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MITESD_77S10_assn04 (1)

# MITESD_77S10_assn04 (1) - MASSACHUSETTS INSTITUTE OF...

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MASSACHUSETTS INSTITUTE OF TECHNOLOGY 16.888/ESD.77 MSDO 16.888/ESD.77J Multidisciplinary System Design Optimization (MSDO) Spring 2010 Assignment 4 Instructors: Prof. Olivier de Weck Prof. Karen Willcox Dr. Anas Alfaris Dr. Douglas Allaire TAs: Andrew March Kaushik Sinha Issued: Lecture 13 Due: Lecture 17 You are expected to solve Part (a) individually and Part (b) in your project team. Each person must submit their own Part (a) but you should submit Part (b) as a group. Please indicate the name(s) of your teammate(s). Topics : genetic algorithms, mixed-integer optimization, scaling Part (a) Part A1 The following questions refer to a Genetic Algorithm as defined in Lecture 10: a) Which of the following will most increase population diversity? a. Increasing mutation rate b. Changing the crossover location c. Increasing the amount of elitism d. All of the above e. None of the above b) In a binary GA, how many bits are needed to represent numbers between 1 and 10 with a resolution of 0.0001? a. 3 b. 4 c. 16 d. 17 e. 18 c) In a binary GA, what is the minimum number of bits required to represent a discrete design variable that can have values, 1, 2, 3 or 4? Page 1 of 6

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MASSACHUSETTS INSTITUTE OF TECHNOLOGY 16.888/ESD.77 MSDO a. 1 b. 2 c. 3 d. 4 d) For a discrete variable that can have the values, 1, 2, 3, or 4, in the binary representation of this variable with the minimum number of bits, what would the representation of 3 be? a. 1 b. 01 c. 10 d. 111 e. 010 f. 0110 e) Given the parents 01001101 and 01100100, which of the following are possible single point crossovers? A: 11001101 B: 01000100 C: 01001100 D: 01111101 a. A & B b. B & C c. A & D d. A & C e. A, B, C & D f) In a population, the fitness function values of each member are: F 1 =100, F 2 =800, F 3 =1, F 4 =90, F 5 =9. Using roulette wheel selection, what is the approximate probability the member with F 1 will be chosen as a parent? a. 0.01 b. 0.10 c. 0.80 d. 0.90 e. 0.99 g) In a population, the fitness function values of each member are: F 1 =100, F 2 =800, F 3 =1, F 4 =90, F 5 =9. Now, using the fraction of the population a member dominates as the selection criterion, what is the approximate probability the member with F 1 will be chosen as a parent? a. 1 b. 0.90 c. 0.80 d. 0.50 e. 0.10 Page 2 of 6
MASSACHUSETTS INSTITUTE OF TECHNOLOGY 16.888/ESD.77 MSDO h) In a binary encoded GA with two design variables, one with 4 bits, and one with 16 bits, what is the total number of possible population members?

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MITESD_77S10_assn04 (1) - MASSACHUSETTS INSTITUTE OF...

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