Читать книгу Power Magnetic Devices - Scott D. Sudhoff - Страница 42

1 It is desired to minimize the functionWhat is a possible fitness function (the answer is not unique) if using a canonical GA?

2 The fitness values of the members of a population are 23, 96, 42, 12, 8, 7, and 47. What is the expected number of times the individual with a fitness of 42 will appear in the mating pool? Use roulette wheel selection.

3 Consider two parents, with x1 = 0.2 and x2 = 0.5. Consider simulated binary crossover with ηc = 1. Form 105 children, and plot a histogram of the children arranged in 20 equally spaced bins on the interval 0 to 1. Implement gene repair using ring mapping.

4 Repeat Problem 3 with x2 = 0.25.

5 Suppose a design problem was coded with five genes on a single chromosome, and single‐point crossover was used. During the crossover between two parents, how many different children (in terms of genotype) could be produced?

6 A logarithmically mapped gene has a range from 10−3 to 106. If the value for this gene for a particular individual is 37.6, what is its’ normalized value? What would its’ normalized value be if it were linearly mapped.

7 During an evolution, the minimum, maximum, and average fitness of a population is 1.2, 270, and 40, respectively. If the most fit individual is to be three times more likely than the average fit individual to be selected, and the least fit individual is 1/3 as likely as the average fit individual to be selected, what is the scaled fitness of an individual whose raw fitness is 58.

8 Below are the objective function values for an inductor design. It is desired to minimize both objectives.Individual123456Mass (kg)531424Loss (kW)236541Use Kung’s algorithm to identify the nondominated individuals.

9 Consider Problem 8. Compute the crowding distance of all nondominated individuals.