eTSSO: Adaptive Search Method for Stochastic Global Optimization Under Finite Budget

TSSO is a recently proposed search algorithm based on the modified nugget effect kriging metamodel, which solves unconstrained stochastic simulation optimization problems with heterogeneous variances, when the total simulation budget is fixed, through a budget allocation followed by a two–stage sequential procedure. Despite the efficiency and performance of TSSO, no analysis of the structural properties of the algorithm in terms of asymptotic behaviour has been provided. Furthermore, the algorithm arbitrarily assigns the budget per iteration when the procedure starts. However, given a finite budget, the choice of the number of replications per iteration is particularly critical and a fixed a–priori assignment can affect the ability to control the algorithm making it particularly sensitive to the initial settings. This work tries to fill these gaps. An analysis of the convergence properties of a modified version of the TSSO is provided. A new allocation of the budget per iteration is proposed, leading to the Extended TSSO (eTSSO) algorithm, which mitigates the TSSO sensitivity to the parameter settings and increases its effectiveness. Specifically, the new budget allocation adaptively increases the available budget at each iteration based on the updated information coming from the simulation. Numerical examples give evidence of the algorithm performance.