The function evaluates if one additional experimental point is required. If this is the case, the function
provides with details about the additional experiment to be performed.
Logical; if "yes", a plot of the MARS model is produced. Note that a plot is produced only if the model
contains more than one explanatory variable.
fn1
The first function to be optimised. Use fn1 = NULL if the function is unknown (e.g. when designing experiments in
applied problems).
fn2
The second function to be optimised. Use fn2 = NULL if the function is unknown (e.g. when designing experiments in
applied problems).
fn3
The third function to be optimised. Use fn3 = NULL if the function is unknown (e.g. when designing experiments in
applied problems).
fn4
The fourth function to be optimised. Use fn4 = NULL if the function is unknown (e.g. when designing experiments in
applied problems).
nresp
The response to be plotted. Use nresp = 1 to plot the first response...
Details
Once the experiments identified by emma are implemented, the observed response values, the predicted
response values, the target and the scalar distances from the target are updated. The
solution with the response values closest to the target is thus identified. If such a solution has
not been tested yet, emmacheck selects it as an additional experimental point that needs
to be investigated.
Value
An object of class emmatn with the components listed below:
xpop
Experimental points investigated.
ypop
Response values observed at the experimental points investigated.
xspace
Experimental region. It is given by all the possible combinations of the factors' levels
and contains xpop. The rownames uniquely identify the experimental points and are reported
also in xpop.
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).
Gb
ID of the best experimental point investigated. Use xspace[Gb,] to visualise the
best experimental point and use yspace[Gb,] to visualise the measured response value(s).
Gb identifies the experimental point whose response values are closest to the target. The
target is a set of desirable response values which are automatically selected on the basis of
the measured and predicted response values.
add
Logical. If '0' indicates that an additional experimental point needs to be investigated; if '1'
indicates that an additional experimental point is not required.
test
IDs of the tested experimental points.
time
Current time instant of the EMMA procedure.
weight
Importance of each response. If only one response is investigated, then
weight = 1; if multiple responses are investigated, the sum of the values in weight must
be 1.
Author(s)
Laura Villanova, Kate Smith-Miles and Rob J Hyndman
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.
Friedman J. H. (1991) 'Multivariate adaptive regression splines' (with
discussion), The Annals of Statistics 19, 1:141.
Examples
## 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"
weight <- 1
C <- 10
pr.mut <- c(0.1, 0.07, 0.04, rep(0.01, C-3))
## Not run:
#######################################################
## simulated problem (with known objective function) ##
#######################################################
## identify the initial set of experimental runs (initialization)
tn <- emmat0(in.name, nlev, lower, upper, out.name, nd = 10, fn1 = ackley)
## identify the experimental runs during subsequent steps of the
## EMMA procedure
for(t in 1:(C - 1))
{
tn <- emmatn(t, tn, na = 5, opt = "mn", weight, pr.mut = pr.mut,
graph = "yes", fn1 = ackley)
tn <- emmacheck(tn, graph = "no", fn1 = ackley)
}
## End(Not run)
###########################################################
## applicative problem (with unknown objective function) ##
###########################################################
## identify the initial set of experimental runs (initialization)
tn <- emmat0(in.name, nlev, lower, upper, out.name, nd = 10)
## perform the experiments in code{tn$xpop} and measure the response
## values, then load the measured response values in code{tn$ypop}
tn$ypop <- ackley(tn$xpop)
## identify the experimental runs during subsequent steps of the
## EMMA procedure
for(t in 1:(C-1))
{
tn <- emmatn(t, tn, na = 5, opt = "mn", weight, pr.mut = pr.mut,
graph = "no")
tn$ypop <- ackley(tn$xpop)
tn <- emmacheck(tn, graph = "no")
if(tn$add==1) tn$ypop <- ackley(tn$xpop)
}