Need help looping a notebook evaluation

Question

I'm a new user and would like to find the minimum value of soln1[30] obtained after repeating the following evaluation (below) for 1000 cycles (for instance). I can obtain sequential values of soln[30] if I reevaluate the entire notebook manually each time, but I want to be able to automate this process until a minimum value of soln1[30] is reached. The difficulty that I am encountering is that the entire notebook requires evaluation in order to generate a different random integer each time- I am having trouble figuring out how to force the evaluation to include the randominteger step using commands like Table, etc. I'm probably missing something simple- any help would be appreciated. Thanks in advance...

Clear[w, t, q, soln1]

f1[t_] := 5*t;

w = RandomInteger[{1111, 9999}];
a = IntegerDigits[w][[1]];
b = IntegerDigits[w][[2]];
c = IntegerDigits[w][[3]];
d = IntegerDigits[w][[4]];
p = 0.1;
k = 0.6;

end1 = a;
p1 = end1 + p;
end2 = p1 + b;
p2 = end2 + p;
end3 = p2 + c;
p3 = end3 + p;
end4 = p3 + d;

soln1[t_] := Piecewise[{{f1[t], t < end1}, {k*f1[end1], 
 end1 <= t < p1}, {f1'[t]*(t - p1) + k*f1[end1], 
 p1 <= t < epnd2}, {k*f1[end2], 
 end2 <= t < p2}, {f1'[t]*(t - p2) + k*f1[end2], 
 p2 <= t < end3}, {k*f1[end3], 
 end3 <= t < p3}, {f1'[t]*(t - p3) + k*f1[end3], p3 <= t <= 30}}];

 soln1[30]

Answer 1

This is equivalent to your code, and iterates dynamically:

f1[t_] := 5*t
p = 1/10;   k = 6/10; r = {};
SeedRandom[42];
Dynamic[ Refresh[
   a = (IntegerDigits@RandomInteger[{1111, 9999}])[[;; 3]];
   AppendTo[r, N[f1'[30]*(30 - Tr@a - 3 p) + k*f1[Tr@a + 2 p]]];
   {ListLinePlot@r, Min@r}]]

Edit

Perhaps better:

r = {FromDigits@#, N[f1'[30]*(30 - Tr@# - 3 p) + k*f1[Tr@# + 2 p]]} & /@ 
                                                             IntegerDigits@Range[110, 999];
{ListLinePlot@r, Pick[r, Thread[#[[2]] == Min[r[[All, 2]]]] & /@ r]}