The annealing acceptance criterion noted above is sensitive to the temperature that is assumed at each iteration of the solution generation process. Early in the search, when the temperature is relatively high, the result of the acceptance criterion function is one of the larger numbers on the 0-1 scale. Thus the random number drawn between 0 and 1 will likely be lower than the result of the acceptance criterion, and subsequently more inferior adjustments to a solution will be allowed. As the temperature cools, however, the result of the acceptance criterion function will move to the lower end of the 0-1 scale, and fewer inferior adjustments will be allowed to a solution as it is being developed.
As one may gather, the choice of the initial temperature and the choice of the cooling rate will influence how many inferior adjustments to solutions will occur. If the initial temperature is too low, for example, very few inferior adjustments will be allowed, since the result of the acceptance criteria function will be on the lower end of the 0-1 scale. If the initial temperature is high, and the cooling rate is also high, resulting in a slow decline in temperature, a relatively large number of inferior adjustments will be allowed to the solution. Some calibration may be needed to assure that the choice of initial temperature produces probabilities near 1.0, and at lower temperatures, produces probabilities near 0.0. The high acceptance rate of the initial temperature makes the starting solution somewhat less important than with some other heuristics.
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