Simulation optimization via kriging: a sequential search using expected improvement with computing budget constraints

TLDR

Metamodels, especially kriging, are widely used as fast surrogates to facilitate optimization of simulation models, including deterministic and stochastic variants. The article proposes a two-stage sequential framework to optimize stochastic simulations with heterogeneous variances under computing budget constraints. The framework uses a kriging model, optimal computing budget allocation, and expected improvement to guide and refine the estimation of the global optimum. Empirical results show the framework efficiently obtains optimal solutions, outperforming alternative metamodel-based techniques, and it yields promising results when applied to a real ocean liner bunker fuel management problem. Supported by the Neptune Orient Lines Fellowship program (grant R‑266‑000‑051‑720).

Abstract

Abstract Metamodels are commonly used as fast surrogates for the objective function to facilitate the optimization of simulation models. Kriging (or the Gaussian process model) is a very popular metamodel form for deterministic and, recently, stochastic simulations. This article proposes a two-stage sequential framework for the optimization of stochastic simulations with heterogeneous variances under computing budget constraints. The proposed two-stage framework is based on the kriging model and incorporates optimal computing budget allocation techniques and the expected improvement function to drive and improve the estimation of the global optimum. Empirical results indicate that it is effective in obtaining optimal solutions and is more efficient than alternative metamodel-based techniques. The framework is also applied to a complex real ocean liner bunker fuel management problem with promising results. Keywords: Simulation optimizationhetergeneous varianceskrigingoptimal computing budget allocationexpected improvementbunker fuel management Acknowledgements This research was supported by the Neptune Orient Lines Fellowship program through grant R-266-000-051-720.