BBOB Functions#

The Black-Box Optimization Benchmarking (BBOB) suite is part of the COCO (Comparing Continuous Optimizers) platform. It is the standard benchmark for comparing continuous optimization algorithms.

What is BBOB?#

BBOB is a carefully designed benchmark suite with:

24 noiseless functions: Covering different optimization challenges
Systematic design: Functions grouped by difficulty characteristics
Standard methodology: Results comparable across publications
Competition use: Used in GECCO BBOB workshops

When you benchmark on BBOB, you can compare your results directly with hundreds of published optimizers.

Function Groups#

BBOB functions are organized into five groups based on their characteristics:

Group	Characteristics	Example Functions
Separable	Variables independent	Sphere, Ellipsoidal
Low/Moderate Conditioning	Manageable condition numbers	Rosenbrock, Attractive Sector
High Conditioning	Ill-conditioned	Bent Cigar, Sharp Ridge
Multi-modal (adequate)	Multiple optima, exploitable structure	Rastrigin, Schaffer F7
Multi-modal (weak)	Many optima, weak global structure	Schwefel, Gallagher

Available BBOB Functions#

Function	Group	Properties
`Sphere`	Separable	Simplest, baseline
`EllipsoidalSeparable`	Separable	Ill-conditioned, separable
`RastriginSeparable`	Multi-modal	Highly multimodal, separable
`BuecheRastrigin`	Multi-modal	Asymmetric Rastrigin
`LinearSlope`	Separable	Linear function
`AttractiveSector`	Low conditioning	Sector-based optima
`StepEllipsoidal`	Low conditioning	Discrete steps
`RosenbrockOriginal`	Low conditioning	Classic Rosenbrock
`RosenbrockRotated`	Low conditioning	Rotated variant
`EllipsoidalRotated`	High conditioning	Rotated, ill-conditioned
`Discus`	High conditioning	Single sensitive direction
`BentCigar`	High conditioning	Narrow ridge
`SharpRidge`	High conditioning	Sharp narrow ridge
`DifferentPowers`	High conditioning	Variable sensitivities
`RastriginRotated`	Multi-modal	Rotated Rastrigin
`Weierstrass`	Multi-modal	Rugged landscape
`SchaffersF7`	Multi-modal	Asymmetric, ill-conditioned
`SchaffersF7Ill`	Multi-modal	More ill-conditioned
`GriewankRosenbrock`	Multi-modal	Combined landscape
`Schwefel`	Multi-modal (weak)	Deceptive optima
`Gallagher101`	Multi-modal (weak)	101 random peaks
`Gallagher21`	Multi-modal (weak)	21 random peaks
`Katsuura`	Multi-modal (weak)	Fractal-like
`LunacekBiRastrigin`	Multi-modal (weak)	Two funnels

Usage Example#

from surfaces.test_functions.benchmark.bbob import (
    Sphere,
    RosenbrockRotated,
    RastriginRotated,
    Schwefel,
)

# Create functions
sphere = Sphere(n_dim=10)
rosenbrock = RosenbrockRotated(n_dim=10)
rastrigin = RastriginRotated(n_dim=10)
schwefel = Schwefel(n_dim=10)

# Evaluate
for func in [sphere, rosenbrock, rastrigin, schwefel]:
    result = func(func.search_space_sample())
    print(f"{func.__class__.__name__}: {result:.4f}")

Why Use BBOB?#

Comparable Results#

BBOB has been used in optimization research for over a decade. When you report results on BBOB functions, readers can directly compare with:

Published papers
COCO data archive
Your own previous experiments

Systematic Coverage#

BBOB functions systematically cover different optimization challenges:

Separability
Conditioning
Multi-modality
Global structure

This ensures you test all aspects of your optimizer.

Standard Methodology#

The COCO platform provides standardized:

Performance measures (ERT, success rate)
Visualization tools
Statistical comparisons

BBOB vs Algebraic#

Aspect	Algebraic	BBOB
Purpose	General benchmarking	Rigorous comparison
Standardization	Varies by paper	COCO standard
Transformations	Usually none	Shifted, rotated
Comparability	Limited	Extensive literature

Next Steps#

CEC Functions - CEC competition benchmarks
/api_reference/test_functions/bbob - Complete API reference
COCO Platform - Official BBOB implementation