Implements Karaboga (2005) Artificial Bee Colony (ABC) Optimization algorithm.
abc_optim(par, fn, ..., FoodNumber = 20, lb = rep(-Inf, length(par)), ub = rep(+Inf, length(par)), limit = 100, maxCycle = 1000, optiinteger = FALSE, criter = 50, parscale = rep(1, length(par)), fnscale = 1) # S3 method for abc_answer print(x, ...) abc_cpp(par, fn, ..., FoodNumber = 20, lb = rep(-Inf, length(par)), ub = rep(+Inf, length(par)), limit = 100, maxCycle = 1000, criter = 50, parscale = rep(1, length(par)), fnscale = 1) # S3 method for abc_answer plot(x, y = NULL, main = "Trace of the Objective Function", xlab = "Number of iteration", ylab = "Value of the objective Function", type = "l", ...)
| par | Numeric vector. Initial values for the parameters to be optimized over |
|---|---|
| fn | A function to be minimized, with first argument of the vector of parameters over which minimization is to take place. It should return a scalar result. |
| ... | In the case of |
| FoodNumber | Number of food sources to exploit. Notice that the param
|
| lb, ub | Numeric vectors or scalars. Upper and lower bounds of the parameters to be optimized. |
| limit | Integer scalar. Limit of a food source. |
| maxCycle | Integer scalar. Maximum number of iterations. |
| optiinteger | Logical scalar. Whether to optimize binary parameters or not. |
| criter | Integer scalar. Stop criteria (numer of unchanged results) until stopping |
| parscale | Numeric vector of length |
| fnscale | Numeric scalar. Scale applied function. If |
| x | An object of class |
| y | Ignored |
| main, xlab, ylab, type | Passed to |
An list of class abc_answer, holding the following elements:
Numeric matrix. Last position of the bees.
Numeric vector. Value of the function evaluated at each set of Foods.
Numeric vector. Fitness of each Foods.
Integer vector. Number of trials at each Foods.
Numeric scalar. Value of the function evaluated at the optimum.
Numeric vector. Optimum found.
Integer scalar. Number of cycles.
Numeric matrix. Trace of the global optimums.
This implementation of the ABC algorithm was developed based on the basic
version written in C and published at the algorithm's official
website (see references).
abc_optim and abc_cpp are two different implementations of the
algorithm, the former using pure R code, and the later using C++,
via the Rcpp package. Besides of the output, another important
difference between the two implementations is speed, with abc_cpp
showing between 50% and 100% faster performance.
Upper and Lower bounds (ub, lb) equal to infinite will be replaced
by either .Machine$double.xmax or -.Machine$double.xmax.
lb and ub can be either scalars (assuming that all the
parameters share the same boundaries) or vectors (the parameters have
different boundaries each other).
The plot method shows the trace of the objective function
as the algorithm unfolds. The line is merely the result of the objective
function evaluated at each point (row) of the hist matrix return by
abc_optim/abc_cpp.
For now, the function will return with error if ... was passed to
abc_optim/abc_cpp, since those argumens are not stored with the
result.
D. Karaboga, An Idea based on Honey Bee Swarm for Numerical Optimization, tech. report TR06,Erciyes University, Engineering Faculty, Computer Engineering Department, 2005 http://mf.erciyes.edu.tr/abc/pub/tr06_2005.pdf
Artificial Bee Colony (ABC) Algorithm (website) http://mf.erciyes.edu.tr/abc/index.htm
Basic version of the algorithm implemented in C (ABC's official
website) http://mf.erciyes.edu.tr/abc/form.aspx
# EXAMPLE 1: The minimum is at (pi,pi) -------------------------------------- fun <- function(x) { -cos(x[1])*cos(x[2])*exp(-((x[1] - pi)^2 + (x[2] - pi)^2)) } abc_optim(rep(0,2), fun, lb=-10, ub=10, criter=50)#> #> An object of class -abc_answer- (Artificial Bee Colony Optim.): #> par: #> x[1]: 3.141593 #> x[2]: 3.141593 #> #> value: #> -1.000000 #> #> counts: #> 177# This should be equivalent abc_cpp(rep(0,2), fun, lb=-10, ub=10, criter=50)#> #> An object of class -abc_answer- (Artificial Bee Colony Optim.): #> par: #> x[1]: 3.141593 #> x[2]: 3.141593 #> #> value: #> -1.000000 #> #> counts: #> 262# We can also turn this into a maximization problem, and get the same # results fun <- function(x) { # We've removed the '-' from the equation cos(x[1])*cos(x[2])*exp(-((x[1] - pi)^2 + (x[2] - pi)^2)) } abc_cpp(rep(0,2), fun, lb=-10, ub=10, criter=50, fnscale = -1)#> #> An object of class -abc_answer- (Artificial Bee Colony Optim.): #> par: #> x[1]: 3.141592 #> x[2]: 3.141593 #> #> value: #> -1.000000 #> #> counts: #> 149# EXAMPLE 2: global minimum at about (-15.81515) ---------------------------- fw <- function (x) 10*sin(0.3*x)*sin(1.3*x^2) + 0.00001*x^4 + 0.2*x+80 ans <- abc_optim(50, fw, lb=-100, ub=100, criter=100) ans[c("par", "counts", "value")]#> $par #> [1] -15.81515 #> #> $counts #> function #> 227 #> #> $value #> [1] 67.46773 #># EXAMPLE 3: 5D sphere, global minimum at about (0,0,0,0,0) ----------------- fs <- function(x) sum(x^2) ans <- abc_optim(rep(10,5), fs, lb=-100, ub=100, criter=200) ans[c("par", "counts", "value")]#> $par #> [1] 2.897570e-09 3.570606e-09 1.671462e-09 -2.291569e-10 -3.896331e-09 #> #> $counts #> function #> 419 #> #> $value #> [1] 3.917283e-17 #># EXAMPLE 4: An Ordinary Linear Regression ---------------------------------- set.seed(1231) k <- 4 n <- 5e2 # Data generating process w <- matrix(rnorm(k), ncol=1) # This are the model parameters X <- matrix(rnorm(k*n), ncol = k) # This are the controls y <- X %*% w # This is the observed data # Objective function fun <- function(x) { sum((y - X%*%x)^2) } # Running the regression ans <- abc_optim(rep(0,k), fun, lb = -10000, ub=10000) # Here are the outcomes: Both columns should be the same cbind(ans$par, w)#> [,1] [,2] #> [1,] -0.08051177 -0.08051177 #> [2,] 0.69528553 0.69528553 #> [3,] -1.75956316 -1.75956316 #> [4,] 0.36156427 0.36156427# [,1] [,2] # [1,] -0.08051177 -0.08051177 # [2,] 0.69528553 0.69528553 # [3,] -1.75956316 -1.75956316 # [4,] 0.36156427 0.36156427 # This is just like OLS, with no constant coef(lm(y~0+X))#> X1 X2 X3 X4 #> -0.08051177 0.69528553 -1.75956316 0.36156427# X1 X2 X3 X4 #-0.08051177 0.69528553 -1.75956316 0.36156427