Give the description of the Simulated Annealing function optimization method for minimizing continuous functions: Algorithmic and Computational Mathematics Course Work, UOL, UK

Give the description of the Simulated Annealing function optimization method for minimizing continuous functions. Include its concept, mathematical formulation, and algorithmic implementation.
In what aspect(s) the method can be varied? How do variations influence its performance? What are the advantages and deficiencies of the variants of the method?
Minimize the function for ???? = 2 using your implementation of the method. Analyze the results for various values of the parameters of the method.
Quantitatively estimate the performance of the method. Explain the differences in performance depending on the parameters of the method.
Plot the optimization trajectory, and analyze its dependence on the parameter of the method.

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