Tweakable block cipher (TBC) is an extension of conventional block cipher. We study how to build a TBC based on generalized Feistel structure (GFS), a classical block cipher construction. While known dedicated TBC proposals are based on substitution-permutation network (SPN), GFS has not been used for building TBC. In particular, we take 64-bit GFS block cipher TWINE and try to make it tweakable with a minimum change. To find a best one from a large number of candidates, we performed a comprehensive search with a help of mixed integer linear programming (MILP) solver. As a result, our proposal TWINE is quite efficient, has the same number of rounds as TWINE with extremely simple tweak schedule.