geospt (version 0.4-9)

seqPtsOptNet: Design of optimal sampling networks through the sequential points method

Description

Search for the optimum location of one additional point to be added to an initial network, minimizing the average standard error of kriging through a genetic algorithm. It takes as input to optimize, the minimum and maximum values of the coordinates that enclose the study area. This function uses previous samples information to direct additional sampling. The location of the new point is searched randomly.

Usage

seqPtsOptNet(formula, locations, spDatF, fitmodel, n, prevSeqs, popSize, 
generations, xmin, ymin, xmax, ymax, plotMap=FALSE, spMap=NULL, ...)

Value

an object of class rbga containing the population and the evaluation of the objective function for each chromosome in the last generation, the best and mean evaluation value in each generation, and additional information

References

Delmelle, E., 2005. Optimization of second-phase spatial sampling using auxiliary information. Ph.D. Thesis, Dept. Geography, State University of New York, Buffalo, NY. Santacruz, A., 2011. Evolutionary optimization of spatial sampling networks. An application of genetic algorithms and geostatistics for the monitoring of soil organic carbon. Editorial Acad�mica Espa�ola. 183 p. ISBN: 978-3-8454-9815-7 (In Spanish)

See Also

See rbga in the genalg package and krige in the gstat package

Examples

## Load data
data(COSha10)
data(COSha10map)
data(lalib)

## Calculate the sample variogram for data, generate the variogram model and  
## fit ranges and/or sills from the variogram model to the sample variogram
ve <- variogram(CorT~1, loc=~x+y, data=COSha10, width = 230.3647)
PSI <- 0.0005346756; RAN <- 1012.6411; NUG <- 0.0005137079
m.esf <- vgm(PSI, "Sph", RAN, NUG)
(m.f.esf <- fit.variogram(ve, m.esf))

## Optimize the location of the first additional point 
## Only 25 generations are evaluated in this example
## Users can visualize how the location of the additional point is optimized 
## if plotMap is set to TRUE
old.par <- par(no.readonly = TRUE)
par(ask=FALSE)
optpt <- seqPtsOptNet(CorT~ 1, loc=~ x+y, COSha10, m.f.esf, popSize=30, 
    generations=25, xmin=bbox(lalib)[1], ymin=bbox(lalib)[2], xmax=bbox(lalib)[3], 
    ymax=bbox(lalib)[4], plotMap=TRUE, spMap=lalib)
par(old.par)

## Summary of the genetic algorithm results
summary(optpt, echo=TRUE)

## Graph of best and mean evaluation value of the objective function 
## (average standard error) along generations
plot(optpt)

## Find and plot the best set of additional points (best chromosome) in   
## the population in the last generation
(bnet1 <- bestnet(optpt))
l1 = list("sp.polygons", lalib)
l2 = list("sp.points", bnet1, col="green", pch="*", cex=5)
spplot(COSha10map, "var1.pred", main="Location of the optimized point", 
    col.regions=bpy.colors(100), scales = list(draw =TRUE), xlab ="East (m)", 
    ylab = "North (m)", sp.layout=list(l1,l2))

## Average standard error of the optimized sequential point
min(optpt$evaluations)

## Optimize the location of the second sequential point, taking into account 
## the first one
old.par <- par(no.readonly = TRUE)
par(ask=FALSE)
optpt2 <- seqPtsOptNet(CorT~ 1, loc=~ x+y, COSha10, m.f.esf, prevSeqs=bnet1, 
    popSize=30, generations=25, xmin=bbox(lalib)[1], ymin=bbox(lalib)[2], 
    xmax=bbox(lalib)[3], ymax=bbox(lalib)[4], plotMap=TRUE, spMap=lalib)
par(old.par)

## Find the second optimal sequential point and use it, along with the first
## one, to find another optimal sequential point, and so on iteratively  
bnet2 <- bestnet(optpt2)
bnet <- rbind(bnet1, bnet2)

old.par <- par(no.readonly = TRUE)
par(ask=FALSE)
optpt3 <- seqPtsOptNet(CorT~ 1, loc=~ x+y, COSha10, m.f.esf, prevSeqs=bnet,
    popSize=30, generations=25, xmin=bbox(lalib)[1], ymin=bbox(lalib)[2], 
    xmax=bbox(lalib)[3], ymax=bbox(lalib)[4], plotMap=TRUE, spMap=lalib)
par(old.par)