115 lines
4.8 KiB
R
115 lines
4.8 KiB
R
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##########################################################################################################################
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#
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# PROBLEMS
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#
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##########################################################################################################################
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#
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# - Use GA search (using the ga() function in the GA package) to find the minimum of the real-valued function
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# f(x) = abs(x) + cos(x). Restrict the search interval to [-20, 20]. Carefully define the fitness function,
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# since the ga() can only maximize it!
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#
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##########################################################################################################################
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#
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# - Use GA search to find the minimum of the real-valued two-dimensional function
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# 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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#
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##########################################################################################################################
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#
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# - We are given the following data:
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#
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# 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)
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# 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)
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#
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# Use GA search to fit the data to the model:
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# Velocity = (M * Substrate) / (K + Substrate), where M and K are the model parameters. Restrict the search interval
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# for M to [40.0, 50.0] and for K to [3.0, 5.0].
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#
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##########################################################################################################################
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#
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# - Use a binary GA to select (sub)optimal attribute subset for a linear model:
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#
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# train.data <- read.table("AlgaeLearn.txt", header = T)
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# test.data <- read.table("AlgaeTest.txt", header = T)
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# lm.model <- lm(a1 ~., train.data)
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#
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##########################################################################################################################
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library(GA)
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# - Use GA search (using the ga() function in the GA package) to find the minimum of the real-valued function
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# f(x) = abs(x) + cos(x). Restrict the search interval to [-20, 20]. Carefully define the fitness function,
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# since the ga() can only maximize it!
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f <- function(x) {
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abs(x) + cos(x)
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}
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curve(f, from=-20, to=20, n=1000)
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# For the maximization of this function we may use f directly as the fitness function
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GA <- ga(type = "real-valued", fitness = f, lower = -20, upper = 20)
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# The object returned can be plotted
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plot(GA)
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summary(GA)
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# plot the solution
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curve(f, from = -20, to = 20, n = 1000)
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points(GA@solution, f(GA@solution), col="red")
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# - Use GA search to find the minimum of the real-valued two-dimensional function
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# 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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# https://stackoverflow.com/a/68635397
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fitness_f <- function(x1, x2) {
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20 + x1^2 + x2^2 - 10*(cos(2*pi*x1) + cos(2*pi*x2))
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}
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# For the maximization of this function we may use f directly as the fitness function
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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)
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# The object returned can be plotted
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plot(GA)
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summary(GA)
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# - We are given the following data:
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#
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# 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)
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# 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)
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#
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# Use GA search to fit the data to the model:
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# Velocity = (M * Substrate) / (K + Substrate), where M and K are the model parameters. Restrict the search interval
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# for M to [40.0, 50.0] and for K to [3.0, 5.0].
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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)
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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)
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# param[1] = M, param[2] = K
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model <- function(params) {
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(params[1] * Substrate) / (params[2] + Substrate)
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}
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fitness_f <- function(params) {
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-sum((Substrate - model(params))^2)
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}
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GA2 <- ga(type = "real-valued", fitness = fitness_f, lower = c(40.0, 3.0), upper = c(50.0, 5.0),
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popSize = 500, crossover = gareal_blxCrossover, maxiter = 5000, run = 200, names = c("M", "K"))
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summary(GA2)
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# Let's plot our solution
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plot(Substrate, Velocity)
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lines(Substrate, model(GA2@solution))
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# - Use a binary GA to select (sub)optimal attribute subset for a linear model:
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#
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# train.data <- read.table("AlgaeLearn.txt", header = T)
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# test.data <- read.table("AlgaeTest.txt", header = T)
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# lm.model <- lm(a1 ~., train.data)
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train.data <- read.table("./data/AlgaeLearn.txt", header = T)
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test.data <- read.table("./data/AlgaeTest.txt", header = T)
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lm.model <- lm(a1 ~., train.data)
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