cubic_5D {OptimaRegion}

Simulated dataset based on a cubic function (5 factors)

Description

The dataset is simulated from the following function

f(x) = 10 - (x_1-1.5)^2 - (x_2-2)^2 - (x_3-2.5)^2 - (x_4-3)^2- (x_5-3.5)^2 + 0.1 x_1^3 - 0.1 x_2^3 - 0.1 x_3^3 - 0.1 x_4^3 - 0.1 x_5^3 + x_2 x_4 - x_3 x_4

defined in the region R = { 0 <= x_i <= 5, for i = 1, ..., 5}, with its maximum at (2.28, 2.44, 1.02, 2.65, 2.54). The sample locations are generated via a Hyper Latin Square (HLS) design within R, and the noisy level is sigma = 2.

Usage

cubic_5D

Format

A list consisting of 2 components:

design_matrix

300 design points generated by a HLS design within R

responses

300 noisy responses simulated at the design points with sigma = 2