OR Spectrum

, Volume 36, Issue 1, pp 39–56 | Cite as

Interactive multiobjective optimization with NIMBUS for decision making under uncertainty

  • Kaisa Miettinen
  • Jyri Mustajoki
  • Theodor J. Stewart
Regular Article


We propose an interactive method for decision making under uncertainty, where uncertainty is related to the lack of understanding about consequences of actions. Such situations are typical, for example, in design problems, where a decision maker has to make a decision about a design at a certain moment of time even though the actual consequences of this decision can be possibly seen only many years later. To overcome the difficulty of predicting future events when no probabilities of events are available, our method utilizes groupings of objectives or scenarios to capture different types of future events. Each scenario is modeled as a multiobjective optimization problem to represent different and conflicting objectives associated with the scenarios. We utilize the interactive classification-based multiobjective optimization method NIMBUS for assessing the relative optimality of the current solution in different scenarios. This information can be utilized when considering the next step of the overall solution process. Decision making is performed by giving special attention to individual scenarios. We demonstrate our method with an example in portfolio optimization.


Multiple objective programming Interactive methods  Scenarios Uncertainty handling Pareto optimality Classification of objectives 



The authors are grateful to Petri Eskelinen, Sauli Ruuska and Margaret M. Wiecek for their contribution in the earlier phases of the work. The research of Kaisa Miettinen was partly supported by the Jenny and Antti Wihuri Foundation, Finland, and Jyri Mustajoki by the Academy of Finland (project 127264).


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Kaisa Miettinen
    • 1
  • Jyri Mustajoki
    • 2
    • 3
  • Theodor J. Stewart
    • 4
  1. 1.Department of Mathematical Information TechnologyUniversity of JyväskyläUniversity of JyväskyläFinland
  2. 2.Department of Automation Science and EngineeringTampere University of TechnologyTampereFinland
  3. 3.Finnish Environmental Institute, Freshwater CentreHelsinkiFinland
  4. 4.Department of Statistical SciencesUniversity of Cape TownRondeboschSouth Africa

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