emma (version 0.1-0)

emmat0: Defining the initial design

Description

The function initializes the EMMA procedure. It generates the experimental space and selects the initial set of experimental points, namely the initial set of experiments to be performed. Random sampling is used for that purpose.

Usage

emmat0(in.name, nlev, lower, upper, out.name, nd, fn1 = NULL, 
	fn2 = NULL, fn3 = NULL, fn4 = NULL)

Arguments

in.name

A vector containing the names of the input variables (factors).

nlev

A numeric vector of the same length as in.name, containing the number of factor levels.

lower

A numeric vector of the same length as in.name, containing the lower values of the factors.

upper

A numeric vector of the same length as in.name, containing the upper values of the factors.

out.name

A vector containing the name(s) of the output/response variable(s).

nd

Number of experimental points to be selected when t = 0.

fn1

The first function to be optimised; use fn1 = NULL if the objective function is unknown, like in applied problems.

fn2

The first function to be optimised; use fn2 = NULL if the objective function is unknown, like in applied problems.

fn3

The third function to be optimised; use fn3 = NULL if the objective function is unknown, like in applied problems.

fn4

The fourth function to be optimised; use fn4 = NULL if the objective function is unknown, like in applied problems.

Value

An object of class emmat0 with the components listed below:

xpop

Experimental points investigated.

ypop

Response values observed at the experimental points investigated.

xspace

Experimental region.

yspace

Response values that have been either observed or predicted. Observed response values are stored also in ypop. Predicted response values are obtained using a MARS model fitted to the available data.

opt

Indicates if each single function is either minimized ('mn') or maximized ('mx').

nd

Number of experimental points selected initially (t=0).

na

Number of experimental points selected in subsequent iterations (t>0).

tested

ID of the tested experimental points.

time

Current time instant of the EMMA procedure.

opt

Indicates if each single objective function is either minimized ('mn') or maximized ('mx').

Details

At the moment the function does not implement the use of constraints for the factors. Unfeasible experiments are easily excluded by manipulating the matrix xspace in an object of class emmat0.

References

Villanova L., Falcaro P., Carta D., Poli I., Hyndman R., Smith-Miles K. (2010) 'Functionalization of Microarray Devices: Process Optimization Using a Multiobjective PSO and Multiresponse MARS Modelling', IEEE CEC 2010, DOI: 10.1109/CEC.2010.5586165

Carta D., Villanova L., Costacurta S., Patelli A., Poli I., Vezzu' S., Scopece P., Lisi F., Smith-Miles K., Hyndman R. J., Hill A. J., Falcaro P. (2011) 'Method for Optimizing Coating Properties Based on an Evolutionary Algorithm Approach', Analytical Chemistry 83 (16), 6373-6380.

Examples

#########################
## 1 response variable ##
#########################
## define the problem variables
in.name <- c("x1","x2")
nlev <- c(20, 20)
lower <- c(-2.048, -2.048)
upper <- c(2.048, 2.048)
out.name <- "y"

## identify the initial set of experimental runs (initialization)
## simulated problem (with known objective function)
tn <- emmat0(in.name, nlev, lower, upper, out.name, nd = 10, fn1 = ackley)

## applicative problem (with unknown objective function)
tn <- emmat0(in.name, nlev, lower, upper, out.name, nd = 10)
## perform the experiments in \code{tn$xpop} and measure the 
##	response values, then load in \code{tn$ypop} the measured 
##	response values 
# tn$ypop<-...


##########################
## 2 response variables ##
##########################
in.name <- c("x1", "x2")
nlev <- c(20, 20)
lower <- c(-3, -3)
upper <- c(3, 3)
out.name <- c("y1", "y2")
weight <- c(0.2, 0.8)
C <- 10
pr.mut <- c(0.1, 0.07, 0.04, rep(0.01, C-3))

tn <- emmat0(in.name, nlev, lower, upper, out.name, nd = 10, fn1 = ackley, 
	fn2 = peaks)