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NAUTILUS Navigator: free search interactive multiobjective optimization without trading-off

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Abstract

We propose a novel combination of an interactive multiobjective navigation method and a trade-off free way of asking and presenting preference information. The NAUTILUS Navigator is a method that enables the decision maker (DM) to navigate in real time from an inferior solution to the most preferred solution by gaining in all objectives simultaneously as (s)he approaches the Pareto optimal front. This means that, while the DM reaches her/his most preferred solution, (s)he avoids anchoring around the starting solution and, at the same time, sees how the ranges of the reachable objective function values shrink without trading-off. The progress of the motion towards the Pareto optimal front is also shown and, thanks to the graphical user interface, this information is available in an understandable form. The DM provides preference information to direct the movement in terms of desirable aspiration levels for the objective functions, bounds that are not to be exceeded as well as the motion speed. At any time, (s)he can change the navigation direction and even go backwards if needed. One of the major advantages of this method is its applicability to any type of problem, as long as an approximation set of the Pareto optimal front is available and, particularly, to problems with time-consuming function evaluations. Its functionality is demonstrated with an example problem.

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Acknowledgements

This work was partially financed by the Academy of Finland (Project 287496) and the Spanish Ministry of Economy and Competitiveness (Projects ECO2016-76567-C4-4-R and ECO2014-56397-P). Ana B. Ruiz would like to thank the University of Málaga for the financial support received (post-doctoral fellowship “Captación de Talento para la Investigación”). This research is related to the thematic research area Decision Analytics utilizing Causal Models and Multiobjective Optimization (DEMO) of the University of Jyvaskyla. This work was supported by the research project ECO2013-47129-C4-2-R of Universidad de Málaga granted by the Spanish Ministry of Science and Innovation, where Ms. Laura Delgado-Antequera is also part of, via the fellowship BES-2014-068507.

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Authors and Affiliations

  1. Department of Applied Economics (Mathematics), Universidad de Málaga, Calle Ejido 6, 29071, Málaga, Spain

    Ana B. Ruiz & Francisco Ruiz

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

    Kaisa Miettinen & Vesa Ojalehto

  3. Programa de Doctorado de Economía y Empresa de la Universidad de Málaga, Campus El Ejido s/n, 29071, Málaga, Spain

    Laura Delgado-Antequera

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  1. Ana B. Ruiz
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  2. Francisco Ruiz
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  5. Vesa Ojalehto
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Correspondence to Ana B. Ruiz.

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Ruiz, A.B., Ruiz, F., Miettinen, K. et al. NAUTILUS Navigator: free search interactive multiobjective optimization without trading-off. J Glob Optim 74, 213–231 (2019). https://doi.org/10.1007/s10898-019-00765-2

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