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Exponential

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Function

Latex

A minimization problem:

$$f(x_1 \cdots x_n) = \sum_{i=1}^n e^{ix_i}i + \alpha$$

$$\alpha = -\sum_{i=1}^n e^{-5.12i}$$

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

$$\text{minimum at }f(-5.12, \cdots, -5.12) = 0$$

Python

def fitnessFunc(self, chromosome):
	"""F3 Exponential function
	unimodal, asymmetric, separable"""
	alpha = 0
	for i in range(1, len(chromosome)+1):
		alpha += math.e**(-5.12*i)
	alpha = -alpha
	fitness = 0
	for i in range(len(chromosome)):
		fitness += math.e**((i+1)*chromosome[i])
	return fitness + alpha

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}
}

Notes