Preference-Driven Multiobjective Optimization Using Robust Ordinal Regression for Cone Contraction

We present a new interactive procedure for multiobjective optimization problems (MOO), which involves robust ordinal regression in contraction of the preference cone in the objective space. The most preferred solution is achieved by means of a systematic dialogue with the decision maker (DM) during which (s)he specifies pairwise comparisons of some non-dominated solutions from a current sample. The origin of the cone is located at a reference point chosen by the DM. It is formed by all directions of isoquants of the achievement scalarizing functions compatible with the pairwise comparisons of non-dominated solutions provided by the DM. The compatibility is assured by robust ordinal regression, i.e. the DM’s statements concerning strict or weak preference relations for pairs of compared solutions are represented by all compatible sets of weights of the achievement scalarizing function. In successive iterations, when new pairwise comparisons of solutions are provided, the cone is contracted and gradually focused on a sub-region of the Pareto optimal set of greatest interest. The DM is allowed to change the reference point and the set of pairwise comparisons at any stage of the Institute of Computing Science, Poznań University of Technology, Piotrowo 2, 60-965 Poznań, Poland, e-mail: milosz.kadzinski@cs.put.poznan.pl Institute of Computing Science, Poznań University of Technology, Piotrowo 2, 60-965 Poznań, Poland, e-mail: roman.slowinski@cs.put.poznan.pl; Systems Research Institute, Polish Academy of Sciences 68 M. Kadziński, R. S lowiński method. Such preference information does not need much cognitive effort on the part of the DM. The phases of preference elicitation and cone contraction alternate until the DM finds at least one satisfactory solution, or there is no such solution for the current problem setting.

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