Out of three genetic operators viz. selection, cross-over and mutation, list and justify which operator or combination there of will be required for the following: (3)
i) To fill the population with copies of the best individual from the population.
ii) For the convergence of an algorithm to good but sub-optimal solution.
In soft computing and evolutionary algorithms, such as genetic algorithms, the choice of genetic operators—selection, crossover, and mutation—plays a crucial role in shaping the evolution of the population and influencing the convergence of the algorithm to desirable solutions.
i) To fill the population with copies of the best individual from the population:
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State whether the following statements are True or False. Give short proof or a counter example in support of your answer.
a) The length of chromosomes to determine the maximum value of the set:
S ={X 0 ≤x ≤ 4096}is 12.
b) In the Hopfield network, the neurons belonging to the same layer receive input from
the neurons of the previous layer and send their value only to the neurons of the next
layer.
c) In a single layer neural network, if x ,0
ω > then the output is −1.
d) The fuzzy relation (R) given below, is an equivalence relation.
e) The Self Organizing Map (SOM) is a supervised learning technique.
Consider the fuzzy sets A and B defined on the interval ,0[ ].5 Their membership functions are:
and
Determine the membership function and graph them for each of the following:
i) Ac ,Bc
ii) A ∪B
iii) A ∩B
iv) (A ∪B)c
v) (A∩B)c
Implement AND function using McCulloch-Pitts neuron.
Approximate the function )x(f =1+ cosπx for −1≤ x ≤ ,1 by solving 1− 2 −1network, using Back propagation algorithm. The weighted structure and initial input are as follows: (10) Weighted structures are:
The initial input is 1.
Draw the architecture of the model. Perform one iteration.
Find the length and order of the following schema:
i) S1 =1** 0 0 *1* *
ii) S2 = *0 0 *1 * *
iii) S * * * 0 * * * *
iv) S4 = *1 * 0 1 *
Consider a dataset of five observations given in the following table, each of which has two features f and f 2:
Assume the number of cluster c = 3 and the real number m = 2 . Also, assume the initial cluster centers as V )1,1( 1 = and V )2,2( 2 = . Apply fuzzy c-mean algorithm to find the modified cluster center after one iteration.
Consider the single layer perception given below:
Obtain the output for each of the following input pattern:
| Patterns | p1 | p2 | p3 | p4 |
| x1 | 1 | 0 | 1 | 1 |
| x2 | 0 | 1 | 0 | 1 |
| x3 | 0 | 1 | 1 | 1 |