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When picking a neighbor should the algorithm's temperature be considered? So for example, if the temperature is high when picking a neighbor should be permutation be made? Or does the temperature only affect the acceptance probability?

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Only the acceptance probability in the simulated annealing algorithm is influenced by the temperature. The higher the temperature, the more "bad" moves are accepted to escape from local optima. If you select neighbors(preselected) with low energy values, you'll basically contradict the idea of Simulated Annealing and turn it into a greedy search.

And for better understanding of NEIGHBORHOOD SIZE IN THE SIMULATED ANNEALING ALGORITHM, refer the following link:

https://pdfs.semanticscholar.org/8f55/6af294f39f03f585f0f269661dc50f472ce9.pdf

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