Multimodal optimization aims to search multiple optima (global and/or local optima) simultaneously

which gives rise to a challenging task for traditional optimization algorithms.This paper proposes a two-stage algorithm to solve multimodal optimization problems.In the first stage

NCDE with neighborhood mutation strategy tries its best to find as many approximate positions of optimal solutions as possible on the fitness landscape.After NCDE runs a certain number of iterations

DMC method is employed to divide the entire population into multiple clusters

and then CMA-ES algorithm is used to perform fine search on each cluster which is found by NCDE.Additionally

search point replenishment strategy is put forward to balance cluster size and to increase search capability of our algorithm in the beginning of the running.Extensive comparative experiments is made between our proposed approach and 9 state-of-the-art algorithms on two benchmark sets

the results show that the new algorithm is effective and superior to the other algorithms on the majority of test functions.