Dipartimento di Ingegneria informatica, automatica e gestionale

Decision-making in real-world applications often involves multiple competing objectives, with decision-makers applying their own preferences to balance trade-offs. Inverse Multiobjective Optimization (IMO) aims to infer both the underlying objective functions and the implicit preferences that drive observed decisions. 

In this work, we propose a novel approach that integrates clustering into inverse optimization to group decision-makers based on their preference structures rather than their observed decisions. Our method is an optimization-based clustering IMO framework that minimizes optimality gaps ―the difference between the objective value of observed decisions and the optimal value under the inferred preference structure―, resulting in Mixed-Integer Quadratic Programs (MIQPs). 

To enhance computational efficiency, we derive a heuristic that provides a warm-start solution for the global optimization models, improving convergence and solution quality. Additionally, we incorporate interpretability requirements to ensure that inferred preferences are meaningful and align with domain knowledge. 

We validate our approach with computational experiments on a real-world diet recommendation problem, demonstrating its ability to uncover interpretable and robust decision-making patterns.

 

Nuria is a PhD Student at Department of Statistics and Operations Research, Faculty of Mathematics, University of Seville
(IMUS).