Homework3

# Homework3 - CEE 5290/CS 5722/ORIE 5340 Heuristic Methods...

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1 CEE 5290/CS 5722/ORIE 5340: Heuristic Methods for Optimization Homework 3: Binary Genetic Algorithm Assigned: Wednesday, September 14, 2010 Due: Friday, September 23, 2010 TA Office Hours: Thu, Sep 15 th (3:00-4:30), Tue, Sep 20 th (10:00-11:00am), Thu, Sep 22 nd (3:00-4:30) in Hollister 203 Prof. Shoemaker office hours: 2:30-3:30 on Fri 9/15, M 9/19, and Tu 9/21 in Hollister 210 1. If you wish to improve any of the basic approaches specified by the GA then feel free to do so – creativity is a small consideration in your final grade. In these cases, make sure you first answer the specific homework questions and then briefly describe, provide code and compare your new approach to the approach requested in the question. Provide this material in an appendix. 2. Marks may be deducted for a lack of neatness. The modified pseudocode from the text is as follows: 1 Procedure ( Genetic Algorithm ) 2 M = population size % number of possible solutions at any instance 3 N g = number of generations % number of iterations 4 N o = number of offspring % to be generated by crossover 5 P μ = mutation probability % Also called mutation rate (M r ) 6 P ß Ξ (M) % Construct initial population, P Ξ is the population constructor 7 For j=1:M 8 Evaluate f(P[j]) % Evaluate fitness of all individuals % This is done before the GA algorithm is implemented 9 Endfor 10 Start Genetic Algorithm 11 For i=1:N g 12 For j=1: N o 13 (x,y) ß ϕ (P) %Select two parents x and y from current population 14 Offspring[j] ß χ (x,y) % Generate offspring by crossover of parents x and y 15 EndFor 16 For i=1: N 17 Mutated[j] ß μ(y) % With probability P μ apply mutation all the offspring 18 EndFor 19 Evaluate fitness for offspring after crossover and mutation %CORRECTED 20 P ß select (P, offspring) %Select best M solutions from parents and offspring 21 End ( Genetic algorithm ) % CORRECTED 22 Return highest scoring configuration in P 23 End 1. This question will cover the optimization of a simple cost function using binary representation with Genetic Algorithms. Note that by convention, GAs are coded to maximize the fitness function.

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2 Consider the 2-D cost function used in Homework 2: F(s1,s2) = 10^9-(625-(s1-25)^2) *(1600-(s2-10)^2)*sin((s1)*pi/10)*sin((s2)*pi/10) For question 1 here we will maximize this function. The global maximum is F(125,115) = 1088359375. Since each decision variable can take on integer values from 0 to 127, the input variables s1 and s2 can each be represented by 7-bit binary string. Hence the domain of this cost function can be represented by a 14-bit binary string as, s = [sb 1 , sb 2 , . .. sb 14 ], where the first seven elements form the binary representation of s1 and the last seven bits represent s2. i.e. = = 7
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Homework3 - CEE 5290/CS 5722/ORIE 5340 Heuristic Methods...

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