Design and Voltage Supply of High-Speed Induction - Aaltodoc

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Whole non-uniform boundary mutation: the same as non-uniform boundary mutation but the
operator affects all the design variables of x.
Whole arithmetical crossover: two parent vectors x p1 and x p2 are selected. Two new design vectors
are then of the form
x −
p2(
1)
( 1 a)
p1(
2)
1(
2)
= ax + x
(C7)
where a ∈ ]0 1] is an operator parameter. Because of the convexity of the search space, the new
design vectors automatically fulfill the constraints.
Simple arithmetical crossover: two parent vectors x p1 and x p2 are selected. Two new design vectors
are then of the form
p1(
2)
p1(
2)
p1(
2)
p2(
1)
p1(
2)
[ x ,..., x , ( ax + ( 1 − a)
x ) , ..., ax + ( 1 − a)
1(
2)
= 1
c
c+
1
c+
1
p2(
1)
( x )]
x (C8)
where a ∈ ]0 1] is an operator parameter. In this case the validity of the new vectors in respect to
the constraints must be checked. a is given different values and the validity is checked. If no
eligible solution is found within a reasonable number of trials, a is given the value of unity and
p1(
2)
x 1(
2)
= x
(C9)
The selection of the parent designs for the crossover operators is based on ranking the individual
designs in the population. The best design is ranked first and the worst is ranked last. Each design,
i:th in rank, is assigned a probability p(i)
( ) 1 i −
1−
Q
p ( i)
= Q , i=1,...,S (C10)
where Q ∈ ]0 1[ is a probability parameter and S is the number of designs in the population. The
greater the probability, the better the chances of being selected. A design can be chosen to be a
parent in more than one crossover operation. To keep the size of the population constant, old
designs must be removed in order to make room for the offspring of the crossover operations. The
probability of removal is calculated in the same manner as the probability of parenthood. The only
exception is the best design, which cannot be removed. This exception is called an elitist rule that
assures smooth evolvement of the population. Optimization algorithm also checks that mutated
designs are not removed.
A mutation can happen to every design regardless of its rank. Then the probability for mutation is
the same for every design. The only exception is, again, the best design, which is kept intact. A
mutation changes an old design in such a way that the size of the population does not change. v
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