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## Two dimensional view ## One dimensional view ## Fine grain view ## Function ## Latex

A minimization problem:

$$f(x_0 \cdots x_n) = \sum_{i=0}^n i x_i^4 + \text{random}[0,1)$$

$$-1.28 \leq x_i \leq 1.28$$

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

## Python

def fitnessFunc(self, chromosome):
""""""
total = 0.0
for i in xrange(len(chromosome)):
total += (i+1.0) * chromosome[i]**4.0


## Sources

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

Evolutionary Programming Made Faster
@ARTICLE{771163,
author={Xin Yao and Yong Liu and Guangming Lin},
journal={Evolutionary Computation, IEEE Transactions on}, title={Evolutionary programming made faster},
year={1999},
month={jul},
volume={3},
number={2},
pages={82 -102},
keywords={Cauchy mutation;combinatorial optimization problems;convergence rates;evolutionary programming;global optimum;local minima;multimodal functions;numerical optimization problems;primary search operator;search step size;unimodal functions;convergence;evolutionary computation;optimisation;probability;search problems;},
doi={10.1109/4235.771163},
ISSN={1089-778X},}

This benchmark is listed as F4 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"
}