Cake Mix Optimization Problem

Abstract

We focus on optimizing a system with two types of inputs x = (x_c,x_e) with x_c representing a control variable and x_e representing an environmental variable. Typically, x_c needs to be optimized, whereas x_e are uncontrollable, but are assumed to adhere to some distribution.

Data set

The data set describes a cake mix optimization problem that is robust against inaccurate settings of oven temperature and baking time. The control variables are the ingredients that need to be optimized (amount of flower, amount of sugar, amout of egg powder). Hence, the data set hat 3 control variables and 2 environmental variables. The data points are stored in a Matlab m-file boxcake.m. In the paper below we fitted a Gaussian process model taken as global truth and ran DIRECT for a long time to obtain the global optimum.

References

Perry Groot, Adriana Birlutiu, Tom Heskes. Bayesian Monte Carlo for the Global Optimization of Expensive Functions, 19th European Conference on Artificial Intelligence (ECAI), pages 249-254, 2010. [PDF] [BNAIC 2010 Abstract]