Dynamic optimization problems (DOPs) are those whose specifications change over time during the optimization, resulting in continuously moving optima. Most research work on DOPs is based on the assumption that the goal of addressing DOPs is to track the moving optima. In this paper, we first point out the practical limitations on tracking the moving optima. We then propose to find optimal solutions that are robust over time as an alternative goal, which leads to a new concept of robust optimization over time (ROOT) problem. In order to investigate the properties of ROOT in more depth, we study the new characteristics of ROOT and investigate its similarities to and differences from the traditional robust optimization problem, which hereafter is referred to as robust optimization for short. To facilitate future research on ROOT, we suggest a ROOT benchmark problem by modifying the moving peaks test problem. Several performance measures for comparing algorithms for solving ROOT problems are proposed.