A kriging method for the solution of nonlinear programs with black-box functions

Authors

  • Eddie Davis,

    1. Dept. of Chemical and Biochemical Engineering, Rutgers—The State University of New Jersey, Piscataway, NJ 08854
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  • Marianthi Ierapetritou

    Corresponding author
    1. Dept. of Chemical and Biochemical Engineering, Rutgers—The State University of New Jersey, Piscataway, NJ 08854
    • Dept. of Chemical and Biochemical Engineering, Rutgers—The State University of New Jersey, Piscataway, NJ 08854
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Abstract

In this article, a new methodology is developed for the optimization of black-box systems lacking a closed-form mathematical description. To properly balance the computational cost of building the model against the probability of convergence to global optimum, a hybrid methodology is proposed. A kriging approach is first applied to provide information about the global behavior of the system considered, whereas a response surface method is considered close to the optimum to refine the set of candidate local optima and find the global optimum. The kriging predictor is a global model employing normally distributed basis functions, so both an expected sampling value and its variance are obtained for each test point. The presented work extends the capabilities of existing response surface techniques to address the refinement of optima located in regions described by convex asymmetrical feasible regions containing arbitrary linear and nonlinear constraints. The performance of the proposed algorithm is compared to previously developed stand-alone response surface techniques and its effectiveness is evaluated in terms of the number of function calls required, number of times the global optimum is found, and computational time. © 2007 American Institute of Chemical Engineers AIChE J, 2007

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