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This paper considers the novel problem of upgrading a 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 legacy switches with SDN switches and reroute traffic to power off as many unused cables as possible to save energy. Also, the operator must 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 produce only up to 0.63% higher energy saving in scenario-1 than in scenario-2, (ii) the mixed integer program (heuristic algorithm) for both scenarios give an energy saving up to 71.93% (71.64%), (iii) using a larger budget and/or number of stages can increase the energy saving, and (iv) the saving achieved by the heuristic solution for each scenario is within 4% from the optimal saving.