Bee_colony_Optimization

# EXAMPLE 1: The minimum is at (pi,pi) --------------------------------------
library(ABCoptim)
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:
##            178

# 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:
##            254

# 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]:  3.141593
##     x[2]:  3.141593
## 
##  value:
##           -1.000000
## 
##  counts:
##            257

# 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 
##      306 
## 
## $value
## [1] 67.46773

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]  2.184767e-09  3.683812e-09  2.523966e-09 -3.345184e-09 -1.913355e-09
## 
## $counts
## function 
##      425 
## 
## $value
## [1] 3.956527e-17

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

# 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