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Langermann

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Function

Latex

A minimization problem:

$$f(x_0 \cdots x_n) = \sum_{i=1}^n c_i exp((1/\pi)||x-A(i)||^2) cos(\pi ||x - A(i)||^2)$$

$$0 \leq x_i \leq 10$$

Python

#The following values come from here:
#http://www.scribd.com/doc/74351406/11/Langermann%E2%80%99s-function
self.m = 5
self.a = [[rd.randint(1,10) for _ in xrange(problemDimensions)] for _ in xrange(self.m)]
self.c = [1,2,5,2,3]

def fitnessFunc(self, chromosome):
	""""""
	total = 0
	length = len(chromosome)
	for i in xrange(self.m):
		subtotal = 0
		for j in xrange(length):
			subtotal += (chromosome[j] - self.a[i][j])**2
		total += self.c[i] * math.exp((-1/math.pi)*subtotal) * \
			math.cos(math.pi*subtotal)
	return total

Sources

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

Macroevolutionary algorithms: a new optimization method on fitness landscapes
@ARTICLE{797970, 
author={Marin, J. and Sole, R.V.}, 
journal={Evolutionary Computation, IEEE Transactions on}, 
title={Macroevolutionary algorithms: a new optimization method on fitness landscapes}, 
year={1999}, 
month={nov}, 
volume={3}, 
number={4}, 
pages={272 -286}, 
keywords={candidate solutions;extinction patterns;fitness landscapes;macroevolutionary algorithms;mean field theoretical approach;optimization method;tournament selection;evolutionary computation;probability;}, 
doi={10.1109/4235.797970}, 
ISSN={1089-778X},}

scribd: Langermann's function

mkwies: Langermann's function

Notes