Minimizing with differential evolutionMinimizing a function of many coordinatesMinimizing a function with...

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Minimizing with differential evolution


Minimizing a function of many coordinatesMinimizing a function with some restrictionsMinimizing Multiple FunctionsProblem in minimizing expressionSolving 4 coupled differential equation and minimizing the solutionProblem when minimizing user-defined function in Mathematica with Minimize[]Minimizing with constraintsMinimizing functions with parametersMinimizing a conditional function with parametersMinimizing a function problem













4












$begingroup$


A differential evolution algorithm is given here. I would like to get this kind of animation. I thought I could use NMinimize, given
DifferentialEvolution as an option, but it turns out that does not work as I espected.



Is it possible to extract intermediate step in DifferentialEvolution, or do I have to implement algorithm myself?



f[x_, y_] := 

  -20 E^(-0.2 Sqrt[0.5 (x^2 + y^2)]) - E^(0.5 (Cos[2 π x] + Cos[2 π y])) + E + 20



p1 = 

  Plot3D[f[x, y], {x, -5, 5}, {y, -5, 5}, 

  PerformanceGoal -> "Quality",

  ColorFunction -> "WatermelonColors", 

  Mesh -> None, 

  BoxRatios -> {1, 1, 1}];   



p2 = 

   DensityPlot[f[x, y], {x, -5, 5}, {y, -5, 5}, 

     ColorFunction -> "WatermelonColors", 

     PlotPoints -> 200, 

     PerformanceGoal -> "Quality", 

     Frame -> False, 

     PlotRangePadding -> None];



p3 = Plot3D[0, {x, -5, 5}, {y, -5, 5}, PlotStyle -> Texture[p2], Mesh -> None];



Show[p1, p3, PlotRange -> {0, 15}]


enter image description here



When I use StepMonitor to track iterations as follows, it does not work.



{fit, intermediates} = 

  Reap[NMinimize[{f[x, y], -5 <= x <= 5, -5 <= y <= 5}, {x, y}, 

    MaxIterations -> 1000, 

    Method -> {"DifferentialEvolution", "InitialPoints" -> Tuples[Range[-5, 5], 2]}, 

    StepMonitor :> Sow[{x, y}]]];



Table[

  ListPlot[Take[intermediates[[1, i ;; i + 10]]], 

    Frame -> True, ImageSize -> 350, AspectRatio -> 1], 

  {i, 10, 1000, 100}]


EDIT
Here is the result when we used @Michael E2 solution. Cool!!



f[x_, y_] := -20 E^(-0.2 Sqrt[0.5 (x^2 + y^2)]) - 

  E^(0.5 (Cos[2 [Pi] x] + Cos[2 [Pi] y])) + E + 20



p1 = Plot3D[f[x, y], {x, -5, 5}, {y, -5, 5}, 

   PerformanceGoal -> "Quality", ColorFunction -> "WatermelonColors", 

   Mesh -> None, BoxRatios -> {1, 1, 1}];



p2 = DensityPlot[f[x, y], {x, -5, 5}, {y, -5, 5}, 

   ColorFunction -> "WatermelonColors", PerformanceGoal -> "Quality", 

   Frame -> False, PlotRangePadding -> None];



p3 = Plot3D[-0.5, {x, -5, 5}, {y, -5, 5}, PlotStyle -> Texture[p2], 

   Mesh -> None];



p4 = Show[p1, p3, PlotRange -> {-0.5, 15}]



Block[{f}, 

  f[x_, y_] := -20 E^(-0.2 Sqrt[0.5 (x^2 + y^2)]) - 

    E^(0.5 (Cos[2 [Pi] x] + Cos[2 [Pi] y])) + E + 20;

  {fit, intermediates} = 

   Reap[NMinimize[{f[x, y], -5 <= x <= 5, -5 <= y <= 5}, {x, y}, 

     MaxIterations -> 30, 

     Method -> {"DifferentialEvolution", 

       "InitialPoints" -> Tuples[Range[-5, 5], 2]}, 

     StepMonitor :> 

      Sow[{Optimization`NMinimizeDump`vecs, 

        Optimization`NMinimizeDump`vals}]]];] // Quiet



Multicolumn[

 Table[Show[p4, 

   ListPointPlot3D[{Append[#, 0] & /@ intermediates[[1, i, 1]]}, 

    PlotRange -> {{-5, 5}, {-5, 5}, {-5, 5}}, Boxed -> False, 

    PlotStyle -> Directive[AbsolutePointSize[3], Black]]], {i, 1, 30, 

   2}], 5, Appearance -> "Horizontal"]


enter image description here






mathematical-optimization







share|improve this question











$endgroup$












  • $begingroup$
    Note that blocking f (Block[{f}, ...]) isn't necessary. It was just to prevent f from being defined, which is a habit I have with single-lettter symbols on SE, esp. ones I use like f, x, etc. -- thanks for the accept!
    $endgroup$
    – Michael E2
    52 mins ago


















