Real-world problems often present two characteristics that are challenging to examine theoretically: 1) they are dynamic (they change over time), and 2) they have multiple objectives. However, current research in the field of dynamic multi-objective optimization (DMO) is relatively sparse. In this chapter, we review recent work in this field and present our analysis of the subset sum problem in the DMO variant. Our approach uses a genetic algorithm with an external archive and a combination of Pareto dominance and aggregated fitness function. We show that the algorithm performs better on a smaller number of objectives, on type III dynamicity problems, and sometimes, counter-intuitively, on a larger data set.