emmatn: Defining the additional experimental points
In emma: Evolutionary model-based multiresponse approach

Description Usage Arguments Details Value Author(s) References Examples

View source: R/emmatn.R

Given the set of experimental points investigated in previous steps of the EMMA procedure and their measured response values, emmatn returns a new set of experimental points to be investigated (and thus new experiments to be performed).

1 2	emmatn(t, x, na, opt, weight, C, w1, w2, c1i, c1f, c2i, c2f, b, pr.mut, graph, fn1 = NULL, fn2 = NULL, fn3 = NULL, fn4 = NULL, nresp)

`t`	A numeric value indicating the current time instant of the EMMA procedure.
`x`	An object of class `emmat0` or `emmatn`. Use `emmat0` if `t = 1`; use `emmatn` if `t > 1`.
`na`	A numeric value indicating the number of experimental points to be selected when `t > 0`.
`opt`	A character vector of the same length as the number of responses, indicating for each response function, if the response must be minimized ('mn') or maximized ('mx').
`weight`	A numerical vector of the same length as the number of responses, reflecting the relevance of each response. Use `weight = 1` if only one response is investigated; if multiple responses are investigated, the sum of the values in `weight` must be 1.
`C`	A numeric value indicating the maximum number of iterations. The default is `C = 20`.
`w1`	The first numeric value used to calculate the inertia weight parameter of the time variant PSO algorithm. The default is `w1 = 0.7`.
`w2`	The second numeric value used to calculate the inertia weight parameter of the time variant PSO algorithm. The default is `w2 = 0.4`.
`c1i`	The first numeric value used to calculate the acceleration coefficient `c1` of the time variant PSO algorithm. The default is `c1i = 2.5`.
`c1f`	The second numeric value used to calculate the acceleration coefficient `c1` of the time variant PSO algorithm. The default is `c1f = 0.5`.
`c2i`	The first numeric value used to calculate the acceleration coefficient `c2` of the time variant PSO algorithm. The default is `c2i = 0.5`.
`c2f`	The second numeric value used to calculate the acceleration coefficient `c2` of the time variant PSO algorithm. The default is `c2f = 2.5`.
`b`	A numeric value, used in the mutation operator, that determines the degree of dependence of the mutation on the iteration number. The default is `b = 5`.
`pr.mut`	A numeric vector of the same length as the number of iterations `C` containing the probability of mutation for each time instant.
`graph`	Logical; if 'yes', a plot of the MARS model is produced. 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 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.
`nresp`	The response to be plotted. Use `nresp = 1` to plot the first response...

The parameters w1 and w2 are used to calculate the inertia weight w of the PSO algorithm, namely the parameter that controls the influence of the previous particle velocity on the present velocity. High values of w favour a global search, whereas lower values of w encourage a local search. In EMMA the inertia weight is allowed to decrease linearly with iteration from w1 to w2 thus favouring the exploration initially and the exploitation subsequently. The parameters c1i and c1f are used to calculate the cognitive acceleration coefficient c1 of the PSO algorithm, whereas the parameters c2i and c2f are used to calculate the social acceleration coefficient c2 of the PSO algorithm.Higher values of c1 ensure larger deviation of the particle in the search space (exploration), while higher values of c2 signify the convergence to the current global best (exploitation). In EMMA c1 is allowed to decrease from c1i to c1f and c2 is allowed to increase from c2i to c2f. See Tripathi et al. (2007) for more details.

An object of class emma 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 (`xpop`, `ypop`).
`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`	IDs of the tested experimental points.
`time`	Current time instant of the EMMA procedure.
`weight`	Relative 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.
`Gb`	ID of the best experimental point investigated (global best). `Gb` identifies the experimental point whose response values are closest to the desirable response values (target); the target is automatically selected on the basis of the measured and predicted response values. Use `xspace[Gb,]` to visualise the global best and use `yspace[Gb,]` to visualise its measured response value(s).
`Pb`	ID of the best experimental point investigated by each particle (personal best). Use `xspace[Pb,]` to identify the personal bests and use `yspace[Pb,]` to visualise their measured response values. Among the experimental points associated to one particle, the `Pb` identifies the experimental point that is whose response values are closest to the target.
`Gb.arch`	Archive of the global bests identified. Because the global best changes as new experimental points are investigated, an archive is maintained.
`Pb.arch`	Archive of the personal bests identified. Because the personal bests change as new experimental points are investigated, an archive is maintained.
`v`	Velocities used to update the particles position. The position of a particle is uniquely determined by the predictors' values; it also defines the experiment to be performed. At each step of EMMA, the position of a particle is updated by adding a numerical value (velocity) to the current value of each single predictor.
`sam.x`	IDs of the experiments that have been selected in the current iteration of the procedure. Use `xspace[sam.x,]` to visualise the experiments to be performed.
`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.

Laura Villanova, Kate Smith-Miles and Rob J Hyndman

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.

Tripathi P. K., Bandyopadhyay S., Pal S. K. (2007) 'Multi-objective particle swarm optimization with time variant inertia and acceleration coefficients' Information Sciences, 177, 5033:5049.

## Not run: 
#########################
## 1 response variable ##
#########################

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))

## simulated problem (with known objective function)
tn <- emmat0(in.name, nlev, lower, upper, out.name, nd = 10, fn1 = ackley)

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)
}


## applicative problem (with unknown objective function)
tn <- emmat0(in.name, nlev, lower, upper, out.name, nd = 10)
## use the measured response values to manually fill 'tn$ypop'
tn$ypop<-ackley(tn$xpop)

  for(t in 1:(C-1))
  {
    tn <- emmatn(t, tn, na = 5, opt = "mn", weight, pr.mut = pr.mut, 
	graph = "yes")
    tn$ypop <- ackley(tn$xpop)
    tn <- emmacheck(tn, graph = "no")
    if(tn$add == 1) tn$ypop<-ackley(tn$xpop)
  }

## End(Not run)

##########################
## 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)

for(t in 1:(C-1))
  {
    tn <- emmatn(t, tn, na = 5, opt = c("mn", "mx"), weight, 
	pr.mut = pr.mut, graph = "yes", fn1 = ackley, fn2 = peaks)
    tn <- emmacheck(tn, graph = "no", fn1 = ackley, fn2 = peaks)
  }