Bayesian preference elicitation for multiobjective combinatorial optimization

TL;DR

This paper presents a Bayesian preference elicitation method for multiobjective combinatorial optimization that effectively handles noisy decision-maker responses through an incremental, query-based approach.

Contribution

It introduces a novel Bayesian framework for preference elicitation in multiobjective combinatorial problems, incorporating a mixed integer linear programming strategy for query selection.

Findings

Method effectively manages noisy responses.

Numerical tests demonstrate practical applicability.

Bayesian approach improves solution accuracy.

Abstract

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.