| This paper considers the novel problem of upgrading a \textit{legacy} network into a Software Defined Network (SDN) over multiple stages and saving energy in the upgraded network or hybrid SDN. That is, in each stage, the problem at hand is to select and replace \textit{legacy} switches with SDN switches, and reroute traffic to power off as many unused cables as possible to save energy. The operator has to also consider (i) the available budget at each stage, (ii) maximum path delays, (iii) maximum link utilization, (iv) per-stage increase (decrease) in traffic size (upgrade cost), and (v) the Open Shortest Path First - Equal Cost Multi-Path protocol. This paper addresses two multi-path routing scenarios: 1) non link-disjoint, and 2) link-disjoint. It outlines a Mixed Integer Program and a heuristic algorithm for each scenario. The experimental results show that (i) both solutions for scenario-1 produce only up to $0.63\%$ higher energy saving than those for scenario-2, (ii) the mixed integer program (heuristic algorithm) for both scenarios give an energy saving of up to $71.93\%$ ($71.64\%$), (iii) using a larger budget and/or number of stages increases the energy saving, and (iv) the saving achieved by the heuristic solution for each scenario is within $4\%$ from the optimal saving. |