Dynamic optimization problems involving two or more conflicting objectives appear in many real-world scenarios, and more cases are expected to appear in the near future with the increasing interest in the analysis of streaming data sources in the context of Big Data applications. However, approaches combining dynamic multi-objective optimization with preference articulation are still scarce. In this paper, we propose a new dynamic multi-objective optimization algorithm called InDM2 that allows the preferences of the decision maker (DM) to be incorporated into the search process. When solving a dynamic multi-objective optimization problem with InDM2, the DM can not only express her/his preferences by means of one or more reference points (which define the desired region of interest), but these points can be also modified interactively. InDM2 is enhanced with methods to graphically display the different approximations of the region of interest obtained during the optimization process. In this way, the DM is able to inspect and change, in optimization time, the desired region of interest according to the information displayed. We describe the main features of InDM2 and detail how it is implemented. Its performance is illustrated using both synthetic and real-world dynamic multi-objective optimization problems.