NMinimize to optimize function Module

Question

I am using Nminimize for simulation based optimization. I define the objective function (simulation with a variable "a") as a module to be used in the minimization. What I have found is if I do not print the function value (f[a]) using the EvaluationMonitor, NMinimize outputs 1000s of iterations of possible values for "a" extremely quickly without running the corresponding simulation run (because if it runs simulations, it will need few seconds for each simulation run and can not do 1000s of simulations in no time). However, when I include "f[a]" in the evaluation monitor, NMinimize runs the simulation for each possible value of "a" it outputs, but is disconnected to the optimization process. This is evident because NMinimize does not converge even after 1000s of iterations, when there are only 10 possible values "a" can take and I know the minimum occurs at "a"=10. Will someone help me understand what I am missing?

demand[n_,k_]:=Min[k Vf,n capacity];
supply[n_,k_]:=Min[(n Kj-k) w,n capacity];
flo[n_,Ku_,Kd_]:=Min[demand[n,Ku],supply[n,Kd]];
dx=Vf*dt;capacity=w*Vf*Kj/(Vf+w);Kj=150.;w=20.;Vf=100.;
n=Round[Flen/dx];m=Round[SimTime/dt];p=Round[Rlen/dx];RMLocation=Round[(2/3) p];
\[Alpha][a1_]:=1800.;\[Beta][a2_]:=0.1;L=1.;Flen=4.;Rlen=3.;delta = 1.;SimTime=15./60.;dt=6./3600.;
f[a_]:=Module[{k0=ConstantArray[0,n],kr=Table[Table[0,{i1,1,p}],{i2,1,n}],\[Gamma]=ConstantArray[1,n],\[Phi]},
Clear[j];j=0;RM[x_,t_]:=100 a;k=k0;
For[i=2,i<n,i++,kr[[i,1]]=\[Alpha][i dx] delta/Vf];
NtwrkTT=TT=Plus@@(Plus@@kr);
While[TT>0,
 For[i=2,i<n,i++,
  FQin=If[i==2,Min[demand[L,k0[[i-1]]],supply[L,k0[[i]]]],FQout];
  dem=demand[L,k0[[i]]];dem=If[dem==0,0.001,dem];
  \[Gamma][[i]]=Min[1,supply[L,k0[[i+1]]]/dem];
  \[Phi]=\[Gamma][[i]] demand[1,kr[[i,p]]]/delta;
  Qr=(\[Phi]-\[Beta][i dx] FQin) dx;
  FQout=Min[demand[L,k0[[i]]],supply[L,k0[[i+1]]]];
  k[[i]]=k0[[i]]+(FQin-FQout+Qr)/Vf;kr0=kr[[i]];
  For[ir=2,ir<=p,ir++,
   MR=If[ir==RMLocation+1,RM[i dx,j dt],capacity];
   RQin=Min[MR,If[ir==2,flo[1,kr0[[ir-1]],kr0[[ir]]],RQout]];
   MR=If[ir==RMLocation,RM[i dx,j dt],capacity];
   RQout=Min[MR,If[ir<p,flo[1,kr0[[ir]],kr0[[ir+1]]],\[Phi] delta]];
   kr[[i,ir]]=kr0[[ir]]+(RQin-RQout)/Vf];
  kr[[i,1]]=If[j<=m,\[Alpha][i dx] delta/Vf,0]];
 TT=Plus@@(Plus@@kr);
 TT+=Plus@@k;
 k0=k;NtwrkTT+=TT;j++];
NtwrkTT dt]
NMinimize[{f[a],3<=a<=12&&Element[a,Integers]},a,Method->"SimulatedAnnealing",EvaluationMonitor:>Print["a = ",a]]

edit: I edited this post extensively to make it clear. Apologize for any confusion.

Answer 1

I found the solution on another website "http://eternaldisturbanceincosmos.wordpress.com/2011/04/27/nminimize-in-mathematica-could-drive-you-insane/" which says "It turns out that NMinimize does not hold its arguments. This means that as the list of arguments is read from left to right, each argument is evaluated and replaced by the result of the evaluation". So I used Hold[] in the NMinimize function that fixed the problem.

Edit: Please see the responses/comments on Simulated Annealing Convergence