How can I make patternsearch optimize using additional values?

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Kei Manabe 2020-6-4

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https://ww2.mathworks.cn/matlabcentral/answers/542501-how-can-i-make-patternsearch-optimize-using-additional-values

评论： Kei Manabe 2020-7-3

I am trying to optimize the Page test parameters. In the last two lines, as the cost function of patternsearch, "RSS" is calculated. Basically, I would like to find the parameters to minimize RSS. However, I would like to make patternsearch optimize considering other values: n_1, n_19, n_27, n_29, n_47. These values should be larger than 30. Is there any way or idea to have additional constraints for patternsearch? Thank you so much in advance.

rand1 = rand(1)*1000; rand2 = rand(1)*1000; rand3 = rand(1); rand4 = rand(1)/100;
param0 = [round(max(rand1,rand2)), round(min(rand1,rand2)), round(rand3, 2), round(rand4, 5)];
options = optimoptions('patternsearch', 'PlotFcn', 'psplotbestx', 'MeshTolerance', 1, 'ScaleMesh', false, 'InitialMeshSize',10);
A = [];
b = [];
Aeq = [];
beq = [];
nlcon = [];
lb = [1 1 0.1 1/500000];
ub = [100000 100000 10 1/25000];
fun = @do;
[param, RSS, exitflag, ~] = patternsearch(fun, param0, A, b, Aeq, beq, lb, ub, nlcon, options);
function RSS = do(param)
load y_highpass_TK_short y_highpass_TK_short
n_1_groundtruth = 46;
n_19_groundtruth = 43;
n_27_groundtruth = 38;
n_29_groundtruth = 35;
n_47_groundtruth = 40;
T0 = param(1);
T1 = param(2);
T2 = param(3);
alpha = param(4);
[Vn_1, ~, loc_maxima_1, N_1] = doPagetest_loop(y_highpass_TK_short{1}, T0, T1, T2, alpha);
n_1 = length(Vn_1(loc_maxima_1==1));
[Vn_19, ~, loc_maxima_19, N_19] = doPagetest_loop(y_highpass_TK_short{2}, T0, T1, T2, alpha);
n_19 = length(Vn_19(loc_maxima_19==1));
[Vn_27, ~, loc_maxima_27, N_27] = doPagetest_loop(y_highpass_TK_short{3}, T0, T1, T2, alpha);
n_27 = length(Vn_27(loc_maxima_27==1));
[Vn_29, ~, loc_maxima_29, N_29] = doPagetest_loop(y_highpass_TK_short{4}, T0, T1, T2, alpha);
n_29 = length(Vn_29(loc_maxima_29==1));
[Vn_47, ~, loc_maxima_47, N_47] = doPagetest_loop(y_highpass_TK_short{5}, T0, T1, T2, alpha);
n_47 = length(Vn_47(loc_maxima_47==1));
RSS = sqrt((n_1-n_1_groundtruth)^2 + (n_19-n_19_groundtruth)^2 + (n_27-n_27_groundtruth)^2 ...
    + (n_29-n_29_groundtruth)^2 + (n_47-n_47_groundtruth)^2);

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Answer 1

Alan Weiss 2020-6-5

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https://ww2.mathworks.cn/matlabcentral/answers/542501-how-can-i-make-patternsearch-optimize-using-additional-values#answer_446726

在 MATLAB Online 中打开

Before I get to your specific question, allow me an observation: it is very inefficient to call a load statement in an objective function. I think that you will have much better luck passing in fixed data using a parameterization technique.

Now for your specific question. If you also want to optimize over the variables n_1, n_19, n_27, n_29, and n_47, then I suggest that you make these variables part of your optimization. Append them to your params vector as follows:

function RSS = do(params,extradata) % extradata are the values in y_highpass_TK_short y_highpass_TK_short
T0 = params(1);
T1 = params(2);
T2 = params(3);
alpha = params(4);
n_1 = params(5);
n_19 = params(6);
n_27 = params(7);
n_29 = params(8);
n_47 = params(9);
% Your code here
end

To keep params(5:9) above 30 during the optimization, set lower bounds:

lb = 30*ones(1,9);
lb(1:4) = [1 1 0.1 1/500000];

Extend the ub vector to be of length 9 as well.

Alan Weiss

MATLAB mathematical toolbox documentation

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Alan Weiss 2020-6-7

在 MATLAB Online 中打开

In that case, I believe that you should calculate the parameters

n_1
n_19
n_27
n_29
n_47

in the objective AND nonlinear constraint functions. The nonlinear constraint function could be, assuming that the constraint is that all of these parameters are larger than 30,

function [c,ceq] = nlcon(param)
pagetestoutput = page(param); % the function that computes the values
c = pagetestoutput; % I assume pagetestoutput is a vector of 5 values
ceq = [];
end

It is important that your objective and constraint function both call page. Something like:

function RSS = do(param)
pagetestoutput = page(param); % the function that computes the values
n_1_groundtruth = pagetestoutput(1);
n_19_groundtruth = pagetestoutput(2);
n_27_groundtruth = pagetestoutput(3);
n_29_groundtruth = pagetestoutput(4);
n_47_groundtruth = pagetestoutput(5);
% Now do the remaining calculations
end

You might object at this point that you are calculating page(param) more often than necessary. That is true; for more efficiency, see Objective and Nonlinear Constraints in the Same Function.

Alan Weiss

MATLAB mathematical toolbox documentation

Alan Weiss 2020-7-2

Your understanding is not quite right. Solvers attempt to find a feasible solution, not first a solution and then feasibility. In fact, you might want to check whether any feasible solution exists. Try the suggestions in Converged to an Infeasible Point.

Good luck,

Alan Weiss

MATLAB mathematical toolbox documentation

Kei Manabe 2020-7-3

Thank you so much.

I am relieved to know the MATLAB optimization doesn't apply the nonlinear constraint after optimal answer is found.

I will try to understand more with the linked document.

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