Bayesian preference elicitation for multiobjective combinatorial optimization
This addresses the challenge of accurately capturing preferences in complex decision-making scenarios, though it appears incremental as it builds on existing preference elicitation methods.
The paper tackles the problem of noisy preference elicitation in multiobjective combinatorial optimization by introducing a Bayesian approach that uses pairwise comparisons to reduce uncertainty about a decision maker's preferences, with numerical tests demonstrating its practicability.
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.