# Generate $100$ random cities

cities $=[($random$.$uniform$(0,1),$ random.uniform$(0,1))$ for i in range$(100)]$

# Solve the TSP using simulated annealing

tour $=$ simulated annealing$($cities$,$ jnitatemp$=100,$ alpha$=0\mathrm{.}99)$

# Print the tour and its distance

print$("$Tour: $",$ tour$)$

print$("$Distance: $",$ tournadistance$($tour$,$ cities$))$

# Plot the tour

x$=[$city$[0]$ for city in cities$]$

y$=$ city$[1]$ for city in cities$]$

pltwlot$($x$,$ y$,\text{'}$bu$\text{'})$

for $$ in range$($lep$($tour$))$:

plt$\_$plot$([$cities$[$tour$[$i$]][0],$ cities$[$tour$[($i$+1)\%$len$($tour$)]][0]],$

$[$cities$[$tour$[$i$]][1],$ cities$[$tour$[($i$+1)\%$len$($tour$)]][1]],\text{'}$k$-\text{'})$

Qlt show$()$

The simulated annealing heuristic can find a good solution within a reasonable amount of time,

depending on the size of the problem and the values of the temperature and cooling rate

parameters.

To evaluate its performance, you can run multiple replications and plot the distribution of the

solution times. Here's an example code to run $10$ replications and plot the solution times:

import time

# Run $10$ replications of simulated annealing and record the solution times

solution times $=[]$

for i in range$(10)$:

start time $=$ time. time$()$

tour $=$ simulated annealing$($cities$,$ init temp$=100,$ alpha$=0\mathrm{.}99)$

end time $=$ time.time$()$

solution time $=$ end time $-$ start time

solution times.append$($solution time$)$

# Plot the distribution of

Could you mathematically model this code and write it in GAMS, then explain the code step by step? DON'T ask artificial intelligence because I can understand from its answer that you asked it$,$ and artificial intelligence solves this wrong. There are a lot of errors in the code.