Min-Median-Max metamodel-based unconstrained nonlinear optimization problems

An important direction of metamodeling research focuses on developing methods which can iteratively improve the accuracy of the metamodel. The intention of these kinds of strategies is to use a space reduction strategy to lead response surface refinement to a smaller design space; and new sample points are commonly generated near the optimum. The potential risk is that some characteristics of given problems might be lost, especially for nonlinear problems. Therefore, a novel metamodel-assisted optimization called "Min-Median-Max" (M3) is proposed. This algorithm classifies sample points into three categories (maximum, median and minimum) based on corresponding objective function values, new sample points should be generated by considering combination of three kinds of samples. In order to avoid local convergence and control size of sample points, particle swarm optimization (PSO) algorithm and radial basis function (RBF) metamodeling technique are integrated to implement the suggested M3 strategy. To validate the performance of the M3 strategy, multiple mathematical test functions are used for evaluating the accuracy and efficiency. As a practical engineering application, drawbead design of a stamping system is optimized. The results demonstrate applicability and effectiveness of the M3 algorithm.