The Leverage Space Model 321
in the second generation ends up with exactly the same genetic material as
the first individual in the first generation, or 01010.
Second GenerationIndividual # X BinaryX1 11 01011
2 14 01110
3 10 01010Now, through random mutation, the third bit of the first individual is
flipped, and the resulting values are used to evaluate the objective function:
Second GenerationIndividual # X BinaryXY Fitness Score
1 15 01111 1500 .5102
2 14 01110 1499 .4898
3 10 01010 1475 0
Notice how the averageYscore has gone up, or evolved, after two genera-
tions.
Important Notes
It is often advantageous to carry the strongest individual’s code to the next
generation in its entirety. By so doing, good solution sets are certain to be
maintained, and this has the effect of expediting the algorithm. Then, you
can work to aggressively maintain genetic diversity by increasing the values
used for the probability of crossover and the probability of mutation. I have
found that you can work with a probability of crossover of 2, a probability
of mutation of .05, and converge to solutions quicker, provided you retain
the code of the most fit individual from one generation to the next, which
keeps the algorithm from deteriorating to a random search.
As population size approaches infinity, that is, as you use a larger and
larger value for the population size, the answer converged upon is exact.
Likewise, with the unimproved generations parameter, as it approaches