rosenbrock: Rosenbrock function for optimization problems

In EEEA: Explicit Exploration Strategy for Evolutionary Algorithms

Rosenbrock function for optimization problems

Description

The Rosenbrock function, also known as the "Rosenbrock's valley" or "banana function", is a non-convex function commonly used as a performance test for optimization algorithms. It features a narrow, curved valley that contains the global minimum, which makes it particularly challenging for optimization methods. The global minimum is located at the point where all variables are equal to 1.

Usage

rosenbrock(x)

Arguments

x	A numeric vector of parameters for which the Rosenbrock function is evaluated.

Value

Returns a numeric value, which is the evaluation of the Rosenbrock function at the input vector x.

References

Rosenbrock, H. H. (1960). An Automatic Method for Finding the Greatest or Least Value of a Function. The Computer Journal, 3(3), 175–184. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1093/comjnl/3.3.175")}

Examples

# Evaluation 1: Global minimum point in a four-dimensional space
x <- rep(1, 4)
rosenbrock(x)

# Evaluation 2: A point in a six-dimensional space
x <- c(0, 0.24, 11, -1, -0.7, pi)
rosenbrock(x)

# Contour Plot: Visualizing the Rosenbrock Function
x1 <- seq(-10, 10, length.out = 100)
x2 <- seq(-10, 10, length.out = 100)
z <- outer(x1, x2, FUN = Vectorize(function(x, y) rosenbrock(c(x, y))))
contour(x1, x2, z, nlevels = 20, main = "Contour of the Rosenbrock Function")

# EDA.mnorm() example
res = EDA.mnorm(fun = rosenbrock, lower = c(-10,-10), upper = c(10,10), n = 30, 
                k = 2, tolerance = 0.01, maxiter = 200)
res$sol

# Contour plot: Visualizing solution with EDA.mnorm()
x1 <- seq(-10, 10, length.out = 100)
x2 <- seq(-10, 10, length.out = 100)
z <- outer(x1, x2, FUN = Vectorize(function(x, y) rosenbrock(c(x, y))))
contour(x1, x2, z, nlevels = 20, cex.axis = 0.8, 
        main = "Contour plot of the Rosenbrock Function with EDA.mnorm solution")
points(res$sol[1], res$sol[2], col = "red", pch = 19)

EEEA documentation built on June 10, 2025, 9:13 a.m.