Abstract: In order to overcome the shortcomings of particle swarms in solving complex problems of multimodal functions，such as the convergence speed is slow and it is easy to fall into local optimal values． A multimodal delayed particle swarm optimization algorithm based on Gaussian learning is designed． Firstly，the improved Gaussian learning is introduced to improve the convergence speed of the algorithm． Then for the four evolution states，a delay factor is introduced into the algorithm to avoid the local optimal problem． Simulation experiments are performed by six unimodal multimodal test functions． It is verified that GLPSO ( Gaussian Learning PSO) has better convergence speed when dealing with six functions． And it is verified that the GLMDPSO ( Gaussian Learning Multimodal Delayed PSO ) algorithm has better global search ability when dealing with complex problems of multimodal functions． The improved algorithm solves the multimodal function optimization problem，the algorithm could effectively jump out of the stagnation state，improve the convergence speed and have better optimization ability．

Key words: algorithm theory, particle swarm optimization, delay factor, Gaussian learning, multimodal function