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

The meaning of ‘otherwise’

Confusion about Complex Continued Fraction

What is Tony Stark injecting into himself in Iron Man 3?

Why do phishing e-mails use faked e-mail addresses instead of the real one?

What do *foreign films* mean for an American?

What problems would a superhuman have who's skin is constantly hot?

Is this Paypal Github SDK reference really a dangerous site?

School performs periodic password audits. Is my password compromised?

Haman going to the second feast dirty

Minimizing with differential evolution

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

Is it possible to avoid unpacking when merging Association?

Why is gluten-free baking possible?

Expressing logarithmic equations without logs

What ability score modifier does a javelin's damage use?

How does Ehrenfest's theorem apply to the quantum harmonic oscillator?

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

Called into a meeting and told we are being made redundant (laid off) and "not to share outside". Can I tell my partner?

How many characters using PHB rules does it take to be able to have access to any PHB spell at the start of an adventuring day?

How can I manipulate the output of Information?

Recommendation letter by significant other if you worked with them professionally?

When a wind turbine does not produce enough electricity how does the power company compensate for the loss?

Source permutation

For which categories of spectra is there an explicit description of the fibrant objects via lifting properties?



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
    55 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
    55 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
    55 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
    55 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
55 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
55 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

            El tren de la libertad Índice Antecedentes "Porque yo decido" Desarrollo de la...

            Image
            Feminismo en EspañaAborto en EspañaManifestaciones y protestas en EspañaManifestaciones y protestas en 2014España en 2014Historia de las mujeres en España movimiento socialfeministaderechos sexuales y reproductivosmujeresLey del aborto en España1 de febrero2014MadridAlberto Ruíz Gallardónla ley del aborto vigente del 2010AsturiasTertulia Feminista Les ComadresCongreso de DiputadosAlicia MiyaresAna MatoAlberto Ruiz GallardónEdimburgoRomaParísLuxemburgoBuenos AiresGracia QuerejetaÁngeles González-SindeMabel LozanoIcíar BollaínIsabel CoixetGeorgina CisquellaTeresa FontVirginia Yagüe2010José Luis Rodríguez ZapateroCongreso de Diputados19 de diciembre20095 de julio2010Partido PopularTribunal Constitucional201120 de diciembre2013Partido PopularMariano RajoyGijónTertulia Feminista Les ComadresBegoña PiñeroRenfeAlicia MiyaresTertulia Feminista Les Comadres1 de febrero2014Congreso de DiputadosMariano RajoyAlberto Ruiz GallardónAna MatoAsturiasAndalucíaCanariasCataluñaComunidad ValencianaCasti
            Read more

            Puerta de Hutt Referencias Enlaces externos Menú de navegación15°58′00″S 5°42′00″O /...

            Image
            Localidades de Santa Elena inglésasentamientoisla Santa ElenaLongwoodIglesia de San MateoPico de DianaNapoleón BonaparteHenri Gratien BertrandAlarma ForestalLevelwoodSan Pablo Puerta de Hutt Hutt's Gate Asentamiento Puerta de Hutt Hutt's Gate Coordenadas 15°58′00″S 5°42′00″O  /  -15.96666667, -5.7 Coordenadas: 15°58′00″S 5°42′00″O  /  -15.96666667, -5.7 Entidad Asentamiento  • País   Reino Unido  • Territorio de ultramar   Santa Elena, Ascensión y Tristán de Acuña  • Isla Santa Elena Huso horario UTC+0 [editar datos en Wikidata] Puerta de Hutt (en inglés: Hutt's Gate ) es un pequeño asentamiento ubicado en la isla Santa Elena, que forma parte del distrito de Longwood. Se ubica en las coordenadas 15°58′00″S 5°42′00″O  /  -15.96667, -5.70000 . [ 1 ] ​ Aquí se localiza la Iglesia de San Mateo y en sus cercanías el Pico de Diana [ 2 ] ​ y la tumba de Napoleón Bonaparte. Es una amplia zona residencial y cuent
            Read more

            Castillo d'Acher Características Menú de navegación

            Image
            Montañas de los Pirineos de AragónMontañas de la provincia de Huesca msnmSelva de OzaPirineo aragonésEspañabosque Este artículo o sección necesita referencias que aparezcan en una publicación acreditada. Este aviso fue puesto el 11 de agosto de 2011. El pico desde Selva de Oza. El Castillo d' Acher es una cima de 2.384msnm en la zona de la Selva de Oza en la parte occidental del Pirineo aragonés, en España. Debe su nombre a su aspecto de fortaleza que presenta hacia todas sus vertientes. Características En orden ascendente, la cima pasa de un bosque frondoso de tonalidades verde-amarillenta a laderas rojizas. Su cima, que suele presentarse mucha nieve, es un pequeño valle rectangular rodeado en sus cuatro caras por una muralla que le da un aspecto de fortaleza. This page is only for reference, If you need detailed information, please check here
            Read more