Bayesian preference elicitation for multiobjective combinatorial
  optimization
  We introduce a new incremental preference elicitation procedure able to deal
with noisy responses of a Decision Maker (DM). The originality of the
contribution is to propose a Bayesian approach for determining a preferred
solution in a multiobjective decision problem involving a combinatorial set of
alternatives. We assume that the preferences of the DM are represented by an
aggregation function whose parameters are unknown and that the uncertainty
about them is represented by a density function on the parameter space.
Pairwise comparison queries are used to reduce this uncertainty (by Bayesian
revision). The query selection strategy is based on the solution of a mixed
integer linear program with a combinatorial set of variables and constraints,
which requires to use columns and constraints generation methods. Numerical
tests are provided to show the practicability of the approach.
