Two-stage computing budget allocation approach for the response surface method

Response surface methodology (RSM) is one of the main statistical approaches to search for an input combination that optimizes the simulation output. In the early stages of RSM, an iterative steepest ascent search procedure is frequently used. In this paper, we attempt to improve this procedure by considering a more realistic case where there are computing budget constraints, and formulate a new computing budget allocation problem to look into the important issue of allocating computing budget to the design points in the local region of experimentation. We propose a two-stage computing budget allocation approach, which uses a limited budget to estimate the response surface in the first stage and then uses the rest of the budget to improve the lower bound of the estimated response at the center of the next design region in the second stage. Several numerical experiments are carried out to compare the two-stage approach with the regular factorial design, which allocates budget equally to each design point. The results show that our two-stage allocation outperforms the equal allocation, especially when the system noise is large.