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Deriving integer and continuous values from Temperature (Simulated Annealing)

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I would like to use the technique related to Simulated Annealing for my problem. Let's say I have an initial temperature T0 and I have 50 iterations.
At each iteration I would like to calcualte three values depending on the current temperature:
  • An integer value: The value should start at 10 and increase to 100 in a way between linear and logarithmic.
  • A continuous value: The value should start at 1 and decrease to 0 in a way between linear and exponential.
At each iteration the temperature can be either increased or decreased.
Which formulas are reasonable to use (or exists) for the increasing/decreasing of the temperature and for producing both values?

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