An important part of writing code is writing efficient code that

takes as little time as possible to run. This particularly important

when dealing with large problems, as is often the case for real$-$world

optimisation problems.

Here the task is to compare the efficiency of your code written in

Question $3$ with the code given in Question $4$ to see which format

is best $($that is$,$ fastest$).$

For this question you cannot use the AMPL version downloaded

from learnOnline as this version will only solve small problems.

Download and install the AMPL Community Edition, and use the

open$-$source solver HiGHS which allows problems of any size. Choose

the HiGHS solver with

option solver highs ;

$($a$)$ The code

display $\_$total$\_$solve$\_$time ;

will show the time taken to complete the last solve command.

Place this code at the end of your code written in Question $3$

and at the end of the code given in Question $4.$

Systematically run the code from both Question $3$ and Ques$-$

tion $4$ for all numbers of cities $n$ given in and record the time

taken to solve each problem. Since the solve time can be

quite variable, you should do each test multiple times and

then calculate the average time $($use your judgement to deter$-$

mine how many runs you should do$).$ Also, you want this to

be a fair test so do all runs on the same computer under the

same conditions.

Note that two largest problems $n=30,40$ will take some time

to run, and it is possible that your computer is not able to

solve them using both codes. If you fail to solve these larger

problems, then make a note of this and complete this question

without these results $($you will not be penalised$).$

Tabulate your results. Comment on anything that you think

is interesting or important about these results. In particular,

comment on the efficiency of the code.

$($b$)$ Plot the average run times against $n$ for both codes on the

same graph. Make sure your graph is displaying useful in$-$

formation $($for example, you might find that a log plot or a

semilog plot is more informative than a linear plot$).$

From your plot, estimate how long it might take to solve a

TSP with $n=100$ cities $($assuming it is possible to do so$).$