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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 134) Figure 910 shows a small instance of graph partitioning, along with the search space of solutions.

They also noted that the presence of asymptomatic bruits in men (but not in women) did carry a slightly increased risk of stroke but, more importantly, that the subsequent stroke often did not coincide in its angioanatomic locus and laterality with the cervical bruit Similar ndings have been reported by Ford and coworkers and by Chambers and Norris On the other hand, Wiebers and colleagues found that patients with asymptomatic carotid bruits who were followed for 5 years were approximately three times more likely to have ischemic strokes than an age- and sex-matched population sample without carotid bruits.

More and more, hospitals are incorporating nontraditional methods and services into their usual caregiving responsibilities. They are promoting preventive care and wellness services and are taking advantage of dynamic partnerships with other institutions, sometimes even in other countries, to provide better care for all patients.

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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 910, each run of local search has a reasonable chance of nding the global optimum This isn t always true.

In an attempt to clarify the role of surgery for asymptomatic carotid stenosis, the Asymptomatic Carotid Atherosclerotic Study (ACAS), as reported by their Executive Committee, has suggested that the frequency of strokes can be reduced from 11 to 5 percent over 5 years by removing the plaque in asymptomatic patients in whom there is a stenosis greater than 60 percent (diameter) These ndings have been tempered by a reanalysis of the ACAS data, pointing out that almost half of the strokes in these patients were lacunar or cardioembolic in origin (Inzitari et al) Data from a recent European trial, encompassing 3120 patients, obtained similar results [MRC Asymptomatic Carotid Surgery Trial (ACST) Collaborative Group] The latter study has indicated that asymptomatic carotid stenosis of over 70 percent carries only a 2 percent annual risk of stroke over a 5-year period and that the risk is reduced to 1 percent with endarterectomy.

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 910, 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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Answer 3-1

It was concluded that endarterectomy may be justi ed for asymptomatic carotid stenosis of this degree, but the authors emphasized that an audited surgical risk below 3 percent is required to obtain favorable results From the results of several trials, it can be concluded that endarterectomy does not reduce strokes in patients who have asymptomatic carotid stenosis with luminal narrowing that is less than 70 percent of normal diameter All these comments probably apply to patients who are about to undergo major surgery such as cardiac bypass.

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