4












$begingroup$


A differential evolution algorithm is given here. I would like to get this kind of animation. I thought I could use NMinimize, given
DifferentialEvolution as an option, but it turns out that does not work as I espected.



Is it possible to extract intermediate step in DifferentialEvolution, or do I have to implement algorithm myself?



f[x_, y_] := 

  -20 E^(-0.2 Sqrt[0.5 (x^2 + y^2)]) - E^(0.5 (Cos[2 π x] + Cos[2 π y])) + E + 20



p1 = 

  Plot3D[f[x, y], {x, -5, 5}, {y, -5, 5}, 

  PerformanceGoal -> "Quality",

  ColorFunction -> "WatermelonColors", 

  Mesh -> None, 

  BoxRatios -> {1, 1, 1}];   



p2 = 

   DensityPlot[f[x, y], {x, -5, 5}, {y, -5, 5}, 

     ColorFunction -> "WatermelonColors", 

     PlotPoints -> 200, 

     PerformanceGoal -> "Quality", 

     Frame -> False, 

     PlotRangePadding -> None];



p3 = Plot3D[0, {x, -5, 5}, {y, -5, 5}, PlotStyle -> Texture[p2], Mesh -> None];



Show[p1, p3, PlotRange -> {0, 15}]


enter image description here



When I use StepMonitor to track iterations as follows, it does not work.



{fit, intermediates} = 

  Reap[NMinimize[{f[x, y], -5 <= x <= 5, -5 <= y <= 5}, {x, y}, 

    MaxIterations -> 1000, 

    Method -> {"DifferentialEvolution", "InitialPoints" -> Tuples[Range[-5, 5], 2]}, 

    StepMonitor :> Sow[{x, y}]]];



Table[

  ListPlot[Take[intermediates[[1, i ;; i + 10]]], 

    Frame -> True, ImageSize -> 350, AspectRatio -> 1], 

  {i, 10, 1000, 100}]


EDIT
Here is the result when we used @Michael E2 solution. Cool!!



f[x_, y_] := -20 E^(-0.2 Sqrt[0.5 (x^2 + y^2)]) - 

  E^(0.5 (Cos[2 [Pi] x] + Cos[2 [Pi] y])) + E + 20



p1 = Plot3D[f[x, y], {x, -5, 5}, {y, -5, 5}, 

   PerformanceGoal -> "Quality", ColorFunction -> "WatermelonColors", 

   Mesh -> None, BoxRatios -> {1, 1, 1}];



p2 = DensityPlot[f[x, y], {x, -5, 5}, {y, -5, 5}, 

   ColorFunction -> "WatermelonColors", PerformanceGoal -> "Quality", 

   Frame -> False, PlotRangePadding -> None];



p3 = Plot3D[-0.5, {x, -5, 5}, {y, -5, 5}, PlotStyle -> Texture[p2], 

   Mesh -> None];



p4 = Show[p1, p3, PlotRange -> {-0.5, 15}]



Block[{f}, 

  f[x_, y_] := -20 E^(-0.2 Sqrt[0.5 (x^2 + y^2)]) - 

    E^(0.5 (Cos[2 [Pi] x] + Cos[2 [Pi] y])) + E + 20;

  {fit, intermediates} = 

   Reap[NMinimize[{f[x, y], -5 <= x <= 5, -5 <= y <= 5}, {x, y}, 

     MaxIterations -> 30, 

     Method -> {"DifferentialEvolution", 

       "InitialPoints" -> Tuples[Range[-5, 5], 2]}, 

     StepMonitor :> 

      Sow[{Optimization`NMinimizeDump`vecs, 

        Optimization`NMinimizeDump`vals}]]];] // Quiet



Multicolumn[

 Table[Show[p4, 

   ListPointPlot3D[{Append[#, 0] & /@ intermediates[[1, i, 1]]}, 

    PlotRange -> {{-5, 5}, {-5, 5}, {-5, 5}}, Boxed -> False, 

    PlotStyle -> Directive[AbsolutePointSize[3], Black]]], {i, 1, 30, 

   2}], 5, Appearance -> "Horizontal"]


enter image description here






mathematical-optimization







share|improve this question











$endgroup$












  • $begingroup$
    Note that blocking f (Block[{f}, ...]) isn't necessary. It was just to prevent f from being defined, which is a habit I have with single-lettter symbols on SE, esp. ones I use like f, x, etc. -- thanks for the accept!
    $endgroup$
    – Michael E2
    52 mins ago
















