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Unformatted text preview: Practice “homework” for Differential Evolution for Theory Students
1. Differential Evolution
You are trying to minimize a three dimensional function f(x1,x2,x3) with Differential
Evolution with a population of size 20. Let
The parent vector is
(3,5,7). Assume you have picked xR1 =(1,2,3)), xR2 =(5,1,2),
and xR3= (1,2,4). Let CR= 0.4, F= 0.5 and NP=20.
a) The random numbers you have generated are randb(1)=.5, randb(2)=.3, randb(3)= .1
and rnbr(i) = 3. Give the values of the mutant, trial and child vectors.
The parent vector and its fitness are:
X1,G = (3,5,7) Mutated vector: Probability of accepting the mutation for each element is CR = 0.4
Randb(1) = 0.5 > 0.4 so element 1 is not perturbed
Randb(2) = 0.3 <0.4 so element 2 is perturbed
Randb(3) = 0.1 < 0.4 so element 3 is perturbed
So the trial vector U1,G+1 is then And the fitness is Tournament selection of the parent vector and the trial vector shows that F x1 > Fu1,
therefore U1 becomes the child for the next generation. (NOTE THE CHANGE IN THE
SOLUTION HERE) b) (Assume what is given at the top, but not any assumptions stated in part a).) Assume
that the randb(j) is uniformly distributed on [0,1] and rnbr(i)=3. What is the
probability that the trial vector has the same two first element values as the parent,
(i.e. in this example the trial vector would be (3,5,x)), where x is any number)?
The probability that any element will be perturbed in the vector is CR = 0.4
Therefore the probability that any element will NOT be perturbed in the vector is 1 CR = 0.6
The mutated vector calculated given the information above is: Therefore the probability that the first element wi ll be the same is 1
So the probability that the trial vector has the same two firs t elements is the
probability that the first two elements are not perturbed, 1*0.6 = 0.6.
Note that the 3rd element in the vector will always be perturbed, since rnbr(i) = 3.
Try to solve this by yourselves, but you do not need to hand in an answer and the
problem will not be graded. The answer will be posted before the exam. ...
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This note was uploaded on 10/02/2011 for the course ORIE 5430 taught by Professor Shoemaker during the Fall '11 term at Cornell.
 Fall '11
 Shoemaker

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