Simulation-based Scheduling by Bayesian Optimization based on Gaussian Process Regression with Rank Correlation Kernel

Bayesian optimization (BO), which approximates computationally complex simulations to speed-up optimization searches has been studied intensively. However, BO is difficult to apply to the scheduling problem due to the difficulties in feature engineering from schedules i.e., ordinal variables. In this paper, we propose a kernel for ordinal variables. This new kernel is based on the Spearman rank correlation coefficient, which expresses the similarity between ordinal variables. Applying the GPR model based on the proposed kernel to BO enables it to be directly applied to the scheduling problem. We compare BO using the proposed kernel with the most popularly used genetic algorithm (GA). The experimental results demonstrate that BO using the proposed kernel found a near-optimal solution significantly faster than the GA under small numbers of searches.