4












4








4


2



$begingroup$


A differential evolution algorithm is given here. I would like to get this kind of animation. I thought I could use NMinimize, given
DifferentialEvolution as an option, but it turns out that does not work as I espected.



Is it possible to extract intermediate step in DifferentialEvolution, or do I have to implement algorithm myself?



f[x_, y_] := 

  -20 E^(-0.2 Sqrt[0.5 (x^2 + y^2)]) - E^(0.5 (Cos[2 π x] + Cos[2 π y])) + E + 20



p1 = 

  Plot3D[f[x, y], {x, -5, 5}, {y, -5, 5}, 

  PerformanceGoal -> "Quality",

  ColorFunction -> "WatermelonColors", 

  Mesh -> None, 

  BoxRatios -> {1, 1, 1}];   



p2 = 

   DensityPlot[f[x, y], {x, -5, 5}, {y, -5, 5}, 

     ColorFunction -> "WatermelonColors", 

     PlotPoints -> 200, 

     PerformanceGoal -> "Quality", 

     Frame -> False, 

     PlotRangePadding -> None];



p3 = Plot3D[0, {x, -5, 5}, {y, -5, 5}, PlotStyle -> Texture[p2], Mesh -> None];



Show[p1, p3, PlotRange -> {0, 15}]


enter image description here



When I use StepMonitor to track iterations as follows, it does not work.



{fit, intermediates} = 

  Reap[NMinimize[{f[x, y], -5 <= x <= 5, -5 <= y <= 5}, {x, y}, 

    MaxIterations -> 1000, 

    Method -> {"DifferentialEvolution", "InitialPoints" -> Tuples[Range[-5, 5], 2]}, 

    StepMonitor :> Sow[{x, y}]]];



Table[

  ListPlot[Take[intermediates[[1, i ;; i + 10]]], 

    Frame -> True, ImageSize -> 350, AspectRatio -> 1], 

  {i, 10, 1000, 100}]


EDIT
Here is the result when we used @Michael E2 solution. Cool!!



f[x_, y_] := -20 E^(-0.2 Sqrt[0.5 (x^2 + y^2)]) - 

  E^(0.5 (Cos[2 [Pi] x] + Cos[2 [Pi] y])) + E + 20



p1 = Plot3D[f[x, y], {x, -5, 5}, {y, -5, 5}, 

   PerformanceGoal -> "Quality", ColorFunction -> "WatermelonColors", 

   Mesh -> None, BoxRatios -> {1, 1, 1}];



p2 = DensityPlot[f[x, y], {x, -5, 5}, {y, -5, 5}, 

   ColorFunction -> "WatermelonColors", PerformanceGoal -> "Quality", 

   Frame -> False, PlotRangePadding -> None];



p3 = Plot3D[-0.5, {x, -5, 5}, {y, -5, 5}, PlotStyle -> Texture[p2], 

   Mesh -> None];



p4 = Show[p1, p3, PlotRange -> {-0.5, 15}]



Block[{f}, 

  f[x_, y_] := -20 E^(-0.2 Sqrt[0.5 (x^2 + y^2)]) - 

    E^(0.5 (Cos[2 [Pi] x] + Cos[2 [Pi] y])) + E + 20;

  {fit, intermediates} = 

   Reap[NMinimize[{f[x, y], -5 <= x <= 5, -5 <= y <= 5}, {x, y}, 

     MaxIterations -> 30, 

     Method -> {"DifferentialEvolution", 

       "InitialPoints" -> Tuples[Range[-5, 5], 2]}, 

     StepMonitor :> 

      Sow[{Optimization`NMinimizeDump`vecs, 

        Optimization`NMinimizeDump`vals}]]];] // Quiet



Multicolumn[

 Table[Show[p4, 

   ListPointPlot3D[{Append[#, 0] & /@ intermediates[[1, i, 1]]}, 

    PlotRange -> {{-5, 5}, {-5, 5}, {-5, 5}}, Boxed -> False, 

    PlotStyle -> Directive[AbsolutePointSize[3], Black]]], {i, 1, 30, 

   2}], 5, Appearance -> "Horizontal"]


enter image description here






mathematical-optimization







share|improve this question











$endgroup$




A differential evolution algorithm is given here. I would like to get this kind of animation. I thought I could use NMinimize, given
DifferentialEvolution as an option, but it turns out that does not work as I espected.



