# Pseudo-random search algorithm of Price (1997) 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. ```r 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 ## Returns 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 ## Examples ```r 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")) ``` ## 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. ## See Also `optim` the R default. ## 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.

pricefit function