Phononic　crystals　(PnCs)　have　attracted　considerable　interest　due　to　their　unique　and　outstanding　band-gap　characteristics.　In　many　applications,　it　is　desirable　to　have　a　unit　cell　with　specific　band-gaps.　The　distribution　of　elastic　materials　within　a　unit　cell　has　significant　effect　on　the　band-gaps,　which　is　extremely　difficult　to　be　determined　without　systematic　synthesis　method.　In　this　paper,　topology　optimization　techniques　are　utilized　to　obtain　two-dimensional　(2D)　square　lattice　PnCs　with　maximized　relative　band-gaps　between　multiple　consecutive　bands.　The　optimization　follows　two-stage　design　process　using　Genetic　algorithms　(GAs)　in　combination　with　finite　element　method　(FEM).　Three　numerical　examples　are　given　to　optimize　2D　steel/epoxy　PnCs　in　one-eighth　symmetry　for　coupled　mode,　shear　mode　and　mixed　mode　respectively.　The　results　show　that　the　optimized　PnCs　with　different　band-gaps,　which　can　easily　be　found　by　the　developed　method,　have　different　materials　layout,　and　the　PnCs　with　the　lowest　order　band-gap　are　simple　lattice　and　have　the　highest　value　of　application　in　noise　reduction　and　vibration　isolation.　Some　optimized　PnCs　with　higher　order　band-gaps　have　the　same　lattice　as　those　with　the　lowest　order　band-gap,　and　whose　absolute　band-gaps　are　inversely　proportional　to　the　minimum　feature　size　of　primitive　cells.　(C)　2015　Elsevier　B.V.　All　rights　reserved.