A budget allocation strategy minimizing the sample set quantile for initial experimental design

The increased complexity of manufacturing systems makes the acquisition of the system performance estimate a black-box procedure (e.g., simulation tools). The efficiency of most black-box optimization algorithms is affected significantly by initial designs (populations). In most population initializers, points are spread out to explore the entire domain, e.g., space-filling designs. Some population initializers also consider exploitation procedures to speed up the optimization process. However, they are either application-dependent or require an additional budget. This article proposes a generic method to generate, without an additional budget, several good solutions in the initial design. The aim of the method is to optimize the quantile of the objective function values in the generated sample set. The proposed method is based on a clustering of the solution space; feasible solutions are clustered into groups and the budget is allocated to each group dynamically based on the observed information. The asymptotic performance of the proposed method is analyzed theoretically. The numerical results show that, if proper clustering rules are applied, an unbalanced design is generated in which promising solutions have higher sampling probabilities than non-promising solutions. The numerical results also show that the method is robust to wrong clustering rules.