griewank: Griewank Function for Benchmarking Optimization Algorithms

In EEEA: Explicit Exploration Strategy for Evolutionary Algorithms

Griewank Function for Benchmarking Optimization Algorithms

Description

The Griewank function is a common test function for optimization algorithms. It combines a sum-of-squares term and a cosine-based product term, making it a useful benchmark for exploring search space properties and assessing the performance of optimization methods on functions with numerous local minima.

Usage

griewank(x)

Arguments

x	A numeric vector representing the input variables. The length of x determines the dimensionality of the problem.

Value

Returns a numeric value representing the evaluation of the Griewank function at the given input vector x.

References

Griewank, A. O. (1981). Generalized Descent for Global Optimization. Journal of Optimization Theory and Applications, 34(1), 11–39.

Examples

# Evaluation 1: Global minimum point in a four-dimensional space
x <- rep(0, 4)
griewank(x)

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

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

# EDA.mnorm() example
res = EDA.mnorm(fun = griewank, 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) griewank(c(x, y))))
contour(x1, x2, z, nlevels = 20, cex.axis = 0.8, 
        main = "Contour plot of the Griewank 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.