Reference point based decision support tools for interactive multiobjective optimization

In this thesis we propose a set of reference point based decision support tools for interactive multiobjective optimization. The tools can be considered as an supplementary methods that can be used to extend the possibilities of existing interactive methods. These tools are designed for computationally demanding problems and special attention is paid to reduction of all unnecessary computation as far as possible. All proposed methods are learning-oriented in the sense that they allow the decision maker to do free-search. The thesis contains four independent essays. In the first essay we survey interactive multiobjective optimization methods that utilize so-called objective trade-off information in a way or another. We discuss theoretical issues behind these methods and study them from the trade-off utilization point of view. We also point out some major benefits and drawbacks that can be related to objective trade-off information in general. In addition we make some analysis related to the methods presented. In the second essay a trade-off analysis tool with an applicability study is presented. The development of the tool is based on the findings made in the first essay. The trade-off analysis tool can be connected to some existing reference point based method, and the decision maker can use this tool to make local trade-off analysis related to Pareto optimal solutions obtained in an interactive method. The supplementary applicability study method can be used to notify the decision maker if the trade-off analysis produces unrealistic approximated Pareto optimal solutions. In the third essay we suggest methods which can be used to incorporate preference information into an achievement scalarizing function. This allows us to take into account preferences of the decision maker when we are projecting a given reference point into the set of Pareto optimal solutions. Three methods are proposed which can be utilized based on amount of preference information the decision maker is willing to give. The fourth essay proposes a Pareto navigator method that can be seen as a nonlinear extension to the Pareto race method. The idea is to produce polyhedral approximation for the Pareto optimal set in the objective space. The decision maker is able to navigate on this approximation by using a specially designed intuitive user interface. When the decision maker has located an interesting area in the objective space the obtained approximated Pareto optimal solution can be used, for instance, as a reference point to produce the corresponding actual Pareto optimal solution. Keywords: Multiobjective optimization, Reference point method, Decision support, Multiple criteria decision making, Pareto optimalit