Design by adaptive infill sampling with multi-objective optimization for exploitation and exploration

A surrogate-based design optimization with an adaptive sampling technique based on the innovative infill sampling criteria (ISC) is developed, where key issues are mathematically formulated on where in the design space and how many sample points are infilled to guarantee desirable accuracy at minimal computational cost. The ISC developed in the study involve multi-objective optimization (MOO) to determine infilling sample points separately for exploitation and exploration of the design space, which represent the global and the local accuracy of the surrogate model, respectively. The infill samples are found by the MOO on the Pareto front in terms of variance of estimation uncertainty and a predicted function value. To dynamically control the location and the count of the infilling points per iteration for the sample infilling, two criteria of the balancing and the dynamic switching approach are developed. The balancing approach selects infill sample points equally from the two far ends of the Pareto front as well as on the middle of it. The dynamic switching approach uses cut-off variance of uncertainty estimation to dynamically switch the ISC exclusively from the exploration to the exploitation, or vice versa adaptively to the accuracy of the model. Solution optimality and computation efficiency of the present method for the EGO, are compared for two analytic functions with those of the EGO with a conventional, multi-point Expected Improvement (q-EI) ISC and a Latin Hypercube Sampling (LHS) method. The gradient-based optimization without using the surrogate model was also carried out independently for the comparison purpose on the solution accuracy and efficiency. The proposed method shows the greatest efficiency, requiring the smallest number sample points in the training set and becomes even compatible with the gradient-based optimization method. For the practical design problem, high-life multi-element airfoil is chosen to maximize a lift coefficient with non-increasing drag constraints. The proposed method showed about 18% increase of lift force.