Is it possible to extract intermediate step in DifferentialEvolution, or do I have to implement algorithm myself?



f[x_, y_] := 

  -20 E^(-0.2 Sqrt[0.5 (x^2 + y^2)]) - E^(0.5 (Cos[2 π x] + Cos[2 π y])) + E + 20



p1 = 

  Plot3D[f[x, y], {x, -5, 5}, {y, -5, 5}, 

  PerformanceGoal -> "Quality",

  ColorFunction -> "WatermelonColors", 

  Mesh -> None, 

  BoxRatios -> {1, 1, 1}];   



p2 = 

   DensityPlot[f[x, y], {x, -5, 5}, {y, -5, 5}, 

     ColorFunction -> "WatermelonColors", 

     PlotPoints -> 200, 

     PerformanceGoal -> "Quality", 

     Frame -> False, 

     PlotRangePadding -> None];



p3 = Plot3D[0, {x, -5, 5}, {y, -5, 5}, PlotStyle -> Texture[p2], Mesh -> None];



Show[p1, p3, PlotRange -> {0, 15}]


enter image description here



When I use StepMonitor to track iterations as follows, it does not work.



{fit, intermediates} = 

  Reap[NMinimize[{f[x, y], -5 <= x <= 5, -5 <= y <= 5}, {x, y}, 

    MaxIterations -> 1000, 

    Method -> {"DifferentialEvolution", "InitialPoints" -> Tuples[Range[-5, 5], 2]}, 

    StepMonitor :> Sow[{x, y}]]];



Table[

  ListPlot[Take[intermediates[[1, i ;; i + 10]]], 

    Frame -> True, ImageSize -> 350, AspectRatio -> 1], 

  {i, 10, 1000, 100}]


EDIT
Here is the result when we used @Michael E2 solution. Cool!!



f[x_, y_] := -20 E^(-0.2 Sqrt[0.5 (x^2 + y^2)]) - 

  E^(0.5 (Cos[2 [Pi] x] + Cos[2 [Pi] y])) + E + 20



p1 = Plot3D[f[x, y], {x, -5, 5}, {y, -5, 5}, 

   PerformanceGoal -> "Quality", ColorFunction -> "WatermelonColors", 

   Mesh -> None, BoxRatios -> {1, 1, 1}];



p2 = DensityPlot[f[x, y], {x, -5, 5}, {y, -5, 5}, 

   ColorFunction -> "WatermelonColors", PerformanceGoal -> "Quality", 

   Frame -> False, PlotRangePadding -> None];



p3 = Plot3D[-0.5, {x, -5, 5}, {y, -5, 5}, PlotStyle -> Texture[p2], 

   Mesh -> None];



p4 = Show[p1, p3, PlotRange -> {-0.5, 15}]



Block[{f}, 

  f[x_, y_] := -20 E^(-0.2 Sqrt[0.5 (x^2 + y^2)]) - 

    E^(0.5 (Cos[2 [Pi] x] + Cos[2 [Pi] y])) + E + 20;

  {fit, intermediates} = 

   Reap[NMinimize[{f[x, y], -5 <= x <= 5, -5 <= y <= 5}, {x, y}, 

     MaxIterations -> 30, 

     Method -> {"DifferentialEvolution", 

       "InitialPoints" -> Tuples[Range[-5, 5], 2]}, 

     StepMonitor :> 

      Sow[{Optimization`NMinimizeDump`vecs, 

        Optimization`NMinimizeDump`vals}]]];] // Quiet



Multicolumn[

 Table[Show[p4, 

   ListPointPlot3D[{Append[#, 0] & /@ intermediates[[1, i, 1]]}, 

    PlotRange -> {{-5, 5}, {-5, 5}, {-5, 5}}, Boxed -> False, 

    PlotStyle -> Directive[AbsolutePointSize[3], Black]]], {i, 1, 30, 

   2}], 5, Appearance -> "Horizontal"]


enter image description here






mathematical-optimization




mathematical-optimization






share|improve this question















share|improve this question













share|improve this question




share|improve this question








edited 1 hour ago







Okkes Dulgerci

















asked 3 hours ago









Okkes DulgerciOkkes Dulgerci

5,2691917




5,2691917












  • $begingroup$
    Note that blocking f (Block[{f}, ...]) isn't necessary. It was just to prevent f from being defined, which is a habit I have with single-lettter symbols on SE, esp. ones I use like f, x, etc. -- thanks for the accept!
    $endgroup$
    – Michael E2
    52 mins ago




















