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d s = v ·
1
(14.21)
accel : increment in the control signal in a sampling time.
The summation is extended at all samples, which are taken every 0.1 s, and divided
by the square of T , so longer simulations have smaller costs. The first term in the
sum penalizes distances different to the safety distance, but the cost is double when
the actual distance is less than the safety distance. The second term penalizes large
variations in the control signal. Obviously, the accelerations and decelerations of the
car ahead are the same in all simulations, so that the comparison is meaningful.
Once the cost of all chromosomes has been obtained, they are sorted in descending
order, and their fitness values are their positions in the list.
14.3.3 Elitism
A new empty population is created, and the better classified individuals are directly
passed to it. These better individuals are called the elite . The number of elements in
the elite is very small compared with the size of the population, being two in this
work. This step is not mandatory but it is recommended, because in this way the cost
of the best individual in each generation cannot increase.
14.3.4 Selection
There are several methods of selection, themost common being the roulette wheel and
the tournament . In this work, the former is used. In the roulette wheel, a probability
of selection is assigned to each individual, according to its fitness. None of the
individuals should have too big a probability compared with the others, because this
would increase the risk of premature convergence to a local optimum. In the same
way, none of them should have too small a probability, because in this case some
regions in the search space might remain unexplored. Here, given the fitness f i of
the individual i , its probability of selection is:
f i
f i
p i
=
(14.22)
where the summation is extended to all the individuals in the population. Then,
two individuals in the present population are randomly selected according to their
probabilities of selection.
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