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Schaffer's F7

Two dimensional view

Fine grain view

Function

Latex

A minimization problem:

$$f(x_0 \cdots x_n) = [\frac{1}{n-1}\sqrt{s_i} \cdot (sin(50.0s_i^{\frac{1}{5}})+1)]^2 s_i = \sqrt{x_i^2 + x_{i+1}^2}$$

$$-100.0 \leq x_i \leq 100.0$$

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

Python

def fitnessFunc(self, chromosome):
	""" """
	fitness = 0
	normalizer = 1.0/float(len(chromosome)-1)
	for i in range(len(chromosome)-1):
		si = math.sqrt(chromosome[i]**2 + chromosome[i+1]**2)
		fitness += (normalizer * math.sqrt(si) * (math.sin(50*si**0.20) + 1))**2
	return fitness

Sources

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

Empirical review of standard benchmark functions using evolutionary global optimization
@article{DBLP:journals/corr/abs-1207-4318,
  author    = {Johannes M. Dieterich and
               Bernd Hartke},
  title     = {Empirical review of standard benchmark functions using evolutionary
               global optimization},
  journal   = {CoRR},
  volume    = {abs/1207.4318},
  year      = {2012},
  ee        = {http://arxiv.org/abs/1207.4318},
  bibsource = {DBLP, http://dblp.uni-trier.de}
}


Notes