Skip to main content

mathematical optimization - Simulated Annealing Convergence


I am using Simulated Annealing method for a simulation based optimization of a process that has 3 variables, using NMinimize. I print the input/output during every iteration using the "Evaluation Monitor". I have noticed that after about 3000 iterations, Mathematica gives me a convergence result. But checking the results from "Evaluation Monitor" shows that the ultimate convergence result is not the global minimal, but the process has visited a better minimal during one of the iterations. Why is this happening?


Here is a sample code:



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; n=Round[Flen/dx]; m=Round[SimTime/dt];  
p=Round[Rlen/dx];   θ=Vf/w; capacity=w*Vf*Kj/(Vf+w); α[a1_]:=1800.; β[a2_]:=0.1; L=3.; 
Flen=8.; Rlen=3.; SimTime=30./60.; Kj=150.; w=20.; Vf=100.; dt=12./3600.; d=1.; 
RMLocation=Round[(2/3) p]; j=0;

f[a1_,a2_,a3_]:=Module[{b1=a1,b2=a2,b3=a3,TT=0,NtwrkTT=0,j=0},
   RM[x_,t_]:=Piecewise[{{100 b1,x<=3},{100 b2,3
   NtwrkTT=0; Clear[k0,kr,k,γ];
   k0=ConstantArray[0,n]; 
   kr=Table[Table[0,{k,1,p}],{i,1,n}]; 
   γ=ConstantArray[1,n];
   For[i=2, i   TT=Plus@@(Plus@@kr); NtwrkTT=TT; k=k0;
   While[TT>0, TT=0;
     For[i=2, i  dem=demand[L,k0[[i]]]; dem=If[dem==0,0.001,dem];
  γ[[i]]=Min[1,supply[L,k0[[i+1]]]/dem];

  ϕ=γ[[i]] demand[1,kr[[i,p]]]/d;
  Qr=(ϕ-β[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
   kr[[i,ir]]=kr0[[ir]]+(RQin-RQout)/Vf];
  kr[[i,1]]=If[j<=m,α[i dx] d/Vf,0]];
 TT=Plus@@(Plus@@kr);
 TT+=Plus@@k;
 k0=k;NtwrkTT+=TT;j++];
NtwrkTT dt]
NMinimize[{f[a,b,c],3<=a<=12&&3<=b<=12&&3<=c<=12&&Element[a|b|c,Integers]},{a,b,c},Method->{"SimulatedAnnealing","SearchPoints"->5^5},EvaluationMonitor:>Print["a = ",a," , b = ",b," , c = ",c," , f[a,b,c] = ",f[a,b,c]]]

Hope this helps.


Ps. Any suggestions to improve the performance of this code will be greatly appreciated. Thank You.



edit:


As per @@Kuba's suggestion, I split the original question in to two. The second part is at Simulated Annealing Parameters and Results



Answer



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:


As suggested by Szabolcs, it worked with ?NumericQ alone and no Hold[]


Comments

Post a Comment

Popular posts from this blog

functions - Get leading series expansion term?

Given a function f[x] , I would like to have a function leadingSeries that returns just the leading term in the series around x=0 . For example: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x)] x and leadingSeries[(1/x + 2 + (1 - 1/x^3)/4)/(4 + x)] -(1/(16 x^3)) Is there such a function in Mathematica? Or maybe one can implement it efficiently? EDIT I finally went with the following implementation, based on Carl Woll 's answer: lds[ex_,x_]:=( (ex/.x->(x+O[x]^2))/.SeriesData[U_,Z_,L_List,Mi_,Ma_,De_]:>SeriesData[U,Z,{L[[1]]},Mi,Mi+1,De]//Quiet//Normal) The advantage is, that this one also properly works with functions whose leading term is a constant: lds[Exp[x],x] 1 Answer Update 1 Updated to eliminate SeriesData and to not return additional terms Perhaps you could use: leadingSeries[expr_, x_] := Normal[expr /. x->(x+O[x]^2) /. a_List :> Take[a, 1]] Then for your examples: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x), x] leadingSeries[Exp[x], x] leadingSeries[(1/x + 2 + (1 - 1/x...
Post a Comment
Read more

How to thread a list

I have data in format data = {{a1, a2}, {b1, b2}, {c1, c2}, {d1, d2}} Tableform: I want to thread it to : tdata = {{{a1, b1}, {a2, b2}}, {{a1, c1}, {a2, c2}}, {{a1, d1}, {a2, d2}}} Tableform: And I would like to do better then pseudofunction[n_] := Transpose[{data2[[1]], data2[[n]]}]; SetAttributes[pseudofunction, Listable]; Range[2, 4] // pseudofunction Here is my benchmark data, where data3 is normal sample of real data. data3 = Drop[ExcelWorkBook[[Column1 ;; Column4]], None, 1]; data2 = {a #, b #, c #, d #} & /@ Range[1, 10^5]; data = RandomReal[{0, 1}, {10^6, 4}]; Here is my benchmark code kptnw[list_] := Transpose[{Table[First@#, {Length@# - 1}], Rest@#}, {3, 1, 2}] &@list kptnw2[list_] := Transpose[{ConstantArray[First@#, Length@# - 1], Rest@#}, {3, 1, 2}] &@list OleksandrR[list_] := Flatten[Outer[List, List@First[list], Rest[list], 1], {{2}, {1, 4}}] paradox2[list_] := Partition[Riffle[list[[1]], #], 2] & /@ Drop[list, 1] RM[list_] := FoldList[Transpose[{First@li...
Post a Comment
Read more

front end - keyboard shortcut to invoke Insert new matrix

I frequently need to type in some matrices, and the menu command Insert > Table/Matrix > New... allows matrices with lines drawn between columns and rows, which is very helpful. I would like to make a keyboard shortcut for it, but cannot find the relevant frontend token command (4209405) for it. Since the FullForm[] and InputForm[] of matrices with lines drawn between rows and columns is the same as those without lines, it's hard to do this via 3rd party system-wide text expanders (e.g. autohotkey or atext on mac). How does one assign a keyboard shortcut for the menu item Insert > Table/Matrix > New... , preferably using only mathematica? Thanks! Answer In the MenuSetup.tr (for linux located in the $InstallationDirectory/SystemFiles/FrontEnd/TextResources/X/ directory), I changed the line MenuItem["&New...", "CreateGridBoxDialog"] to read MenuItem["&New...", "CreateGridBoxDialog", MenuKey["m", Modifiers-...
Post a Comment
Read more