Ultimate Algorithmic Trading System

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GENETIC OPTIMIZATION, WALK FORWARD
With this in mind you have a one-in-six chance of rolling a six or a probability of
16.6666667 percent.
P = Possible favorable outcomes / Potential outcomes
P = 1/6, or 16.6666667%
Keep in mind probabilities are the cornerstone of GA as well as trading algorithms.
Okay, now on to our selection process. Remember, we need to nudge the
computer into making the right decision. The computer will, in effect, roll the dice
to choose which chromosome will be carried into the next step for reproduction. If
this is a random event, then how do we nudge the computer’s decision? Think of a
dartboard that has six slices and the slices are the same size. Now assume you train a
monkey to throw darts while blindfolded at the dartboard. Also, it is important to
assume he always hits the dartboard. The monkey has a one-in-six chance of hitting
a particular slice. What if the slices were not the same size? Then he would have a
higher probability of hitting the larger slices. This is the concept that will be used
to nudge the computer’s selection; the more fit chromosomes will get the bigger
slices. Here again, we must let the computer decide the sizes of the slices but we
can feed it a formula that will give priority to the more fit chromosomes. The first
step is to calculate the fitness of each chromosome in terms of the size of the slice.
This is a very simple formula as well:
Chromosome[slice size] =1 ∕(1 + ABS(Chromosome[fitness] –40))
Notice how we use the ABS (absolute value) function in our formula. This function
simply removes a negative sign from the difference between a chromosome’s fitness
and our objective of 40; we don’t want to have a negative-sized slice. We subtract
40 from each chromosome’s fitness because we need to put the fitness in terms
of our objective; the closer we are the smaller the fitness value. Since we want to
allocate a bigger slice to chromosomes that are closer to our solution we divide
one by our fitness score. In doing so, we are making the size of each slice inversely
proportional to the fitness score; a lower fitness value (or closer value to 40) will
increase size. The number 1 is also added in the denominator to prevent division by
zero; computers hate division by zero. Utilizing the above formula we come up with:
Fitness 1 in terms of slice size:
Chromosome (0) = 1/(1+ 71) = 0.01389
Chromosome (1) = 1/(1+ 54) = 0.01812
Chromosome (2) = 1/(1+ 24) = 0.04000
Chromosome (3) = 1/(1+ 50) = 0.01961
Chromosome (4) = 1/(1+124) = 0.00800
Chromosome (5) = 1/(1+ 53) = 0.01852
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