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final 2010

# final 2010 - Name Heuristic Methods for Optimization Final...

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Name: _____________________________ Heuristic Methods for Optimization Final 2010 (Non-theory section) Read and sign the pledge before beginning the exam: Academic integrity is expected of all students of Cornell University at all times, whether in the presence or absence of members of the faculty Understanding this, I declare that I shall not give, use, or receive unauthorized aid in this examination. Signature: _________________________________ Show your work so the grader can read and understand what you have done. Clearly state any assumptions you make and give any equations (if any) you are using. 1. (25 points) Selecting algorithms & parameters Below you are given several different one-dimensional functions defined in the domain. Assume that you want to minimize COST(S) and that S current is the current value of S in the search algorithm you are using to find a minimum value. S new is the new value you are considering in the next iteration. Assume each algorithm has NMAX iterations. Assume also that the initial value of S o is selected randomly from a uniform distribution over the allowable range, but is the same S o for all algorithms you are comparing. In all three algorithms listed below, the algorithm is not prevented from returning to points S for which it has evaluated the cost function COST(S) in a previous iteration. Random sampling (RS) Greedy Stochastic search (GS) Simulated Annealing (SA) : The SA parameter to be decided is T o (initial temperature), which you should pick to optimize algorithm performance. Assume that you have restricted T o to be between 30 and 5000. Assume α = 0.99 , and M=1 The neighborhood function for GS and SA is defined as follows : Pick a random number s from a uniform distribution over [-25, 25]. Let S new = max(1,S current + s) if s is negative or min(1000, S current + s) if s is positive. Part (a): Continuous problem with S a real number between 1 and 1000 ( The distance between jagged peaks is around 125 on average. )

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i. (9 pts) Assume you are using T o = 1000 for SA, how would you rank the three methods (from best to worst) for solving this minimization problem accurately with NMAX=100? Base your judgment on which you think would be the best methods on average. Explain the reasons for your ranking. The performance of the algorithms will be ranked as follows: 1) Simulated Annealing, 2) Greedy Search, and 3) Random Sampling. SA will accept uphill moves, so it can get out of the local minimums and find the global minimum the fastest. GS will get stuck in a local minimum depending on where it starts, but has a higher probability of finding the global minimum compared to RS, which jumps around the entire search space looking for the minimum.
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final 2010 - Name Heuristic Methods for Optimization Final...

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