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How will the function change

Assignment Help Python Programming
Reference no: EM133296136

For the function f(xi) = ∑i=1n -xi sin √xi defined in the region xi < 1000, i = 1...n:

Part 1

Question 1. Give the description of Simulated Annealing function optimisation method for minimising continuous functions. Include its concept, mathematical formulation, and algorithmic implementation.

Question 2. 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?

Question 3. Minimise the function for n = 2 using your implementation of the method. Analyse the results for various values of the parameters of the method.

Question 4. Quantitatively estimate the performance of the method. Explain the differences in performance depending on the parameters of the method.

Question 5. Plot the optimisation trajectory, analyse its dependence on the parameter of the method.

Part 2

For the function defined in Coursework 1 and n = 2 :

Question 1. Construct a new function as the intersection of f(xi) with the plane x1 = x2. Provide mathematical expression for this function and plot it. Analyse the function for its roots, extreme points and its behaviour at the limits

Question 2. Find the root(s) of the function using a numerical method of your choice. Compare to the analytical result.

Question 3. Integrate the function using a numerical method of your choice and analytically. Compare the results.

Question 4. How will the function change if constructed as the intersection with the plain containing a different line on the x1 - x2 plane?

Reference no: EM133296136

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Reviews

len3296136

12/20/2022 10:46:02 PM

Hello, I've been struggling with this assignment and I need help with it. I would really appreciate the help. With regards to the questions, If needed, the problems should be solved with the help of a programming code (python/c++). Providing code is a plus but should be commented explaining the above points. In any case, a clear description of the algorithm of the code should be provided. The same applies to the output of the code. Please find attached the lecture notes and recommended reading material. The "assignment brief" as stated in the assignment instructions is listed below; For each task, the following should be provided/demonstrated: - the mathematical concept used for solving the problem, with definitions and formulas; - the algorithm (with the results at intermediate steps if necessary); - the numerical (and analytical, if asked) results. If needed, the problems should be solved with the help of a programming code (Python). Providing code is a plus but should be commented explaining the above points. In any case, a clear description of the algorithm of the code should be provided. The same applies to the output of the code.

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