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# PROBLEMS
#
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# - Use GA search (using the ga() function in the GA package) to find the minimum of the real-valued function 
#   f(x) = abs(x) + cos(x). Restrict the search interval to [-20, 20]. Carefully define the fitness function, 
#   since the ga() can only maximize it! 
#
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#
# - Use GA search to find the minimum of the real-valued two-dimensional function 
#   f(x1, x2) = 20 + x1^2 + x2^2 - 10*(cos(2*pi*x1) + cos(2*pi*x2)), where x1 and x2 are from the interval [-5.12, 5.12].
#	
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# - We are given the following data:
#
#   Substrate <- c(1.73, 2.06, 2.20, 4.28, 4.44, 5.53, 6.32, 6.68, 7.28, 7.90, 8.80, 9.14, 9.18, 9.40, 9.88)
#   Velocity <- c(12.48, 13.97, 14.59, 21.25, 21.66, 21.97, 25.36, 22.93, 24.81, 25.63, 24.68, 29.04, 28.08, 27.32, 27.77)
#
#   Use GA search to fit the data to the model:
#   Velocity = (M * Substrate) / (K + Substrate), where M and K are the model parameters. Restrict the search interval 
#   for M to [40.0, 50.0] and for K to [3.0, 5.0].
#
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#
# - Use a binary GA to select (sub)optimal attribute subset for a linear model:
#
#   train.data <- read.table("AlgaeLearn.txt", header = T)
#   test.data <- read.table("AlgaeTest.txt", header = T)
#   lm.model <- lm(a1 ~., train.data)
#
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library(GA)

# - Use GA search (using the ga() function in the GA package) to find the minimum of the real-valued function
#   f(x) = abs(x) + cos(x). Restrict the search interval to [-20, 20]. Carefully define the fitness function, 
#   since the ga() can only maximize it! 
f <- function(x) {
  abs(x) + cos(x)
}

curve(f,  from=-20, to=20, n=1000)

# For the maximization of this function we may use f directly as the fitness function
GA <- ga(type = "real-valued", fitness = f, lower = -20, upper = 20)

# The object returned can be plotted
plot(GA)
summary(GA)

# plot the solution
curve(f, from = -20, to = 20, n = 1000)
points(GA@solution, f(GA@solution), col="red")

# - Use GA search to find the minimum of the real-valued two-dimensional function 
#   f(x1, x2) = 20 + x1^2 + x2^2 - 10*(cos(2*pi*x1) + cos(2*pi*x2)), where x1 and x2 are from the interval [-5.12, 5.12].
# https://stackoverflow.com/a/68635397

fitness_f <- function(x1, x2) {
  20 + x1^2 + x2^2 - 10*(cos(2*pi*x1) + cos(2*pi*x2))
}

# For the maximization of this function we may use f directly as the fitness function
GA <- ga(type = "real-valued", fitness = function(x) -fitness_f(x[1], x[2]), lower = c(-5.12, -5.12), upper = c(5.12, 5.12), maxiter=200)

# The object returned can be plotted
plot(GA)
summary(GA)

# - We are given the following data:
#
#   Substrate <- c(1.73, 2.06, 2.20, 4.28, 4.44, 5.53, 6.32, 6.68, 7.28, 7.90, 8.80, 9.14, 9.18, 9.40, 9.88)
#   Velocity <- c(12.48, 13.97, 14.59, 21.25, 21.66, 21.97, 25.36, 22.93, 24.81, 25.63, 24.68, 29.04, 28.08, 27.32, 27.77)
#
#   Use GA search to fit the data to the model:
#   Velocity = (M * Substrate) / (K + Substrate), where M and K are the model parameters. Restrict the search interval 
#   for M to [40.0, 50.0] and for K to [3.0, 5.0].

Substrate <- c(1.73, 2.06, 2.20, 4.28, 4.44, 5.53, 6.32, 6.68, 7.28, 7.90, 8.80, 9.14, 9.18, 9.40, 9.88)
Velocity <- c(12.48, 13.97, 14.59, 21.25, 21.66, 21.97, 25.36, 22.93, 24.81, 25.63, 24.68, 29.04, 28.08, 27.32, 27.77)

# param[1] = M, param[2] = K
model <- function(params) {
  (params[1] * Substrate) / (params[2] + Substrate)
}

fitness_f <- function(params) {
  -sum((Substrate - model(params))^2)
}

GA2 <- ga(type = "real-valued", fitness = fitness_f, lower = c(40.0, 3.0), upper = c(50.0, 5.0),
          popSize = 500, crossover = gareal_blxCrossover, maxiter = 5000, run = 200, names = c("M", "K"))

summary(GA2)

# Let's plot our solution
plot(Substrate, Velocity)
lines(Substrate, model(GA2@solution))


# - Use a binary GA to select (sub)optimal attribute subset for a linear model:
#
#   train.data <- read.table("AlgaeLearn.txt", header = T)
#   test.data <- read.table("AlgaeTest.txt", header = T)
#   lm.model <- lm(a1 ~., train.data)

train.data <- read.table("./data/AlgaeLearn.txt", header = T)
test.data <- read.table("./data/AlgaeTest.txt", header = T)
lm.model <- lm(a1 ~., train.data)