Verify whether the Genetic Algorithm (GA) improves the solution from one generation to the next generation, for the function given below:
Maximize:
f(x) =
Subject to:
1≤ x ≤16
Assume that chromosomes of length 6 are created at random and modified by Roulette-Wheel selection.
In the given scenario, the Genetic Algorithm (GA) aims to maximize the function \( f(x) = \sqrt{x} \) subject to the constraint \( 1 \leq x \leq 16 \). The GA evolves a population of chromosomes, each representing _________ _______ _____ ____ ___ _______ ________ _________ __________ _____.
_________ __________ ___ __________ _____ ____ ____ _______ ___ ___.
___ ________ ________ ____ ____ _________ _____ _____ ________ ____ _______.
___ ____ ______ _______ __________.
_____ __________ _____ __________ ________ _____.
_____ ___ _______ ____ ______ ___ ___.
__________ __________ _________ _____ _______ __________.
_____ _______ ______ _____ _____ _____ ___.
____ __________ _________ ___ _______ ___ ______ ________ _______.
________ ______ ___ ________ _______ ____ ________ _____.
_________ ___ _________ ______ ________ ____ ________ _________.
_________ ________ __________ ________ ______ __________ ____ ______ _______ ______ _________ ___.
___ _________ _____ _________ _________ ______ _____ _______ ____ ____ __________ ___.
____ ____ _______ ____ ______ __________.
______ ________ __________ ________ ________ ________ _____ __________ ___ _____.
________ ______ ________ __________ ______ ______ _______.
__________ ___ ___ _____ _______ _______ ____.
_______ __________ _____ ___ _____ _____ ___ _________.
____ ________ _______ _________ ________ _______ ____ ________ ___ _________ ________ ___.
______ _______ _________ ______ ________ _________ ___ ________ _______ _________.
__________ _________ ____ _________ ___ _______ _________ ________ ______ __________.
____ ________ _______ ______ _________ _______ __________ ________ _____ ___ ________ ________.
___ ________.
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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.
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 the ADALINE filter with three neurons in the input layer having weights 1,3 and − 2and the input sequence ......., ,0,0,0 − 0,0,0,5,4 ,.....}. Find the filter output.
Consider the following table for the connections between input neurons and the hidden layer neurons:
The connection weights from the hidden layer neurons to the output neurons are
− ,6.0 − 3.0 and − ,6.0 for the first, second and third neurons, respectively.
Corresponding threshold value for the output layer is 0.5 and for the hidden layer is 1.8, 0.005 and 0.2 for the first, second and third neurons, respectively.
i) Draw the diagram of the network.
ii) Write the output at each node.
c) Using diagram, show the difference between feed-forward neural network and
recurrent neural network.
Determine the α − cut of the fuzzy set (A) are given below, at 0.7 and 0.2.
Also, compare the α − cut of the two outcomes, and give comments for status of α − value variation.
Verify whether the Genetic Algorithm (GA) improves the solution from one generation to the next generation, for the function given below:
Maximize:
f(x) =
Subject to:
1≤ x ≤16
Assume that chromosomes of length 6 are created at random and modified by Roulette-Wheel selection.
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.