Test Functions

Surfaces provides seven categories of test functions, each designed for specific benchmarking purposes.

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Function Categories

Algebraic Functions

Classic mathematical test functions from the optimization literature. Well-studied, with known properties and analytical formulas.

• 1D Functions: Simple univariate problems

• 2D Functions: Visualizable landscapes

• N-D Functions: Scalable to any dimension

Algebraic Functions

BBOB Functions

Black-Box Optimization Benchmarking suite from the COCO platform. The standard for rigorous optimizer comparison.

• 24 noiseless functions

• Used in GECCO competitions

• Systematic difficulty progression

BBOB Functions

CEC Functions

Competition on Evolutionary Computation benchmark suites. Challenging functions for advanced optimizer testing.

• CEC 2013, 2014, 2017 suites

• Shifted and rotated variants

• Composition functions

CEC Functions

Machine Learning Functions

Test functions based on real ML model training. Realistic hyperparameter optimization landscapes.

• Classification and regression

• Tabular, image, time series

• Surrogate models available

Machine Learning Functions

Engineering Functions

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

• Welded Beam Design

• Pressure Vessel Design

• Tension-Compression Spring

Engineering Functions

Multi-Objective Functions

Standard benchmarks for Pareto-front approximation, with analytic fronts for ground-truth evaluation.

• ZDT1 to ZDT6

• DTLZ1 to DTLZ7

• WFG1 to WFG9

multi_objective

Discrete Functions

Binary / pseudo-boolean test functions for combinatorial optimization benchmarks.

• OneMax, LeadingOnes

• NK Landscape, Trap

• 0/1 Knapsack

discrete

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Choosing the Right Category

Use Case	Recommended Category	Why
Quick prototyping	Algebraic (2D)	Fast, visualizable, simple
Rigorous comparison	BBOB	Standard benchmark, comparable results
Algorithm competition	CEC	Used in IEEE CEC competitions
Real-world relevance	Machine Learning	Actual HPO landscapes
Constrained optimization	Engineering	Physical constraints
Pareto-front approximation	Multi-Objective	ZDT / DTLZ / WFG families with analytic fronts
Binary / combinatorial	Discrete	Pseudo-boolean, tunable ruggedness, deception

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Common Interface

All test functions share the same interface:

from surfaces.test_functions.algebraic import SphereFunction, KNeighborsClassifierFunction

# Same interface for algebraic and ML functions
for func_class in [SphereFunction, KNeighborsClassifierFunction]:
    func = func_class() if func_class == KNeighborsClassifierFunction else func_class(n_dim=3)

    # Evaluate
    result = func(func.search_space_sample())

    # Get search space
    space = func.search_space()

    # Convert to scipy
    objective, bounds, x0 = func.to_scipy()

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