  • $begingroup$
    Note that blocking f (Block[{f}, ...]) isn't necessary. It was just to prevent f from being defined, which is a habit I have with single-lettter symbols on SE, esp. ones I use like f, x, etc. -- thanks for the accept!
    $endgroup$
    – Michael E2
    52 mins ago


















$begingroup$
Note that blocking f (Block[{f}, ...]) isn't necessary. It was just to prevent f from being defined, which is a habit I have with single-lettter symbols on SE, esp. ones I use like f, x, etc. -- thanks for the accept!
$endgroup$
– Michael E2
52 mins ago






$begingroup$
Note that blocking f (Block[{f}, ...]) isn't necessary. It was just to prevent f from being defined, which is a habit I have with single-lettter symbols on SE, esp. ones I use like f, x, etc. -- thanks for the accept!
$endgroup$
– Michael E2
52 mins ago












1 Answer
1






active

oldest

votes


















3












$begingroup$

Here's a way:



Block[{f},

 f[x_, y_] := -20 E^(-0.2 Sqrt[0.5 (x^2 + y^2)]) - 

   E^(0.5 (Cos[2 [Pi] x] + Cos[2 [Pi] y])) + E + 20;

 {fit, intermediates} = 

  Reap[NMinimize[{f[x, y], -5 <= x <= 5, -5 <= y <= 5}, {x, y}, 

    MaxIterations -> 30, 

    Method -> {"DifferentialEvolution", 

      "InitialPoints" -> Tuples[Range[-5, 5], 2]}, 

    StepMonitor :> 

     Sow[{Optimization`NMinimizeDump`vecs, 

       Optimization`NMinimizeDump`vals}]]];

 ]



Manipulate[

 Graphics[{

   PointSize[Medium],

   Point[intermediates[[1, n, 1]], 

    VertexColors -> 

     ColorData["Rainbow"] /@ 

      Rescale[intermediates[[1, n, 2]], 

       MinMax[intermediates[[1, All, 2]]]]]

   },

  PlotRange -> 5, Frame -> True],

 {n, 1, Length@intermediates[[1]], 1}

 ]


enter image description here



You can find out about things like Optimization`NMinimizeDump`vecs by inspecting the code for Optimization`NMinimizeDump`CoreDE.






share|improve this answer









$endgroup$













    Your Answer





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    1 Answer
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    active

    oldest

    votes








    1 Answer
    1






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes









    3












    $begingroup$

    Here's a way:



    Block[{f},
    
 f[x_, y_] := -20 E^(-0.2 Sqrt[0.5 (x^2 + y^2)]) - 
    
   E^(0.5 (Cos[2 [Pi] x] + Cos[2 [Pi] y])) + E + 20;
    
 {fit, intermediates} = 
    
  Reap[NMinimize[{f[x, y], -5 <= x <= 5, -5 <= y <= 5}, {x, y}, 
    
    MaxIterations -> 30, 
    
    Method -> {"DifferentialEvolution", 
    
      "InitialPoints" -> Tuples[Range[-5, 5], 2]}, 
    
    StepMonitor :> 
    
     Sow[{Optimization`NMinimizeDump`vecs, 
    
       Optimization`NMinimizeDump`vals}]]];
    
 ]
    

    
Manipulate[
    
 Graphics[{
    
   PointSize[Medium],
    
   Point[intermediates[[1, n, 1]], 
    
    VertexColors -> 
    
     ColorData["Rainbow"] /@ 
    
      Rescale[intermediates[[1, n, 2]], 
    
       MinMax[intermediates[[1, All, 2]]]]]
    
   },
    
  PlotRange -> 5, Frame -> True],
    
 {n, 1, Length@intermediates[[1]], 1}
    
 ]


    enter image description here



    You can find out about things like Optimization`NMinimizeDump`vecs by inspecting the code for Optimization`NMinimizeDump`CoreDE.






    share|improve this answer









    $endgroup$


















      3












      $begingroup$

      Here's a way:



      Block[{f},
      
 f[x_, y_] := -20 E^(-0.2 Sqrt[0.5 (x^2 + y^2)]) - 
      
   E^(0.5 (Cos[2 [Pi] x] + Cos[2 [Pi] y])) + E + 20;
      
