An effective integrated design optimization method is developed to reduce the maximum von Mises stress around vent holes of a high-pressure turbine sealing disk. It mainly includes four different shape designs (circular, elliptical, race-track, and four-arc) for holes, an updated self-developed modelling and meshing tool, an APDL-based strength analysis, and a self-proposed efficient switching delayed particle swarm optimization (SDPSO) algorithm. The main idea of SDPSO is: (1) by evaluating an evolutionary factor and utilizing a probability transition matrix, a non-homogeneous Markov chain is determined and auto-updated in each generation; (2) the evolutionary factor and the Markov chain are used to adaptively select the inertia weight, acceleration coefficients, and delayed information to adjust the particle’s velocity. The performance of SDPSO is evaluated through two benchmark optimization problems with constraints. The results show that SDPSO is superior to two well-known PSO algorithms in optimization capability, numerical robustness, and convergence speed. Furthermore, SDPSO is used for the stress optimization of vent holes with four different shapes. The results show that: (1) SDPSO is suitable and valuable for practical engineering optimization problems with constraints; (2) the developed integrated design optimization method is effective and advanced for reducing the maximum von Mises stress around the vent holes; and (3) the four-arc hole has more tremendous advantages in reducing the maximum von Mises stress, followed by the elliptical hole, the race-track hole, and the circular hole.