Handling high dimensional problems with multi-objective continuation methods via successive approximation of the tangent space
Ringkamp M, Ober-Blöbaum S, Dellnitz M, Schütze O (2012)
Publication Language: English
Publication Type: Journal article
Publication year: 2012
Journal
Publisher: Taylor & Francis
Book Volume: 44
Pages Range: 1117-1146
Journal Issue: 9
DOI: 10.1080/0305215X.2011.634407
Abstract
In many applications, several conflicting objectives have to be optimized concurrently leading to a multi-objective optimization problem. Since the set of solutions, the so-called Pareto set, typically forms a (k1)-dimensional manifold, where k is the number of objectives considered in the model, continuation methods such as predictor-corrector (PC) methods are in certain cases very efficient tools for rapidly computing a finite size representation of the set of interest. However, their classical implementation leads to trouble when considering higher-dimensional models (i.e. for dimension n>1000 of the parameter space). In this work, it is proposed to perform a successive approximation of the tangent space which allows one to find promising predictor points with less effort in particular for high-dimensional models since no Hessians of the objectives have to be calculated. The applicability of the resulting PC variant is demonstrated on a benchmark model for up to n=100, 000 parameters. © 2012 Taylor & Francis.
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Related research project(s)
Involved external institutions
Universität Paderborn
Germany (DE)
Center for Research and Advanced Studies of the National Polytechnic Institute / Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional (CINVESTAV-IPN)
Mexico (MX)
Germany (DE)
Center for Research and Advanced Studies of the National Polytechnic Institute / Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional (CINVESTAV-IPN)
Mexico (MX)
How to cite
APA:
Ringkamp, M., Ober-Blöbaum, S., Dellnitz, M., & Schütze, O. (2012). Handling high dimensional problems with multi-objective continuation methods via successive approximation of the tangent space. Engineering Optimization, 44(9), 1117-1146. https://dx.doi.org/10.1080/0305215X.2011.634407
MLA:
Ringkamp, Maik, et al. "Handling high dimensional problems with multi-objective continuation methods via successive approximation of the tangent space." Engineering Optimization 44.9 (2012): 1117-1146.
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