 {fit, intermediates} = 
      
  Reap[NMinimize[{f[x, y], -5 <= x <= 5, -5 <= y <= 5}, {x, y}, 
      
    MaxIterations -> 30, 
      
    Method -> {"DifferentialEvolution", 
      
      "InitialPoints" -> Tuples[Range[-5, 5], 2]}, 
      
    StepMonitor :> 
      
     Sow[{Optimization`NMinimizeDump`vecs, 
      
       Optimization`NMinimizeDump`vals}]]];
      
 ]
      

      
Manipulate[
      
 Graphics[{
      
   PointSize[Medium],
      
   Point[intermediates[[1, n, 1]], 
      
    VertexColors -> 
      
     ColorData["Rainbow"] /@ 
      
      Rescale[intermediates[[1, n, 2]], 
      
       MinMax[intermediates[[1, All, 2]]]]]
      
   },
      
  PlotRange -> 5, Frame -> True],
      
 {n, 1, Length@intermediates[[1]], 1}
      
 ]


      enter image description here



      You can find out about things like Optimization`NMinimizeDump`vecs by inspecting the code for Optimization`NMinimizeDump`CoreDE.






      share|improve this answer









      $endgroup$
















        3












        3








        3





        $begingroup$

        Here's a way:



        Block[{f},
        
 f[x_, y_] := -20 E^(-0.2 Sqrt[0.5 (x^2 + y^2)]) - 
        
   E^(0.5 (Cos[2 [Pi] x] + Cos[2 [Pi] y])) + E + 20;
        
 {fit, intermediates} = 
        
  Reap[NMinimize[{f[x, y], -5 <= x <= 5, -5 <= y <= 5}, {x, y}, 
        
    MaxIterations -> 30, 
        
    Method -> {"DifferentialEvolution", 
        
      "InitialPoints" -> Tuples[Range[-5, 5], 2]}, 
        
    StepMonitor :> 
        
     Sow[{Optimization`NMinimizeDump`vecs, 
        
       Optimization`NMinimizeDump`vals}]]];
        
 ]
        

        
Manipulate[
        
 Graphics[{
        
   PointSize[Medium],
        
   Point[intermediates[[1, n, 1]], 
        
    VertexColors -> 
        
     ColorData["Rainbow"] /@ 
        
      Rescale[intermediates[[1, n, 2]], 
        
       MinMax[intermediates[[1, All, 2]]]]]
        
   },
        
  PlotRange -> 5, Frame -> True],
        
 {n, 1, Length@intermediates[[1]], 1}
        
 ]


        enter image description here



        You can find out about things like Optimization`NMinimizeDump`vecs by inspecting the code for Optimization`NMinimizeDump`CoreDE.






        share|improve this answer









        $endgroup$



        Here's a way:



        Block[{f},
        
 f[x_, y_] := -20 E^(-0.2 Sqrt[0.5 (x^2 + y^2)]) - 
        
   E^(0.5 (Cos[2 [Pi] x] + Cos[2 [Pi] y])) + E + 20;
        
 {fit, intermediates} = 
        
  Reap[NMinimize[{f[x, y], -5 <= x <= 5, -5 <= y <= 5}, {x, y}, 
        
    MaxIterations -> 30, 
        
    Method -> {"DifferentialEvolution", 
        
      "InitialPoints" -> Tuples[Range[-5, 5], 2]}, 
        
    StepMonitor :> 
        
     Sow[{Optimization`NMinimizeDump`vecs, 
        
       Optimization`NMinimizeDump`vals}]]];
        
 ]
        

        
Manipulate[
        
 Graphics[{
        
   PointSize[Medium],
        
   Point[intermediates[[1, n, 1]], 
        
    VertexColors -> 
        
     ColorData["Rainbow"] /@ 
        
      Rescale[intermediates[[1, n, 2]], 
        
       MinMax[intermediates[[1, All, 2]]]]]
        
   },
        
  PlotRange -> 5, Frame -> True],
        
 {n, 1, Length@intermediates[[1]], 1}
        
 ]


        enter image description here



        You can find out about things like Optimization`NMinimizeDump`vecs by inspecting the code for Optimization`NMinimizeDump`CoreDE.







        share|improve this answer












        share|improve this answer



        share|improve this answer










        answered 2 hours ago









        Michael E2Michael E2

        148k12198478




        148k12198478






























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