Accu­rate wind power fore­cast­ing is essen­tial to reduce the neg­a­tive impact of wind power on the oper­a­tion of the grid and the oper­a­tion cost of the power sys­tem. Day-​​ahead wind power fore­cast­ing plays an impor­tant role in the day-​​ahead elec­tric­ity spot trad­ing mar­ket. How­ever, the insta­bil­ity of the wind power series makes the fore­cast dif­fi­cult. To improve fore­cast accu­racy, a hybrid opti­miza­tion algo­rithm is estab­lished in this study, which com­bines vari­a­tional mode de– com­po­si­tion (VMD), max­i­mum rel­e­vance & min­i­mum redun­dancy algo­rithm (mRMR), long short– term mem­ory neural net­work (LSTM), and fire­fly algo­rithm (FA) together. Firstly, the orig­i­nal his– tor­i­cal wind power sequence is decom­posed into sev­eral char­ac­ter­is­tic model func­tions with VMD. Then, mRMR is applied to obtain the best fea­ture set by ana­lyz­ing the cor­re­la­tion between each com­po­nent. Finally, the FA is used to opti­mize the var­i­ous para­me­ters LSTM. Adding the fore­cast– ing results of all sub-​​sequences acquires the fore­cast­ing result. It turns out that the pro­posed hybrid algo­rithm is supe­rior to the other six com­par­i­son algo­rithms. At the same time, an addi­tional case is pro­vided to fur­ther ver­ify the adapt­abil­ity and sta­bil­ity of the pro­posed hybrid model.