An efficient multiple meta-model-based global optimization method for computationally intensive problems

Present metamodel based global optimization algorithms usually build an evolving metamodel using initial and updated sample points to speed up the search of the global optimum. In this research, we proposed an efficient and robust multiple meta-model-based global optimization method (EMMGO). The EMMGO starts with two different sets of initial points and two different sets of evolving metamodels to search the design space. One evolving set of meta-models are updated using all sample points at each iteration of the search. The other set of meta-models are constructed using the sample points without the set of points which contains the initial best. These two sets of evolving meta-models consist of three components: radial basis function, Kriging and quadratic function. In the iterative search process, an important region, likely to contain the global optimum, is first identified using a few expensive points, and the search of the global optimum is conducted over this region using both of the two sets of metamodels. Meanwhile, the evolving meta-models fitted using all obtained points are used in the search over the other area and the entire design space to avoid missing the global optimum. The new EMMGO algorithm is tested using several commonly-used benchmark functions. The search efficiency of the new algorithm is also illustrated by solving a practical, computationally intensive global optimization problem in designing a lightweight vehicle, employing finite element analysis and simulation. The results from efficient global optimization and multiple metamodels based design space differentiation are provided for search performance comparison.

Automated summary

The EMMGO algorithm improves the efficiency of global optimization by utilizing multiple evolving metamodels and updating them during the search process, expanding the exploration range of the design space. It identifies important regions likely to contain the global optimum using expensive points, conducts the search over these regions with two sets of metamodels, and also ensures the search over the entire design space using evolving metamodels to avoid missing the global optimum.