Based on a level set model,a topology optimization method has been suggested recently.It uses a level set to express the moving structural boundary,which can flexibly handle complex topological changes.By combining vector level set models with gradient projection technology,the level set method for topological optimization is extended to a topological optimization problem with multi-constraints,multi-materials and multi-load cases.Meanwhile,an appropriate nonlinear speed mapping is established in the tangential space of the active constraints for a fast convergence.Then the method is applied to structure designs,mechanism and material designs by a number of benchmark examples.Finally,in order to further improve computational efficiency and overcome the difficulty that the level set method cannot generate new material interfaces during the optimization process,the topological derivative analysis is incorporated into the level set method for topological optimization,and a topological derivative and level set algorithm for topological optimization is proposed.