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Differential Equations Solutions 89

Differential Equations Solutions 89 - CHALLENGE 17.3(a...

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Chapter 17 Case Study: Monte-Carlo Minimization and Counting: One, Two, . . . , Too Many (coauthored by Isabel Beichl and Francis Sullivan) CHALLENGE 17.1. The programs myfmin.m and myfminL.m on the website solve this problem but do not make the graph. CHALLENGE 17.2. (Partial Solution) The program sim anneal.m on the website is one implementation of simulated annealing, and it can be run using problem1 and 2 .m . To finish the problem, experiment with the program. Be sure to measure reliability as well as cost, and run multiple experiments to account for the fact that the method is randomized. Also comment on the number of runs that converge to x = 1 . 7922, which is a local minimizer with a function value not much worse than the global minimizer.
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Unformatted text preview: CHALLENGE 17.3. (a) Experiments with MATLAB’s travel program show that it works well for up to 50 cities but, as is to be expected, slows down for larger sets. It’s interesting and important to note that the solution is always a tour that does not cross itself. We’ll return to this point shortly. (b) ±igures 17.1–17.3 show the results of simulated annealing for 100 random loca-tions with temperature T = 1 , . 1 , . 01 , where “score” is the length of the tour. The actual tours for T = 0 . 1 and T = 0 . 01 are shown in ±igures 17.4 and 17.5. Note that the result for 0.01 looks pretty good but not that much better than the output 99...
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