V-shaped sampling based on Kendall-Distance to enhance optimization with ranks
Haobin Li, Giulia Pedrielli, Min Chen, Loo Hay Lee, Ek Peng Chew, Chun‐Hung Chen · 2016
In the area of discrete optimization via simulation (DOvS), optimization over rank values has been of concern in computer science and, more recently, in multi-fidelity simulation optimization. Specifically, Chen et al. (2015) proposes the concept of Ordinal Transformation to translate multi-dimensional discrete optimization problems into single-dimensional problems which are simpler, and the transformed solution space is referred as ordinal space. In this paper, we build on the idea of ordinal transformation and its properties in order to derive an efficient sampling algorithm for identifying the solution with the best rank in the setting of multi-fidelity optimization. We refer to this algorithm as V-shaped and we use the concept of Kendall distance adopted in the machine learning theory, in order to characterize solutions in the OT space. The algorithm is presented for the first time and preliminary performance results are provided comparing the algorithm with the sampling proposed in Chen et al. (2015).