Instructions for Obtaining Random Numbers

For each problem or its part where random numbers are needed, obtain them from the

consecutive random digits in Table $1$ as follows. Start from the front of the top row of the table

and form five$-$digit random numbers by placing a decimal point in front of each group of five

random digits $(0\mathrm{.}09656,0\mathrm{.}96657,$ etc.$)$ in the order that you need random numbers. Always

restart from the front of the top row for each new problem or its part.

Table $1.$ Table of random digits

Consider the example of a nonconvex programming problem given in follows.

Maximize $,Z=0\mathrm{.}5x^5-6x^4+24\mathrm{.}5x^3-39x^2+20x,$

subject to

$x5$

$x0,$

Using $x=2\mathrm{.}5$ as the initial trial solution, perform six iterations of the basic simulated annealing

algorithm by hand. Follow the instructions given at the beginning to obtain the random

numbers. For each T value, perform two iterations. Show your work, including the use of the

random numbers.