle datasets of large size. Furthermore, TGPR-MO surrogates produced solutions closer to Pareto optimal solutions compared to full GPRs and sparse GPRs.

Keywords: multi-objective optimisation; Gaussian processes; kriging method; Pareto efficiency

Free keywords: Gaussian processes; kriging; regression trees; metamodelling; surrogate; Pareto optimality

Contributing organizations

Ministry reporting: Yes

Reporting Year: 2023

Preliminary JUFO rating: 2