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Rastrigin

Two dimensional view

One dimensional view

Fine grain view

Function

Latex

A minimization problem:

$$f(x_1 \cdots x_n) = 10n + \sum_{i=1}^n (x_i^2 -10cos(2\pi x_i))$$

$$-5.12 \leq x_i \leq 5.12$$

$$\text{minimum at }f(0, \cdots, 0) = 0$$

Python

def fitnessFunc(self, chromosome):
	"""F5 Rastrigin's function
	multimodal, symmetric, separable"""
	fitness = 10*len(chromosome)
	for i in range(len(chromosome)):
		fitness += chromosome[i]**2 - (10*math.cos(2*math.pi*chromosome[i]))
	return fitness

Sources

The following may or may not contain the originator of this function.

A novel distributed genetic algorithm implementation with variable number of islands
@inproceedings{varIslandNum07,
author = {Takuma Jumonji and Goutam Chakraborty and Hiroshi Mabuchi and Masafumi Matsuhara},
title = {A novel distributed genetic algorithm implementation with variable number of islands},
booktitle = {IEEE Congress on Evolutionary Computation},
year = {2007},
pages = {4698--4705},
doi = {10.1109/CEC.2007.4425088},
masid = {4737000}
}

The influence of migration sizes and intervals on island models
@inproceedings{Skolicki:2005:IMS:1068009.1068219,
 author = {Skolicki, Zbigniew and De Jong, Kenneth},
 title = {The influence of migration sizes and intervals on island models},
 booktitle = {Proceedings of the 2005 conference on Genetic and evolutionary computation},
 series = {GECCO '05},
 year = {2005},
 isbn = {1-59593-010-8},
 location = {Washington DC, USA},
 pages = {1295--1302},
 numpages = {8},
 url = {http://doi.acm.org/10.1145/1068009.1068219},
 doi = {10.1145/1068009.1068219},
 acmid = {1068219},
 publisher = {ACM},
 address = {New York, NY, USA},
 keywords = {evolutionary computation, island model, migration, migration interval, migration size, test suite},
}

Global Optimization
@article{torn1989global,
  title={Global Optimization},
  author={Torn, A. and Zilinskas, A.},
  year={1989},
  journal={Lecture Notes in Computer Science},
  number={350}
}

Evaluating evolutionary algorithms
@article{Whitley1996245,
title = "Evaluating evolutionary algorithms",
journal = "Artificial Intelligence",
volume = "85",
number = "1-2",
pages = "245 - 276",
year = "1996",
note = "",
issn = "0004-3702",
doi = "10.1016/0004-3702(95)00124-7",
url = "http://www.sciencedirect.com/science/article/pii/0004370295001247",
author = "Darrell Whitley and Soraya Rana and John Dzubera and Keith E. Mathias"
}

This benchmark is listed as F6 in "The parallel genetic algorithm as function optimizer"
@article{Muhlenbein1991619,
title = "The parallel genetic algorithm as function optimizer",
journal = "Parallel Computing",
volume = "17",
number = "6-7",
pages = "619 - 632",
year = "1991",
note = "",
issn = "0167-8191",
doi = "10.1016/S0167-8191(05)80052-3",
url = "http://www.sciencedirect.com/science/article/pii/S0167819105800523",
author = "H. M{\"u}hlenbein and M. Schomisch and J. Born",
keywords = "Search methods",
keywords = "optimization methods",
keywords = "parallel genetic algorithm",
keywords = "performance evaluation",
keywords = "speedup results"
}


Notes