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Treed Gaussian Process Regression for Solving Offline Data-Driven Continuous Multiobjective Optimization Problems

Authors: López-Ibáñez, Manuel; Chugh, Tinkle; Hakanen, Jussi; Miettinen; Kaisa; Mazumdar, Atanu;
APC: 1,492 EUR

Treed Gaussian Process Regression for Solving Offline Data-Driven Continuous Multiobjective Optimization Problems

Abstract

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, for example, 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.

Countries
Finland, United Kingdom, United Kingdom, United Kingdom
Related Organizations
Keywords

Pareto optimality, Regression trees, Decision analytics utilizing causal models and multiobjective optimization, Normal Distribution, Gaussian processes, Computational Science, 510, Metamodelling, metamodelling, Hyvinvoinnin tutkimuksen yhteisö, kriging, surrogate, School of Wellbeing, ta113, Päätöksen teko monitavoitteisesti, pareto-tehokkuus, gaussiset prosessit, Surrogate, regression trees, Multiobjective Optimization Group, monitavoiteoptimointi, Biological Evolution, Kriging, kriging-menetelmä, Laskennallinen tiede, Algorithms

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    popularity
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    Top 10%
    influence
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    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
3
Top 10%
Average
Average
Green
hybrid