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Now that we have reviewed the results of the template without data, we can go back into the Report Designer and make a copy of this template and insert a data provider into the template. The following illustration shows the process of Save As to make a copy of the template for your use.
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Randomization and restarts Randomization can be an invaluable ally in local search. It is typically used in two ways: to pick a random initial solution, for instance a random graph partition; and to choose a local move when several are available. When there are many local optima, randomization is a way of making sure that there is at least some probability of getting to the right one. The local search can then be repeated several times, with a different random seed on each invocation, and the best solution returned. If the probability of reaching a good local optimum on any given run is p, then within O(1/p) runs such a solution is likely to be found (recall Exercise 1.34). Figure 9.10 shows a small instance of graph partitioning, along with the search space of solutions. There are a total of 8 = 70 possible states, but since each of them has an identical 4 twin in which the left and right sides of the cut are ipped, in effect there are just 35 solutions. In the gure, these are organized into seven groups for readability. There are ve local optima, of which four are bad, with cost 2, and one is good, with cost 0. If local search is started at a random solution, and at each step a random neighbor of lower cost is selected, then the search is at most four times as likely to wind up in a bad solution than a good one. Thus only a small handful of repetitions is needed. Simulated annealing In the example of Figure 9.10, each run of local search has a reasonable chance of nding the global optimum. This isn t always true. As the problem size grows, the ratio of bad to good local optima often increases, sometimes to the point of being exponentially large. In such cases, simply repeating the local search a few times is ineffective. A different avenue of attack is to occasionally allow moves that actually increase the cost, in the hope that they will pull the search out of dead ends. This would be very useful at the bad local optima of Figure 9.10, for instance. The method of simulated annealing rede nes the local search by introducing the notion of a temperature T . let s be any starting solution 283
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mix, choose Save As from the file menu and see if your editing software can directly encode an MP3 file. As shown in Figure 9-17, Sound Forge allows MP3 files to be saved at 96 Kbps, a perfect format for direct upload to the MP3 player without having to use the player s import software tools. Don t forget to save the original song so you can revert it back the way it was once you have delivered your subliminal message to the subject and had all your evil wishes completely fulfilled. Now all you have to do is wait a few days to see if your subliminal message takes hold as your unsuspecting subject gets his or her groove on. If your message is perfectly mixed and the commands aren t too outlandish, you just never know what might happen. Of course, if you are commanding your buddy to buy you a new entertainment system and then run down the street wearing nothing but a tutu and a pair of flippers, then you might not get what you want! Doesn t hurt to try, though.
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(x + 2)(x 3) = 0 The roots are found by solving the two first-degree equations x+2=0 and x 3=0 giving us x = 2 or x = 3. We can substitute these two values for x into either of the morphed original equations to obtain corresponding values for y. The simpler of the two is y = 2x + 1 For x = 2, we have y = 2 ( 2) + 1 = 4 + 1 = 3
i (t) 1 (t) i (t) (t) (t) (t) i 1 i
I 5.5 EXTRAPOLATION OSCILLATIONS AND
Final Exam
5. Click to the right of the Style option in the menu, and you will see a button that opens
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Ask the Expert
You can use the return statement to return the sum of the two numbers this way:
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