Genetic_Programming_Theory_and_Practice_XIII

252 S. Stijven et al.

Design of Experiment Simulation Model

System Understanding Surrogate Modeling

adaptive sample

strategy

configurations

input-response

data

surrogate

models

FluTE

Symbolic Regression

Model Behavior

Feature Selection

Response Exploration

Prediction Uncertainty

12

4 3

Fig. 8 (Adapted from Willem et al. 2014 ) Workflow of the data-driven simulator analysis and
understanding. The goal of such a workflow is to understand which inputs to the simulator are
impacting the outputs, and build robust and efficiently evaluation able meta-models to reliably
mimic the simulator behavior

4.2.1 Step 1: Design of Experiments

To maximize the information content from the experiments in the high-dimensional
input space with inputs of unknown significance we used space-filling Latin
hypercube designs (LHD) and their approximations to create input data sets for
the FluTE simulations. Latin Hyper cube designs are particularly useful to prevent
the “collapse” in the input data design in cases where input variables might turn out
to be insignificant and will be omitted from consideration. Space-filling designs are
critical in simulation-based optimization applications, where the variable selection
and system understanding happens iteratively and data collection is precious.
In the general case, a sample value from the first interval of the first input
parameter is matched at random with sample values from intervals chosen for
the other input parameters (Ma et al. 1993 ). Then the second interval of the first
input parameter is matched at random with sample values from previously unused
intervals of the other features. Each interval of every input parameter will be
sampled once and only once.
LHD has the advantage that the number of samples is independent of the number
of dimensions of the input space but can be determined based on the computational
budget, the input dimensions and the complexity of the simulation. Computing
a space-filling LHD can be an onerous task and therefore we used the maximin
designs of spacefillingdesigns.nl (Santner et al. 2003 ; Husslage et al. 2006 ). Because
our designs have a rather limited number of sample points, we extended the designs
using the Intersite-projected distance method of the Sequential Experimental Design
(SED) toolbox (Crombecq and Dhaene 2010 ; Crombecq et al. 2009 ; Crombecq
2011 ).