Test Functions for Optimization

Source: R/test-functions.R

Collection of benchmark test functions for evaluating optimization algorithms. These functions are commonly used in the literature to test the performance of metaheuristic optimization algorithms.

Details

The following test functions are implemented:

Unimodal Functions:

  • F01 - Sphere function: Simple quadratic function with a single minimum at the origin. F01

  • F02 - Sum of absolute values and products: Combines sum and product of absolute values. F02

  • F03 - Sum of squared terms: Sum of squared cumulative sums. F03

  • F04 - Maximum absolute value: Returns the maximum absolute value in the vector. F04

  • F05 - Rosenbrock function: Classic test function with a banana-shaped valley. F05

  • F06 - Shifted sphere function: Sphere function shifted to (-0.5, -0.5, ...). F06

  • F07 - Quartic function with noise: Quartic terms with added random noise. F07

Multimodal Functions:

  • F08 - Schwefel function: Multimodal function with many local minima. F08

  • F09 - Rastrigin function: Many local minima arranged in a regular pattern. F09

  • F10 - Ackley function: Global minimum at origin with many local minima. F10

  • F11 - Griewank function: Many local minima regularly distributed. F11

  • F12 - Penalized function 1: Complex landscape with penalty terms. F12

  • F13 - Penalized function 2: Different penalty terms creating complex landscape. F13

  • F14 - Shekel's Foxholes: 25 minima of different depths. F14

  • F15 - Kowalik function: Multimodal function for testing optimization. F15

  • F16 - Six-Hump Camel Back: Six local minima, two global. F16

  • F17 - Branin function: Commonly used for testing optimization algorithms. F17

  • F18 - Goldstein-Price function: Four local minima. F18

  • F19 - Hartman 3D function: 3 dimensions with multiple local minima. F19

  • F20 - Hartman 6D function: 6 dimensions with multiple local minima. F20

  • F21 - Shekel 5 function: Based on Shekel's family with 5 terms. F21

  • F22 - Shekel 7 function: Based on Shekel's family with 7 terms. F22

  • F23 - Shekel 10 function: Based on Shekel's family with 10 terms. F23

References

Faramarzi, A., Heidarinejad, M., Mirjalili, S., & Gandomi, A. H. (2020). Marine Predators Algorithm: A Nature-inspired Metaheuristic. Expert Systems with Applications, 113377. DOI: 10.1016/j.eswa.2020.113377

See also

F01 through F23 for individual function documentation. get_function_details to retrieve function details programmatically.

Examples

# Get details for a specific function
details <- get_function_details("F01")

# Use a test function directly
F01(c(0, 0, 0))  # Returns 0 (global minimum)
#> [1] 0

# List all available test functions
available_functions <- c("F01", "F02", "F03", "F04", "F05", "F06", "F07", "F08", "F09", "F10",
                       "F11", "F12", "F13", "F14", "F15", "F16", "F17", "F18", "F19", "F20",
                       "F21", "F22", "F23")