Practice question on GA

Duration: 5 min

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The video presents a practice question from the UGC NET Paper-2019 on genetic algorithms, focusing on calculating fitness strength using the formula Sf(x) = f(x)/Σf(x), where f(x) = x². The problem involves determining the fitness strength of the binary chromosome (11000), which is converted to decimal as 24, yielding f(24) = 576. The total sum of fitness values for the population P={(01101), (11000), (01000), (10011)} is computed as 1170.2, resulting in Sf(24) ≈ 0.492 or 49.2%, matching option (d). The instructor demonstrates the calculation step-by-step, writing the formula and intermediate values on a board. Later, the video transitions to explaining selection operators in genetic algorithms, introducing Roulette Wheel Selection with the formula pi = fi / Σfi, where individual fitness (fi) is divided by total population fitness to determine selection probability. A table and pie chart illustrate this with example values: individuals with fitness 15, 20, and 30 have selection probabilities of approximately 24%, 31%, and 45% respectively. The lesson also introduces Elitism Selection as a method to preserve high-performing individuals across generations, emphasizing the role of selection in passing genes to offspring.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video presents a UGC NET Paper-2019 question on genetic algorithms, asking to compute the fitness strength of a binary chromosome (11000) using the formula Sf(x) = f(x)/Σf(x), where f(x) = x². The instructor converts the binary chromosome to decimal (24), calculates f(x) as 576, and computes the sum of all fitness values in the population (Σf(x) = 1170). The normalized fitness strength is then calculated as 576/1170 ≈ 49.2, which is identified as the correct answer (d). The solution includes a step-by-step table showing binary-to-decimal conversion, f(x) = x² computation for each chromosome, and summation of fitness values. The instructor writes the formula and steps on screen, emphasizing the calculation process and highlighting option (d) as correct.

  2. 2:00 – 5:00 02:00-05:00

    The video segment explains the calculation of fitness strength in genetic algorithms using a UGC NET practice question. It begins by presenting chromosome (11000) and demonstrates converting binary values to decimal, applying f(x)=x², summing all fitness values (Σf(x) = 1170), and computing normalized fitness Sf(x) = f(x)/Σf(x). For (11000), this yields 576/1170 ≈ 49.2, identified as the correct answer 'd'. The lesson then transitions to selection operators, introducing Roulette Wheel Selection and Elitism Selection. It defines the selection phase as choosing fittest individuals for reproduction, with Roulette Wheel using fitness proportionality—where probability pi = fi / Σfi determines selection likelihood. A table and pie chart illustrate this, showing how higher fitness values increase the chance of being selected in reproduction.

  3. 5:00 – 5:27 05:00-05:27

    In this segment, the instructor explains the roulette wheel selection method used in genetic algorithms, where individuals are selected based on their fitness values. A table displays individual fitness values and their corresponding probabilities, calculated using the formula pi = fi / Σfi. The probability of selecting an individual is proportional to its fitness, with higher values increasing selection likelihood. A pie chart visually represents the probability distribution across individuals, showing how each contributes to the overall selection chance. The example includes numerical values and percentages, illustrating that an individual with a fitness of 15 has a 100% selection probability when normalized against the total fitness sum. This method ensures that fitter individuals are more likely to be chosen for reproduction in the algorithm.

This lesson segment addresses a UGC NET 2019 practice question on genetic algorithms, focusing on fitness strength calculation and selection operators. The core concept is the computation of normalized fitness using Sf(x) = f(x)/Σf(x), where f(x) = x², applied to a binary chromosome (11000). The instructor demonstrates converting the binary value 11000 to decimal (24), computing f(24) = 576, and summing the fitness values of all chromosomes in the population to obtain Σf(x) = 1170.2, resulting in Sf(24) ≈ 49.2%, which matches option (d). The lesson then transitions to selection mechanisms, introducing Roulette Wheel Selection with the formula pi = fi / Σfi, where individual fitness (fi) is divided by total population fitness to determine selection probability. A table and pie chart illustrate this with example values: individuals with fitness 15, 20, and 30 have selection probabilities of approximately 24%, 31%, and 45% respectively. Elitism Selection is also introduced as a method to preserve high-performing individuals across generations, emphasizing the role of selection in passing genes to offspring. The teaching progression moves from concrete calculation (fitness strength) to abstract concepts (selection operators), enabling students to understand both the numerical computation and its biological analogy in genetic algorithms.