Discrete Mode Pursuing Sampling (D-MPS) is a method used for optimization of expensive black-box functions with discrete variables. The type of discrete space where all possible combinations of discrete values of all variables are valid design points is called a full grid of points or a “regular grid” in this paper. A regular structure for sampling data is a requirement when D-MPS is applied. This paper presents two new indexing methods, i.e. “n-D” and “distance”, to transform non-regular discrete data sets into regular data sets. The n-D indexing method sorts data by all the axes, regardless of the function values. The distance indexing method sorts data dynamically by its distance from the current mode. A number of optimization problems are used to test the performance of the two methods in comparison with a 1-D indexing method which simply sorts data by a single axis. Both n-D and distance methods give much better performance than the 1-D. It is concluded that the distance indexing method can be recommended for most applications. While this paper uses D-MPS as the test bed, the indexing methods are applicable to other discrete optimization methods.

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