1D Functions#

One-dimensional test functions are useful for simple benchmarks, visualization of optimizer behavior, and educational purposes.

Available 1D Functions#

Function

Global Minimum

Characteristics

GramacyAndLeeFunction

x* = 0.548

Multiple local minima

ForresterFunction

x* = 0.757

Smooth with one global minimum

Gramacy & Lee Function#

A common 1D test function with multiple local minima.

from surfaces.test_functions.algebraic import GramacyAndLeeFunction

func = GramacyAndLeeFunction()

# Evaluate
result = func({"x0": 0.5})

# Search space
space = func.search_space()
print(f"Bounds: [{space['x0'].min()}, {space['x0'].max()}]")

Properties:

  • Domain: [0.5, 2.5]

  • Global minimum: x* = 0.548, f(x*) = -0.869

Forrester Function#

A smooth 1D function often used for surrogate model testing.

from surfaces.test_functions.algebraic import ForresterFunction

func = ForresterFunction()
result = func({"x0": 0.757})

Properties:

  • Domain: [0, 1]

  • Global minimum: x* = 0.757

Use Cases#

1D functions are particularly useful for:

  • Visualizing optimizer behavior: Plot the function and optimization trajectory

  • Testing convergence: Simple enough to verify optimizer correctness

  • Educational examples: Easy to understand and explain

import numpy as np
import matplotlib.pyplot as plt
from surfaces.test_functions.algebraic import GramacyAndLeeFunction

func = GramacyAndLeeFunction()
space = func.search_space()

# Plot the function
x = space["x0"]
y = [func({"x0": xi}) for xi in x]

plt.plot(x, y)
plt.xlabel("x")
plt.ylabel("f(x)")
plt.title("Gramacy & Lee Function")
plt.show()

Next Steps#