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

A minimization problem:

$$f(x_1 \cdots x_n) = \sum_{i=1}^n \sum_{j=1}^n (\frac{(100(x_i^2-x_j)^2 + (1-x_j)^2)^2}{4000} -cos(100(x_i^2-x_j)^2 + (1-x_j)^2)+1)$$

$$-10.24 \leq x_i \leq 10.24$$

$$\text{minimum at }f(1, 1, \cdots, 1) = 0$$

## Python

def fitnessFunc(self, chromosome):
"""F9 Whitley's function
multimodal, asymmetric, inseparable
http://www.it.lut.fi/ip/evo/functions/node13.html """
fitness = 0
limit = len(chromosome)
for i in range(limit):
for j in range(limit):
temp = 100*((chromosome[i]**2)-chromosome[j]) + \
(1-chromosome[j])**2
fitness += (float(temp**2)/4000.0) - math.cos(temp) + 1
return fitness


## Sources

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

www.it.lut.fi
The fine-grain view of the fitness landscape shown on this webpage does not match the fine-grain view shown in Figure 4 of the paper by Jumonji and Chakraborty, which is cited below, and neither fine-grain view matches my fine-grain view. It remains unclear why this is the case. I invite readers to contact me if they believe they can resolve this issue.

Real-Space Evolutionary Annealing

Note that the following paper has a typo in Table 1 for Whitley's function. The numerator is not squared and there is an unclosed parend. Whitley's function is correctly written elsewhere in the paper. However, I find the function where the numerator is not squared quite interesting. It can be seen here, with fine-grain view here.
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}
}

## Notes

multimodal, asymmetric, inseparable