Out of memory error during parameter optimization with fmincon and parallel computing

Hello all,

I am currently running into a problem while optimizing some paremeters of my Simulink model with fmincon.

I have a really large Simulink model, where I need to optimize some parameters (here it is the third row of a matrix which is an input to a 2d lookup table). To speed up the whole process, I am using the parallel computing toolbox.

The optimization itself runs without problems and produces the required results, though I can never finish the optimization because I get an out of memory error. RAM usage is always around 90 % but it seems that Matlab extends the memory usage to my hard drive. If I wait long enough I can see, that all of my storage is used up and this is, when I get the 'Out of memory' - error.

To avoid this, I started to initialize all constant variables once on every worker and tried to reduce the number of logged signals in Simulink (now around 20 - could actually be just 2 - was around 150) and set the archive options to store 0 runs. This gave me a better performance in speed but also a longer time, until I got the error. Still it was not enough, to finish the optimization process.

I do not understand, why the memory usage is slowly increasing, since every worker initializes the variables in the base workspace once (so the memory should be allocated) and the results from each simulation run should only be available in the function 'calculate_error' and be deleted afterwards.

What is happening here and how can I change any settings to have my optimization finished?

Any help is highly appreciated! :)

% Assumptions:
% - Simulink-Model: 'TestMdl'
% - simulated signal: 'Signal_sim'
% - measured signal: 'Signal_meas'
% - Matrix: 'xMat'
% - third row of matrix has influence on the simulated signal

% load the model
mdl = 'TestMdl';

% load the parameter initial parameter for the optimization
x_opt_0 = xMat(3,:);

% define the goal function
objective = @(x) calculate_error(x, mdl);

% define the number of parameters to be optimized
num_parameters = size(x_opt_0); % Beispiel-Anzahl

% define the limits
lb = 0 * ones(num_parameters);
ub = 8191.875 * ones(num_parameters);

% define the options for fmincon
options = optimoptions('fmincon', ...
    'UseParallel', true, ...
    'MaxFunctionEvaluations', 20000, ...
    'Display', 'iter');

% load the base parameters onto every parallel worker
spmd
    mdl = load_system(mdl);
    set_param(mdl, 'SimulationMode', 'accelerator');
    set_param(mdl, 'FastRestart', 'on');
    assignin('base',"sample_time",sample_time);
    assignin('base',"sim_end_time",sim_end_time);
    assignin('base',"sim_start_time",sim_start_time);
    assignin('base',"meas_dat",meas_dat);
    assignin('base',"xMat",xMat);
end

% optimize
initial_guess = x_opt_0;
[x_opt, fval] = fmincon(objective, initial_guess, [], [], [], [], lb, ub, [], options);

%% calculate the RMSE
function RMSE = calculate_error(x, mdl)
	% assign the optimized variable x to the base workspace of the current worker
	assignin('base', 'x', x)
	% add the variable x to the matrix beeing used in the simulation
	evalin('base', 'xMat(3,:) = x;');
	% start the simulation
	simout = sim(mdl);
	% get the logged signals from the simulation
	logsout = simout.logsout;
	% get the simulated signal
	signal1 = get(logsout, 'Signal_sim').Values.Data;
	% get the measured signal
	signal2 = get(logsout, 'Signal_meas').Values.Data;
	% calculate the squared error
	squared_errors = (signal1 - signal2).^2;
	% calculate the RMSE
	RMSE = sqrt(mean(squared_errors));
end

Answer 1

[Jasvin]

Hi Justus,

While there are many moving components involved here, especially with the parallel workers, I think a possible approach would involve adjusting the solver algorithm itself. Perhaps the one you are currently using “interior-point” which is the default algorithm is not well suited for this optimization problem.

Please check out the following guide to figure out which solver algorithm works best for you,

https://www.mathworks.com/help/optim/ug/choosing-the-algorithm.html

Hope this helps!