Multi-Objective Covariance Matrix Adaptation Evolution Strategy
===============================================================
The multi-objective covariance matrix adaptation evolution strategy
(MO-CMA-ES) is one of the most powerful evolutionary algorithms for
multi-objective real-valued optimization. In Shark, we provide a
reference implementation of the algorithm (see :doxy:`MOCMA.h`).
This tutorial illustrates applying the MO-CMA-ES to the :doxy:`DTLZ2`
benchmark function. Please note that the methods presented here apply
to all multi-objective optimizers available in the Shark
library. That is, applying an optimizer to an objective function
requires the following steps:
* Instantiate and configure the objective function.
* Instantiate the optimizer.
* Configure the optimizer instance for the objective function instance.
* Execute the optimizer until a termination criterion is fulfilled.
First of all, the following header files are required: ::
// Implementation of the MO-CMA-ES
#include
// Access to benchmark functions
#include
Next, an instance of the objective function is created and configured
for a two-dimensional objective space and a three-dimensional search
space, respectively: ::
shark::DTLZ2 dtlz2;
dtlz2.setNumberOfVariables( 3 );
Thereafter, the optimizer is instantiated and initialized for the objective function instance: ::
shark::MOCMA mocma;
// Initialize the optimizer for the objective function instance.
dtlz2.init();
mocma.init( dtlz2 );
Finally, we iterate the optimizer until the objective function
instance has been evaluated 25000 times: ::
// Iterate the optimizer
while( dtlz2.evaluationCounter() < 25000 ) {
mocma.step( dtlz2 );
}
As in all optimizers, the MO-CMA keeps track of the best known solution found so far. In contrast
to single objective optimization, the solution is not a single point but a pareto front approximated by
a set of points. We can print the pareto front using the following snippet::
// Print the optimal pareto front
for( std::size_t i = 0; i < mocma.solution().size(); i++ ) {
for( std::size_t j = 0; j < dtlz2.numberOfObjectives(); j++ ) {
std::cout<< mocma.solution()[ i ].value[j]<<" ";
}
std::cout << std::endl;
}
Running the example and visualizing the resulting Pareto-front approximation with the help of gnuplot will give you the following graphics:
.. image:: ../images/mocma_dtlz2.svg
:width: 700px
:height: 500px
:align: center
Please see the file :doxy:`MOCMASimple.cpp` for the complete source code of this tutorial.