Pattern search with integer decision variable.

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Matlab Noob 2016-5-25

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https://ww2.mathworks.cn/matlabcentral/answers/285753-pattern-search-with-integer-decision-variable

评论： Alan Weiss 2019-2-7

采纳的回答： Alan Weiss

Hello.

I tried to solve Nonlinear integer programming to minimize using Optimization tool box.

I understand how I input both objective function and nonlinear constraint function.

However, I don't know how I obtain some decision variable are integer and others are real variable. Cuz, there is no option in pattern search tool box and function in matlab.

Are there any method to get integer variable using pattern search in matlab tool box?

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Answer 1

Alan Weiss 2016-5-25

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If you have mixed (some integer, some continuous) variables, then no, there is currently no patternsearch solution. Use ga for this type of problem.

However, if all your variables are integer-valued, then you might be able to use patternsearch. Start at an integer point, set ScaleMesh off, and set TolMesh to 0.9 or so. I believe that, with those settings, patternsearch will search only integer points.

Alan Weiss

MATLAB mathematical toolbox documentation

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Doug Rank 2017-11-14

在 MATLAB Online 中打开

Hi Alan,

I have tried with these options:

        opts = optimoptions('patternsearch', ...
            'ScaleMesh', false, ...
            'MeshTolerance', 0.99);

And called patternsearch by:

        [x, fval, exitflag, output] = patternsearch(fitnessFunction, ...
            xo, A, b, [], [], zeros(1, nVariables), ...
            ones(1, nVariables), [], opts);

(where xo is one of the feasible initial population members I was giving to the ga() before, A and b are the original linear constraint matrices I was using, and nVariables is the length of xo).

However, I got this error:

Error using lcondirections (line 38) Constraints are dependent at current iterate. Try increasing OPTIONS.TolBind (< eps).

Error in poll (line 60) [DirVector,TangentCone] = lcondirections(AdaptiveMesh,MeshSize,Iterate.x, ...

Error in pfminlcon (line 62) [successPoll,nextIterate,optimState] = poll(FUN,X,Iterate,MeshSize,Aineq,bineq, ...

Error in patternsearch (line 377) [X,FVAL,EXITFLAG,OUTPUT] = pfminlcon(FUN,objFcnArg,initialX,numberOfVariables,Iterate, ...

Error in optimize (line 385) [x, fval, exitflag, output] = patternsearch(fitnessFunction, ...

I also tried modifying the options after googling the error to:

        opts = optimoptions('patternsearch', ...
            'ScaleMesh', false, ...
            'PollMethod', 'GSSPositiveBasis2N', ...
            'MeshTolerance', 0.99);

and got a similar error ending in:

Error using gssdirections (line 39) Constraints are dependent at current iterate. Try increasing OPTIONS.TolBind (< eps).

Error in poll (line 57) [DirVector,TangentCone,AugmentedDirs] = gssdirections(MeshSize,Iterate.x, ...

Would you happen to know what the issue may be here?

Ryan Potter 2019-2-7

在 MATLAB Online 中打开

Hi, I just wanted to check whether this advice was still valid? I have followed the points above but still generate non-integer values. I'm using the following code:

fun     = @computeMagVol;
x0      = [10,25,20,2];
A       = [];
b       = [];
Aeq     = [];
beq     = [];
lb      = [1, 1, 1,1];
ub      = [21,51,41,4];
nonlcon = @combineConstraints;
options = optimoptions('patternsearch',            ...
                       'PollMethod'     , 'GPSPositiveBasis2N', ...
                       'Display'        , 'Iter',  ...
                       'ScaleMesh'      , 'off',   ...
                       'AccelerateMesh' , false,   ...
                       'TolMesh'        , 0.9,    ...
                       'PlotFcn'        ,{@psplotbestf,@psplotmeshsize});
[x,fval,exitflag,output] = patternsearch(fun,x0,A,b,Aeq,beq,lb,ub,nonlcon,options);

My objective function use the integer variables to select discrete, non-integer variables from a list. After the following computations:

  Iter   Func-count       f(x)      Constraint   MeshSize      Method
    0         1      75615.1        104.4          0.9        
    1        50      71970.7            0        0.001   Increase penalty

I obtain that x = [1 44.5, 21, 4] which causes my objective function calculation to fail. The same functions work with the ga algorithm, however I was hoping to use patternsearch as it supports having the object function and non-linear constraints in a single function. Any advice would be greatly appreciated.

Alan Weiss 2019-2-7

As I said earlier, I am not at all sure that this method works when you have nonlinear constraints. Sorry.

Alan Weiss

MATLAB mathematical toolbox documentation

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Answer 2

Benjamin Duquenne 2017-6-1

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Hi, I would like to use patternsearch for full integer problems. To do so, I set the ScaleMesh off, and set TolMesh to 0.9. However I still have problems with the TolBind that has to be way too high (~1e3) to make the code work, otherwise I have errors like 'Constraints are dependent at current iterate'. Could you help me? Thanks in advance.