A clustering-based framework for preference inference in inverse multiobjective optimization

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 an 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 regrets, which is 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). Additionally, we incorporate interpretability requirements to ensure that inferred preferences are meaningful and align with domain knowledge. To enhance computational efficiency, we derive a heuristic that provides a warm-start solution for the global optimization algorithms, improving convergence and solution quality. We validate our approach on synthetic datasets and a diet recommendation problem, demonstrating its ability to uncover interpretable and robust decision-making patterns.