# How can I make patternsearch optimize using additional values?

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Kei Manabe on 4 Jun 2020
Commented: Kei Manabe on 3 Jul 2020
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);
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);

Alan Weiss on 5 Jun 2020
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:
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);
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
Kei Manabe on 3 Jul 2020
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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