Genetic Algorithm Optimization for Reduced Order Problem Based on Kriging Modeling with Restricted Maximum Likelihood Criterion

1. Abstract Complex and computationally intensive modeling and simulation of real-world engineering systems can include a large number of design variables in the optimization of such systems. Consequently, it is desirable to conduct variable screening to identify significant or active variables so that a simpler, more efficient, and accurate optimization process can be achieved. This paper employs a variable screening method based on Kriging modeling with Restricted Maximum Likelihood criterion to reduce the design space, and the GA method is applied to optimize the re-defined problem with reduced order design space afterwards. The Kriging metamodeling method is more reliable for highly nonlinear systems, such as the complex engineering systems, than the traditional response surface method. Meanwhile, the Restricted Maximum Likelihood criterion makes the variable screening process more efficient. The Improved Distributed Hypercube Sampling method is applied at the first sampling stage in this study. The strategy with the combination of variable screening method based on a Kriging modeling with Restricted Maximum Likelihood criterion and GA optimization method is evaluated using a 20 variables standard nonlinear benchmark function. This optimization strategy then is applied to a rubber material model optimization problem with 18 design variables. After reducing the design space to a less dimension using the variable screening method, the optimal rubber material model is obtained by using GA optimization. These two examples show that the optimization strategy proposed in this paper can solve the problem both efficiently and effectively. 2.