Storing the Results of Optimization Algorithms

Table of Contents

• Storing the results in a text file
• Obtaining the results in form of ACADO data structures
• The ACADO logging functionality (for advanced users)

This tutorial explains how to obtain and store the results of an optimization algorithm. In the previous tutorials (e.g. A Guiding Example: Time Optimal Control of a Rocket Flight ), it has already been explained how to plot the results with Gnuplot. However, once an optimization problem has been solved with ACADO, one of the first question that arises is how to obtain the numerical results.

Storing the results in a text file

The easiest way to store results with ACADO is via text files. Analogous to the Initialization of Nonlinear Optimization Algorithms initialization of optimal control algorithms, the results can e.g. be obtained by the following lines of code:

#include <acado_optimal_control.hpp>
#include <include/acado_gnuplot/gnuplot_window.hpp>

int main( )
{
        USING_NAMESPACE_ACADO
        
        // ... (IMPLEMENTATION OF THE OPTIMIZATION PROBLEM) ...
        
        OptimizationAlgorithm algorithm(ocp);
        algorithm.solve()                   ;
        
        algorithm.getDifferentialStates("states.txt"    );
        algorithm.getParameters        ("parameters.txt");
        algorithm.getControls          ("controls.txt"  );
        
        return 0;
}

The above example will store the results for differential states, parameters, and controls in the text files "states.txt", "parameters.txt", and "controls.txt", respectively. As an easy exercise, it is recommended to test the following:

• Solve an optimal control (e.g. the time optimal rocket problem).
• Store the results in text files as explained above.
• Initiliaze the optimization algorithm with the soultion and run it again.

The result of this exercise should be that the optimization algorithm detects directly that the problem is initialized in the solution and performs only one SQP iteration.

Obtaining the results in form of ACADO data structures

Similar to the storage of results in form of text files, the result can also be obtained in form of a "VariablesGrid". The class "VariablesGrid" has already been introduced in the tutorial Initialization of Nonlinear Optimization Algorithms. The syntax is analogous:

#include <acado_optimal_control.hpp>
#include <include/acado_gnuplot/gnuplot_window.hpp>

int main( )
{
        USING_NAMESPACE_ACADO
        
        // ... (IMPLEMENTATION OF THE OPTIMIZATION PROBLEM) ...
        
        OptimizationAlgorithm algorithm(ocp);
        algorithm.solve()                   ;
        
        Variables Grid states, parameters, controls;
        
        algorithm.getDifferentialStates(states    );
        algorithm.getParameters        (parameters);
        algorithm.getControls          (controls  );
        
        states.print();
        parameters.print();
        controls.print();
        
        return 0;
}

The advantage of getting the results in form of a "VariablesGrid" is that they can for example processed by a user-written C++ routine or modified and then written to a text file. In addition, in a real-time context, communication via files is not recommended and thus a "VariablesGrid" is right medium for communication in this case.

The ACADO logging functionality (for advanced users)

Another way to retrieve results is provided by the logging functionality of ACADO Toolkit. It allows you to setup so-called LogRecords to be passed to the optimization algorithm. Therein, you can specify which information you would like to log and the algorithm will take care of that. After running the optimization algorithm, the desired information is logged within your LogRecord and can be printed onto the screen or to a file. We give a simple example:

#include <acado_optimal_control.hpp>
#include <include/acado_gnuplot/gnuplot_window.hpp>

int main( )
{
        USING_NAMESPACE_ACADO
        
        // ... (IMPLEMENTATION OF THE OPTIMIZATION PROBLEM) ...
        
        OptimizationAlgorithm algorithm(ocp);
        
        // setup a logging object and flush it into the algorithm
        LogRecord logRecord( LOG_AT_EACH_ITERATION,"kkt.txt" );
        logRecord << LOG_KKT_TOLERANCE;
        
        algorithm << logRecord;
        
        // solve the optimization problem
        algorithm.solve( );
        
        // get the logging object back and print it
        algorithm.getLogRecord( logRecord );
        logRecord.print( );
        
        return 0;
}

In this example a LogRecord is defined that logs the KKT tolerance at each iteration that shall be written into the file "kkt.txt". Note that you can add more than one entry to each LogRecord and that you can flush several LogRecords containing different entries with different log schemes into the same algorithm. Also the format of the output on printing can be adjusted in detail. You might either log at each iteration as above, or only at start/end of the optimization using LOG_AT_START/LOG_AT_END, respectively. For example, the following information can be logged:

Logging name	Description
LOG_NUM_NLP_ITERATIONS	Number of iterations of the NLP solver
LOG_KKT_TOLERANCE	KKT tolerance
LOG_OBJECTIVE_FUNCTION	Objective function value
LOG_MERIT_FUNCTION_VALUE	Value of merit function
LOG_LINESEARCH_STEPLENGTH	Steplength of the line search routine (if used)
LOG_ALGREBRAIC_STATES	All algebraic states in the order of occurence
LOG_PARAMETERS	All parameters in the order of occurence
LOG_CONTROLS	All controls in the order of occurence
LOG_DISTURBANCES	All disturbances in the order of occurence
LOG_INTERMEDIATE_STATES	All intermediate states in the order of occurence
LOG_DIFFERENTIAL_STATES	All differential states in the order of occurence

This example shows you how to export multiple variables from ACADO directly to into a Matlab(TM) .m file:

#include <acado_optimal_control.hpp>
#include <include/acado_gnuplot/gnuplot_window.hpp>

int main( )
{
        USING_NAMESPACE_ACADO
        
        // ... (IMPLEMENTATION OF THE OPTIMIZATION PROBLEM) ...
        
        OptimizationAlgorithm algorithm(ocp);
        
        // setup a logging object for all states, controls,  
        // disturbances and parameters with a Matlab style result
        LogRecord logRecord( LOG_AT_END,"output.m" );
        logRecord.addItem(LOG_DIFFERENTIAL_STATES,PS_MATLAB,"STATES");
        logRecord.addItem(LOG_CONTROLS,PS_MATLAB,"CONTROLS");
        logRecord.addItem(LOG_DISTURBANCES,PS_MATLAB,"DISTURBANCES");
        logRecord.addItem(LOG_PARAMETERS,PS_MATLAB,"PARAMETERS");
        
        algorithm << logRecord;
        
        // solve the optimization problem
        algorithm.solve( );
        
        // get the logging object back and print it
        algorithm.getLogRecord( logRecord );
        logRecord.print( );
        
        return 0;
}

The resulting output.m file will contain 4 matrices. The first column will be the time, the next column(s) the appropriate data. These matrices can easily be added to your workspace. Just go to the directory where you have saved output.m and run "<em>output.m;</em>" in your command window.

Next example: Optimal Control of Hybrid- and Multi-Stage Processes