expanded_schaffer: Expanded Schaffer's F6 Function for Benchmarking Optimization...

In EEEA: Explicit Exploration Strategy for Evolutionary Algorithms

Expanded Schaffer's F6 Function for Benchmarking Optimization Algorithms

Description

Expanded Schaffer's F6 function is a standard benchmark function used for testing optimization algorithms. It is a highly multimodal function with a global minimum at x = (0, 0, 0, 0) for 4 dimensions, where the function value is 0.5.

Usage

expanded_schaffer(x)

Arguments

x	A numeric vector representing the input variables for which the Expanded Schaffer's F6 function is evaluated.

Value

Returns a numeric value representing the evaluation of Expanded Schaffer's F6 function at the input vector x.

References

Schaffer, J. D. (1984). Multiple Objective Optimization with Vector Evaluated Genetic Algorithms. In Proceedings of the First International Conference on Genetic Algorithms.

Examples

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

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

# Contour Plot: Visualizing Expanded Schaffer's F6 Function
x1 <- seq(-10, 10, length.out = 100)
x2 <- seq(-10, 10, length.out = 100)
z <- outer(x1, x2, FUN = Vectorize(function(x, y) expanded_schaffer(c(x, y))))
contour(x1, x2, z, nlevels = 20, main = "Contour of Expanded Schaffer's F6 Function")

# EDA.mnorm() example
res = EDA.mnorm(fun = expanded_schaffer, 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) expanded_schaffer(c(x, y))))
contour(x1, x2, z, nlevels = 20, cex.axis = 0.8, 
        main = "Contour plot of the Expanded Schaffer's F6 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.