Curated Test Functions#

Surfaces is not just a random collection of test functions. Every function in this library has been carefully selected to provide meaningful benchmarks for optimization algorithms.

Five Categories of Test Functions#

Surfaces organizes test functions into five distinct categories, each serving a specific purpose in optimization benchmarking.

Algebraic Functions

Classic mathematical test functions from the optimization literature. These functions have well-known properties and are widely used in academic research.

  • 1D Functions: Simple univariate problems

  • 2D Functions: Visualizable landscapes (Ackley, Rastrigin, etc.)

  • N-D Functions: Scalable to any dimension

Learn more

BBOB Functions

The Black-Box Optimization Benchmarking (BBOB) suite from the COCO platform. An established standard for comparing continuous optimizers.

  • 24 noiseless functions

  • Designed for rigorous algorithm comparison

  • Used in GECCO competitions

Learn more

CEC Functions

Competition on Evolutionary Computation benchmark suites. These challenging functions are used in IEEE CEC competitions.

  • CEC 2013, 2014, 2017 suites

  • Shifted and rotated variants

  • Composition functions

Learn more

Machine Learning Functions

Test functions based on real ML model training. Benchmark your optimizer on actual hyperparameter optimization problems.

  • Classification and regression tasks

  • Tabular, image, and time series data

  • Realistic optimization landscapes

Learn more

Engineering Functions

Real-world constrained engineering design problems with physical meaning and practical relevance.

  • Welded Beam Design

  • Pressure Vessel Design

  • Tension-Compression Spring

Learn more

Why Curated Matters#

Standard Benchmarks#

CEC and BBOB are not arbitrary function collections. They are carefully designed benchmark suites used by the research community to compare optimization algorithms fairly.

When you use these functions, you can:

  • Compare your results directly with published research

  • Reproduce experiments from academic papers

  • Trust that the functions test relevant algorithm properties

Real Problems#

Algebraic functions like Sphere or Rastrigin are useful, but they do not represent real optimization challenges. Surfaces includes:

  • ML hyperparameter tuning: Actual model training as objective

  • Engineering design: Physical constraints and multi-modal landscapes

These functions help you understand how your optimizer performs on problems that matter.

Quick Example#

from surfaces.test_functions.algebraic import (
    # Algebraic
    SphereFunction,
    RastriginFunction,
    # BBOB
    # RosenbrockRotated,
    # CEC
    # RotatedRastrigin,
    # Machine Learning
    KNeighborsClassifierFunction,
    # Engineering
    WeldedBeamDesign,
)

# All functions share the same interface
for func_class in [SphereFunction, RastriginFunction]:
    func = func_class(n_dim=5)
    result = func(func.search_space_sample())
    print(f"{func.__class__.__name__}: {result:.4f}")

Next Steps#