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

How to write a chaotic neutral protagonist and prevent my readers from thinking they are evil?

From an axiomatic set theoric approach why can we take uncountable unions?

Why does cron require MTA for logging?

PTIJ: Why does only a Shor Tam ask at the Seder, and not a Shor Mu'ad?

What is better: yes / no radio, or simple checkbox?

What is the generally accepted pronunciation of “topoi”?

Are all players supposed to be able to see each others' character sheets?

Is a piano played in the same way as a harmonium?

Are small insurances worth it?

Why does Solve lock up when trying to solve the quadratic equation with large integers?

Windows Server Datacenter Edition - Unlimited Virtual Machines

Was it really inappropriate to write a pull request for the company I interviewed with?

I need help with tikz tree node and label, offsets and inclination

Would an aboleth's Phantasmal Force lair action be affected by Counterspell, Dispel Magic, and/or Slow?

I reported the illegal activity of my boss to his boss. My boss found out. Now I am being punished. What should I do?

What are some noteworthy "mic-drop" moments in math?

I can't die. Who am I?

What is this diamond of every day?

School performs periodic password audits. Is my password compromised?

What do you call someone who likes to pick fights?

How can I manipulate the output of Information?

Is it safe to abruptly remove Arduino power?

Haman going to the second feast dirty

Is it possible to avoid unpacking when merging Association?



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





    StackExchange.ifUsing("editor", function () {
    return StackExchange.using("mathjaxEditing", function () {
    StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
    StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
    });
    });
    }, "mathjax-editing");

    StackExchange.ready(function() {
    var channelOptions = {
    tags: "".split(" "),
    id: "387"
    };
    initTagRenderer("".split(" "), "".split(" "), channelOptions);

    StackExchange.using("externalEditor", function() {
    // Have to fire editor after snippets, if snippets enabled
    if (StackExchange.settings.snippets.snippetsEnabled) {
    StackExchange.using("snippets", function() {
    createEditor();
    });
    }
    else {
    createEditor();
    }
    });

    function createEditor() {
    StackExchange.prepareEditor({
    heartbeatType: 'answer',
    autoActivateHeartbeat: false,
    convertImagesToLinks: false,
    noModals: true,
    showLowRepImageUploadWarning: true,
    reputationToPostImages: null,
    bindNavPrevention: true,
    postfix: "",
    imageUploader: {
    brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
    contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
    allowUrls: true
    },
    onDemand: true,
    discardSelector: ".discard-answer"
    ,immediatelyShowMarkdownHelp:true
    });


    }
    });














    draft saved

    draft discarded


















    StackExchange.ready(
    function () {
    StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmathematica.stackexchange.com%2fquestions%2f193009%2fminimizing-with-differential-evolution%23new-answer', 'question_page');
    }
    );

    Post as a guest















    Required, but never shown

























    1 Answer
    1






    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






























            draft saved

            draft discarded




















































            Thanks for contributing an answer to Mathematica Stack Exchange!


            • Please be sure to answer the question. Provide details and share your research!

            But avoid …



            • Asking for help, clarification, or responding to other answers.

            • Making statements based on opinion; back them up with references or personal experience.


            Use MathJax to format equations. MathJax reference.


            To learn more, see our tips on writing great answers.




            draft saved


            draft discarded














            StackExchange.ready(
            function () {
            StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmathematica.stackexchange.com%2fquestions%2f193009%2fminimizing-with-differential-evolution%23new-answer', 'question_page');
            }
            );

            Post as a guest















            Required, but never shown





















































            Required, but never shown














            Required, but never shown












            Required, but never shown







            Required, but never shown

































            Required, but never shown














            Required, but never shown












            Required, but never shown







            Required, but never shown







            -

            Popular posts from this blog

            Can't compile dgruyter and caption packagesLaTeX templates/packages for writing a patent specificationLatex...

            Image
            Why does Arabsat 6A need a Falcon Heavy to launch Etiquette around loan refinance - decision is going to cost first broker a lot of money What is the PIE reconstruction for word-initial alpha with rough breathing? Is "remove commented out code" correct English? Why do I get two different answers for this counting problem? Blender 2.8 I can't see vertices, edges or faces in edit mode Where does SFDX store details about scratch orgs? 1960's book about a plague that kills all white people How can saying a song's name be a copyright violation? UK: Is there precedent for the governments e-petition site changing the ...
            Read more

            Schneeberg (Smreczany) Bibliografia | Menu...

            Image
            Szczyty w Niemczech paśmieSmreczanyn.p.m.Ochrza Schneeberg Państwo   Niemcy Położenie Bawaria Pasmo Fichtelgebirge Wysokość 1 051 m n.p.m. Położenie na mapie Bawarii Schneeberg Położenie na mapie Niemiec Schneeberg 50°03′N   11°51′E / 50,050000   11,850000 Multimedia w Wikimedia Commons Schneeberg – szczyt w paśmie Smreczany o wysokości 1051 m n.p.m., na zboczach którego znajdują się źródła rzeki Ochrza. Bibliografia | Rainer H. Schmeisser: Der Schneeberg, Beiträge zur Geschichts- und Landeskunde des Fichtelgebirges Nr. 1, Regensburg 1979 This page is only for reference, If you need detailed information, please check here
            Read more

            Hans Bellmer Spis treści Życiorys | Upamiętnienie | Przypisy | Bibliografia | Linki zewnętrzne |...

            Image
            Ludzie związani z III Liceum Ogólnokształcącym im. Adama Mickiewicza w KatowicachNiemieccy rzeźbiarzeNiemieccy malarze współcześniNiemieccy graficyLudzie urodzeni w KatowicachUrodzeni w 1902Zmarli w 1975 13 marca1902Katowicach23 lutego1975Paryżumalarzrzeźbiarzgrafikul. A. Mickiewiczaul. T. KościuszkiWyższej Szkole TechnicznejinstalacjiPaula EluardaBerlinie„tableaux vivants”NiemczechnazistówzdegenerowanąBerlinsurrealistówII wojnie światowejCamp des MillesAix-en-ProvenceParyżuUnicę ZürnPère-Lachaiseul. T. KościuszkiDział Grafiki im. Pawła Stellera Muzeum Historii Katowic2008Muzeum Historii KatowicNatalia KruszynaBerlinie Tablica pamiątkowa z 2008 roku na domu, w którym mieszkał artysta przy ul. T. Kościuszki 47 w Katowicach (2017) Grób Bellmera na cmentarzu Père-Lachaise Tablica pamiątkowa przy Ehrenfelsstraße 8a w Berlinie Budynek, w którym mieszkał artysta przy ul. T. Kościuszki 47 w Katowicach (2017) Hans Bellmer (ur. 13 marca 1902 w Katowicach [1] , zm. 23 lut...
            Read more