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:
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.
Among the three genetic operators—selection, crossover, and mutation—each plays a distinct role in guiding the evolution of a population toward optimal or near-optimal solutions. For filling the population with copies of the best individual from the population, the required operator is selection, specifically elitist selection. Selection favors individuals with higher ___ ____ ________ _____ __________ ________ _______ ___ _______.
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Consider a dataset of five observations given in the following table, each of which has two features f1 and f2:
| x₁ | x₂ | x₃ | x₄ | x₅ | |
|---|---|---|---|---|---|
| f₁ | 2 | 3 | 4 | 3 | 5 |
| f₂ | 6 | 7 | 5 | 4 | 6 |
Assume the number of cluster and the real number
. Also, assume the initial cluster centers as
and
. Apply fuzzy c-mean algorithm to find the modified cluster center after one iteration.
(क) क्या निम्नलिखित फलन श्वार्ज़-प्रमेय की आवश्यकताओं को (1,1) पर संतुष्ट करता है? अपने उत्तर की पुष्टि कीजिए। (4)
(ख) निम्नलिखित के स्तब्ध बिन्दु निर्धारित करके उनका वर्गीकरण कीजिए : (6)
(i)
(ii)
Determine the fuzzy relation T as a composition between the fuzzy relations R and S given below by using max-min and max-product:
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:
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.
Verify whether the Genetic Algorithm (GA) improves the solution from one generation to the next generation, for the function given below:
Maximize:
Subject to:
Assume that chromosomes of length 6 are created at random and modified by Roulette-Wheel selection.
Implement AND function using McCulloch-Pitts neuron.
Find the length and order of the following schema:
i)
ii)
iii)
iv)