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Many engineering optimization problems frequently encounter mixed variables and nonlinear constraints, which add considerably to the solution complexity. Very few of the existing methods can yield a globally optimal solution when the objective functions are non-convex and non-differentiable. We developed a new particle swarm optimization (PSO) algorithm. The algorithm introduced a mechanism of simulated annealing (SA), crossover and mutation operator. It may improve the evolutionary rate and precision of the algorithm. We put forward a method of stochastic approximation, in order to realize the transformation from continuous variable to discrete variable. For handling constraints, we used death penalty function method. Based on engineering design problem, computational result was better than the other solutions reported in the literature. Therefore, the new algorithm is feasible, and its accuracy and robustness are obviously superior to the other algorithms.