This　paper　introduces　an　evolutionary　algorithm,　Shuffled　Frog　Leaping　Algorithm　(SFLA),　to　solve　the　optimization　problem　in　designing　the　multi-pumped　Raman　Fibre　Amplifier　(RFA).　SFLA　is　a　powerful　optimizer　tool　because　of　its　efficient　mathematical　expressions　and　global　search　capability.　We　utilize　SFLA　to　determine　the　optimal　pump　wavelengths　and　pump　powers　by　minimizing　the　gain　ripple　of　RFA.　To　accelerate　calculations,　a　terminal　value　optimization　strategy　(TVOS)　is　incorporated　into　the　evolution　of　SFLA.　This　proposed　strategy　takes　the　terminal　power　values　of　pumps　as　the　decision　variables　in　optimization.　Then,　the　optimal　original　power　values　of　the　pumps　are　obtained　by　solving　the　Power　Coupled　Equations　once,　without　using　the　traditional　method　of　repetitive　guesses.The　combination　of　SFLA　and　TVOS　enhances　the　efficiency　of　optimization　and　accelerates　calculation,　while　satisfying　the　design　requirements　of　RFA.The　simulation　results　show　that　nearly　65%　of　computational　time　has　been　saved　compared　with　the　traditional　average　power　analysis.　The　4-pumped　C+L　band　of　backward　multi-pumped　RFA　with　the　average　net　gain　of　0 dB,　1 dB　and　2 dB　are　designed　individually,　where　the　gain　ripple　is　less　than　0.64 dB.　The　combination　of　SFLA　and　TVOS　enhance　the　optimization　efficiency　and　improve　the　performance　of　RFA　with　good　gain　profile.　©　2018,　©　2018　Informa　UK　Limited,　trading　as　Taylor　&　Francis　Group.