Multi-fidelity Models for Decomposed Simulation Optimization Problems

Hierarchical problem decomposition methods are widely used in optimization when the scale of the problem is large. The master problem is hierarchically decomposed to several sub-problems and the detail level of the sub-problems increases during the optimization from bottom to top. When simulation is used to estimate unknown functions, models with different detail are used at each level. However, the simulation outputs used to solve the sub-problems of a hierarchy level are not used anymore at higher levels. An approach is proposed in this paper to reuse these experiment data to improve the efficiency of the simulation-optimization algorithm. A multi-fidelity surrogate model is built in each sub-problem to guide the search of the optimum. The performance of the approach is numerically assessed with the goal of understanding its potentialities and the effect of algorithm parameters over optimization results.