The exponential growth of traffic demand, and supporting network infrastructures, is leading to serious energy consumption issues. With proper routing, some network links can be put on a sleep mode if demands can be routed through other links and, with multiperiod traffic, the sleeping links can change between periods. In this paper, we address the energy efficient routing problem, and we study the tradeoff between energy savings and percentage of routing paths allowed to change between periods. We present an ILP model defining the energy efficient routing problem and we propose a GRASP based heuristic to compute good routing solutions.