hw7 - HW #7 Solutions Fall 2010 Total points possible: 20...

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HW #7 Solutions Fall 2010 Total points possible: 20 1. Relative performances of SA, DDS and GA on the “bump” function. Recall the bump function from HW 5 with n = 20: (a) (4 points) Implement the SA algorithm to maximize the 20-variable bump function. In this exercise, define the neighborhood for SA as a perturbation of a randomly selected element of the current solution with a Gaussian number with mean 0 and variance 5. Make sure this perturbation satisfies the bound constraints of the bump function, i.e. the returned element is in the interval [0,10]. Hence if your randomly generated point is outside [0,10] then generate another point randomly until you get a point inside [0,10]. Other neighborhood definitions will be accepted, but they should be described. Run 20 trials of 10,000 cost function evaluations. Save all the best solutions at the end of each trial. Plot the average best bump function value over the 20 trials vs. function evaluations, and save the data for this plot as you will add to it in subsequent parts. See plots in part c. No SA code is required. (b) (4 points) Implement the DDS algorithm to maximize 20-variable bump function. You may write your own DDS code, or use the code provided on the course website The pseudocode for DDS is given at the end of this assignment . Run 20 trials of 10,000 cost function evaluations. Save all the best solutions at the end of each trial. i. Add to the figure in part (a) a plot of the average best bump function value vs function evaluations for DDS. See plot in part c. No DDS code is needed (unless they coded their own DDS function). ii. (Not graded) Suggest some ways you might modify DDS to make it better. Assume the parameter = 0.2 is fixed. Explain why your modification might be good on certain set (type) of problems. You do not need to implement this modification. There are many reasonable answers.
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HW #7 Solutions Fall 2010 (c) ( 3 points – one for each algorithm) Add to the figure in part (b) a plot of the average best bump function value vs. function evaluations for GA. From just looking at the plot, does it appear as if one algorithm dominates another? Students should be taking their results from GA from runs in HW 5. Students’ plots should look something like this: Generally, from the plot should conclude that DDS performs best, SA is slow to start (because of accepting uphill moves) but eventually converges to a better solution than GA.
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This note was uploaded on 10/02/2011 for the course ORIE 5430 taught by Professor Shoemaker during the Fall '11 term at Cornell University (Engineering School).

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hw7 - HW #7 Solutions Fall 2010 Total points possible: 20...

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