AbstractIn interactive multiobjective optimization methods, the preferences of a decision maker are incorporated in a solution process to find solutions of interest for problems with multiple conflicting objectives. Since multiple solutions exist for these problems with various trade-offs, preferences are crucial to identify the best solution(s). However, it is not necessarily clear to the decision maker how the preferences lead to particular solutions and, by introducing explanations to interactive multiobjective optimization methods, we promote a novel paradigm of explainable interactive multiobjective optimization. As a proof of concept, we introduce a new method, R-XIMO, which provides explanations to a decision maker for reference point based interactive methods. We utilize concepts of explainable artificial intelligence and SHAP (Shapley Additive exPlanations) values. R-XIMO allows the decision maker to learn about the trade-offs in the underlying problem and promotes confidence in the solutions found. In particular, R-XIMO supports the decision maker in expressing new preferences that help them improve a desired objective by suggesting another objective to be impaired. This kind of support has been lacking. We validate R-XIMO numerically, with an illustrative example, and with a case study demonstrating how R-XIMO can support a real decision maker. Our results show that R-XIMO successfully generates sound explanations. Thus, incorporating explainability in interactive methods appears to be a very promising and exciting new research area.