Follow the instructions of Prob. 14.3-8 for the following nonconvex programming problem when starting with x = 25 as the initial trial solution.
Maximize f(x) = x6 - 136x5 + 6800x4 - 155,000x3 + 1,570,000x2 - 5,000,000x,
subject to 0 ≤ x ≤ 50.
(a) Using x = 2.5 as the initial trial solution, perform the first iteration of the basic simulated annealing algorithm presented in Sec. 14.3 by hand. Follow the instructions given at the beginning of the Problems section to obtain the random numbers. Show your work, including the use of the random numbers.
(b) Use your IOR Tutorial to apply this algorithm, starting with x = 2.5 as the initial trial solution. Observe the progress of the algorithm and record for each iteration how many (if any) candidates to be the next trial solution are rejected before one is accepted. Also count the number of iterations where a nonimproving move is accepted.