Minimizing with differential evolution












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










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
    53 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










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
    53 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










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






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
    53 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
    53 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
53 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
53 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

            Knooppunt Holsloot

            Altaar (religie)

            Gregoriusmis