Optimistic NAUTILUS navigator for multiobjective optimization with costly function evaluations

Journal of Global Optimization, vol. 83, pp. 865–889

Abstract

Abstract We introduce novel concepts to solve multiobjective optimization problems involving (computationally) expensive function evaluations and propose a new interactive method called O-NAUTILUS. It combines ideas of trade-off free search and navigation (where a decision maker sees changes in objective function values in real time) and extends the NAUTILUS Navigator method to surrogate-assisted optimization. Importantly, it utilizes uncertainty quantification from surrogate models like Kriging or properties like Lipschitz continuity to approximate a so-called optimistic Pareto optimal set. This enables the decision maker to search in unexplored parts of the Pareto optimal set and requires a small amount of expensive function evaluations. We share the implementation of O-NAUTILUS as open source code. Thanks to its graphical user interface, a decision maker can see in real time how the preferences provided affect the direction of the search. We demonstrate the potential and benefits of O-NAUTILUS with a problem related to the design of vehicles.

Authors 6

1. Bhupinder Singh Saini corresponding

   University of Jyväskylä

   Affiliation as printed

   Faculty of Information Technology, University of Jyvaskyla, P.O. Box 35 (Agora), FI-40014, Jyvaskyla, Finland

2. Michael Emmerich Aachen Faculty of Science, Leiden Institute of Advanced Computer Science

   Leiden University · University of Jyväskylä

   Affiliation as printed

   Faculty of Information Technology, University of Jyvaskyla, P.O. Box 35 (Agora), FI-40014, Jyvaskyla, Finland

   Faculty of Science, Leiden Institute of Advanced Computer Science, Niels Bohrweg 1, 2333 CA, Leiden, The Netherlands

3. Atanu Mazumdar

   University of Jyväskylä

   Affiliation as printed

   Faculty of Information Technology, University of Jyvaskyla, P.O. Box 35 (Agora), FI-40014, Jyvaskyla, Finland

4. Bekir Afşar

   University of Jyväskylä

   Affiliation as printed

   Faculty of Information Technology, University of Jyvaskyla, P.O. Box 35 (Agora), FI-40014, Jyvaskyla, Finland

5. Babooshka Shavazipour

   University of Jyväskylä

   Affiliation as printed

   Faculty of Information Technology, University of Jyvaskyla, P.O. Box 35 (Agora), FI-40014, Jyvaskyla, Finland

6. Kaisa Miettinen

   University of Jyväskylä

   Affiliation as printed

   Faculty of Information Technology, University of Jyvaskyla, P.O. Box 35 (Agora), FI-40014, Jyvaskyla, Finland