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U. Glaeser

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FIGURE 39.74 Procedure for simulated annealing algorithm.<br />

FIGURE 39.75 The Metropolis procedure.<br />

much flexibility is allowed in neighborhood generation at higher “temperature,” i.e., many “uphill” moves<br />

are permitted at higher temperatures. The temperature parameter is lowered gradually as the algorithm<br />

proceeds. As the temperature is lowered, fewer and fewer uphill moves are permitted. In fact, at absolute<br />

zero, the SA algorithm turns greedy, allowing only downhill moves.<br />

The SA algorithm is shown in Fig. 39.74 . The core of the algorithm is the Metropolis procedure, which<br />

simulates the annealing process at a given temperature T (Fig. 39.75) [4]. The Metropolis procedure<br />

receives as input the current temperature T, and the current solution CurS, which it improves through<br />

local search. Finally, Metropolis must also be provided with the value M, which is the amount of time<br />

for which annealing must be applied at temperature T. The procedure Simulated_annealing simply invokes<br />

Metropolis at decreasing temperatures. Temperature is initialized to a value T 0 at the beginning of the<br />

procedure and is reduced in a controlled manner (typically in a geometric progression); the parameter<br />

© 2002 by CRC Press LLC

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