In this study, hybrid differential evolution (HDE) was applied to solve four low-pressure chemical vapour deposition (LPCVD) reactor optimal design problems. The mathematical model for this reactor is described using a two-point boundary value differential-algebraic equation (TPBVP-DAE) problem. HDE is not only applied to solve the optimization problems but also to obtain the solution to TPBVP-DAE. Under this situation, the HDE subroutine should call itself to evaluate the optimal solution to the optimization problem and the solution to TPBVP-DAE. In this study, Fortran 90 was used to implement the HDE subroutine to achieve the calling itself requirement. The recursive HDE subroutine can be efficiently applied to solve the four LPCVD reactor optimal design problems. From the computational results, we observed that the combined optimal design obtain the smallest axial uniformity variation. Furthermore, test function maximization problems were used to compare the performance of the HDE with other methods.