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In many engineering optimization problems, like design optimization or structure parameters identification, fitness evaluation is very expensive and time consuming. This problem limited the applications of standard evolutionary computation methods in real world engineering. A cooperative optimization algorithm (GP-PSO) based on Gaussian process (GP) machine learning and particle swarm optimization (PSO) algorithm is presented in this paper for solving computationally expensive optimization problem. Gaussian process is used to predict the most promising solutions before searching the global optimum solution using PSO during each iteration step. The study result indicates GP-PSO algorithm clearly outperforms standard PSO algorithm with much less fitness evaluations on benchmark functions. The result of application to a real world engineering problem also suggests that the proposed optimization framework is capable of solving computationally expensive optimization problem effectively.