CEC Functions#

The CEC (Competition on Evolutionary Computation) benchmark suites are challenging test functions used in IEEE CEC competitions. They are designed to test advanced optimization algorithms.

What is CEC?#

CEC benchmarks are:

  • Competition-grade: Used in IEEE CEC annual competitions

  • Challenging: Shifted optima, rotations, compositions

  • Standardized: Specific rules for fair comparison

  • Evolving: New suites released periodically (2013, 2014, 2017, …)

If your optimizer performs well on CEC functions, it can compete with state-of-the-art algorithms.

Available CEC Suites#

CEC 2013#

28 benchmark functions for real-parameter optimization.

Basic Functions (f1-f5):

Function

Description

Rastrigin

Separable, multimodal

RotatedRastrigin

Non-separable variant

RotatedDiscus

Ill-conditioned

RotatedBentCigar

Ridge structure

DifferentPowers

Variable sensitivities

Multimodal Functions (f6-f20):

  • Rotated versions of classic functions

  • Shifted global optima

  • Non-separable landscapes

Composition Functions (f21-f28):

  • CompositionFunction1 through CompositionFunction8

  • Combine multiple basic functions

  • Create complex multi-basin landscapes

CEC 2014#

30 benchmark functions with improved characteristics:

  • Better coverage of difficulty features

  • Scalable to different dimensions

  • Standardized bounds and optima

CEC 2017#

Updated suite with modern test functions:

  • Hybrid functions

  • Updated composition rules

  • New challenging landscapes

Key Features#

Shifted Optima#

Unlike basic algebraic functions where the optimum is at the origin, CEC functions have shifted optima:

from surfaces.test_functions.benchmark.cec import RotatedRastrigin

func = RotatedRastrigin(n_dim=10)

# Optimum is NOT at origin
result_origin = func({f"x{i}": 0.0 for i in range(10)})
print(f"f(0, ..., 0) = {result_origin}")  # Not the minimum!

This tests whether your optimizer searches the entire space, not just around the origin.

Rotated Search Spaces#

Many CEC functions apply rotation matrices:

  • Variables become correlated

  • Separable algorithms fail

  • Tests true multi-dimensional search

Composition Functions#

Composition functions combine multiple basic functions:

from surfaces.test_functions.benchmark.cec import CompositionFunction1

func = CompositionFunction1(n_dim=10)

# Complex landscape with multiple basins
result = func(func.search_space_sample())

These create realistic multi-modal landscapes where different regions have different characteristics.

Usage Example#

from surfaces.test_functions.benchmark.cec.cec2013 import (
    RotatedRastrigin,
    RotatedBentCigar,
    CompositionFunction1,
)

# Standard 10D benchmark
functions = [
    RotatedRastrigin(n_dim=10),
    RotatedBentCigar(n_dim=10),
    CompositionFunction1(n_dim=10),
]

for func in functions:
    # Run your optimizer
    result = func(func.search_space_sample())
    print(f"{func.__class__.__name__}: {result:.4f}")

CEC vs BBOB vs Algebraic#

Aspect

Algebraic

BBOB

CEC

Difficulty

Easy-Medium

Medium-Hard

Hard

Optima

Often at origin

Shifted

Shifted

Rotation

Usually none

Some functions

Most functions

Composition

No

Limited

Extensive

Competition use

No

GECCO

IEEE CEC

Competition Preparation#

If you’re preparing for CEC competitions:

  1. Use the correct suite: Check which year’s functions are required

  2. Follow the rules: Specific evaluation budgets, dimension settings

  3. Report correctly: Use standard metrics (error values, success rate)

from surfaces.test_functions.benchmark.cec.cec2017 import (
    # Import the specific year's functions
    # ...
)

# Standard competition settings
n_dim = 10  # or 30, 50, 100
max_evaluations = 10000 * n_dim

Next Steps#