pricefit {ecolMod}

Pseudo-random search algorithm of Price (1997)

Description

Pseudo-random search algorithm of Price (1997). Used in the book as an example of a random-based fitting technique, and as an example of how to create a function in R.

Usage

pricefit(par, minpar = rep(-1e8, length(par)),
         maxpar = rep(1e8, length(par)), func, 
         npop = max(5*length(par),50),
         numiter =10000, centroid = 3, varleft = 1e-8,...)

Arguments

par

initial values of the parameters to be optimised

minpar

minimal values of the parameters to be optimised

maxpar

maximal values of the parameters to be optimised

func

function to be minimised, its first argument should bw the vector of parameters over which minimization is to take place. It should return a scalar result, the model cost, e.g the sum of squared residuals.

npop

number of elements in population

numiter

number of iterations to be performed. Defaults to 10000. There is no other stopping criterion.

centroid

number of elements from which to estimate new parameter vector

varleft

relative variation remaining; if below this value algorithm stops

...

arguments passed to funtion func

Details

see the book of Soetaert and Herman for a description of the algorithm AND for a line to line explanation of the function code.

Value

a list containing:

par

the optimised parameter values

cost

the model cost, or function evaluation associated to the optimised parameter values, i.e. the minimal cost

poppar

all parameter vectors remaining in the population, matrix of dimension (npop,length(par))

popcost

model costs associated with all population parameter vectors, vector of length npop

Author(s)

Karline Soetaert <[e-mail]>

References

Soetaert, K. and P.M.J. Herman, 2009. A Practical Guide to Ecological Modelling. Using R as a Simulation Platform. Springer, 372 pp.

Price, W.L., 1977. A controlled random search procedure for global optimisation. The Computer Journal, 20: 367-370.

See Also

optim the R default.

Examples

pricefit  # will display the code 

amp    <- 6
period <- 5
phase  <- 0.5

x <- runif(20)*13 
y <- amp*sin(2*pi*x/period+phase) + rnorm(20, mean = 0, sd = 0.05)
plot(x, y, pch = 16)


cost <- function(par) sum((par[1]*sin(2*pi*x/par[2]+par[3])-y)^2)

p1 <- optim(par = c(amplitude = 1, phase = 1, period = 1), cost)
p2 <- optim(par = c(amplitude = 1, phase = 1, period = 1), cost,
            method = "SANN")
p3 <- pricefit(par = c(amplitude = 1, phase = 1, period = 1),
            minpar = c(0, 1e-8,0), maxpar = c(100, 2*pi,100), 
            func = cost, numiter = 3000)

curve(p1$par[1]*sin(2*pi*x/p1$par[2] + p1$par[3]), lty = 2, add = TRUE)
curve(p2$par[1]*sin(2*pi*x/p2$par[2] + p2$par[3]), lty = 3, add = TRUE)
curve(p3$par[1]*sin(2*pi*x/p3$par[2] + p3$par[3]), lty = 1, add = TRUE)

legend ("bottomright", lty = c(1, 2, 3),
        c("Price", "Mathematical", "Simulated annealing"))