Quantifying uncertainty on Pareto fronts with Gaussian process conditional simulations

Binois, M.; Ginsbourger, David; Roustant, O. (2015). Quantifying uncertainty on Pareto fronts with Gaussian process conditional simulations. European journal of operational research, 243(2), pp. 386-394. Elsevier 10.1016/j.ejor.2014.07.032

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Multi-objective optimization algorithms aim at finding Pareto-optimal solutions. Recovering Pareto fronts or Pareto sets from a limited number of function evaluations are challenging problems. A popular approach in the case of expensive-to-evaluate functions is to appeal to metamodels. Kriging has been shown efficient as a base for sequential multi-objective optimization, notably through infill sampling criteria balancing exploitation and exploration such as the Expected Hypervolume Improvement. Here we consider Kriging metamodels not only for selecting new points, but as a tool for estimating the whole Pareto front and quantifying how much uncertainty remains on it at any stage of Kriging-based multi-objective optimization algorithms. Our approach relies on the Gaussian process interpretation of Kriging, and bases upon conditional simulations. Using concepts from random set theory, we propose to adapt the Vorob’ev expectation and deviation to capture the variability of the set of non-dominated points. Numerical experiments illustrate the potential of the proposed workflow, and it is shown on examples how Gaussian process simulations and the estimated Vorob’ev deviation can be used to monitor the ability of Kriging-based multi-objective optimization algorithms to accurately learn the Pareto front.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematical Statistics and Actuarial Science

UniBE Contributor:

Ginsbourger, David

Subjects:

500 Science > 510 Mathematics

ISSN:

0377-2217

Publisher:

Elsevier

Language:

English

Submitter:

Lutz Dümbgen

Date Deposited:

06 Mar 2015 11:25

Last Modified:

03 Oct 2017 04:13

Publisher DOI:

10.1016/j.ejor.2014.07.032

BORIS DOI:

10.7892/boris.64125

URI:

https://boris.unibe.ch/id/eprint/64125

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