MGEOcpp - A C++ Library for MGEO

MGEOcpp is a C++ library that implements the Multiobjective Generalized Extremal Optimization algorithm. It was coded by Ronan Arraes Jardim Chagas at INPE (National Institute for Space Research, in portuguese).

MGEO

GEO is an evolutionary algorithm developed at INPE [1] that, along with its multiobjective version (M-GEO), has already been successfully applied to a myriad of optimization engineering problems:

Thermal design [2];
Structural optimization [3];
Satellite layout design [4];
Spacecraft attitude controller for a rigid-flexible satellite [5];
Design satellite constellations that minimize the average and the maximum revisit time over a region of interest [6];
Given an analysis interval and a region of interest, design satellite constellations that minimize the number of spacecraft, the mean orbital altitude, and the area not accessible [7].

The flowchart of MGEO is [7]:

The library MGEOcpp codes in C++ the algorithm presented in the MGEO flowchart. MGEOcpp is currently used in the following software:

OrbGEO - An Orbit Selection Tool for Satellite Constellations Using the Multiobjective Generalized Extremal Optimization (MGEO) Algorithm [7];

Note: MGEOcpp contains only templates. Thus, it is not supposed to add any bits to the binary unless an instance of the class MGEO is created.

Usage

The minimal working code for MGEOcpp is:

MGEO<N, nb, nf, Scalar> mgeo1(tau, ngenMax, runMax, rng_seed);
mgeo1.confDesignVars({listOfBits}, {listOfMinimumValues}, {listOfMaximumValues}, {listOfNames});
mgeo1.objectiveFunctions = &objectiveFunctions;
mgeo1.run();
mgeo1.sortParetoFrontier();
mgeo1.printParetoFrontier();

where

Parameter	Description	Type	Example
N	Number of design variables.	Integer	2
nb	Total number of bits in the string.	Integer	16
nf	Number of objective functions.	Integer	2
Scalar	Type of the design variables (OPTIONAL, default = double)	A C++ numeric type	double
tau	Parameter to set the determinism of the search.	Double	3.0
ngenMax	Maximum number of generations that will be created.	Integer	30000
runMax	Maximum number of independent runs.	Integer	50
rng_seed	Seed for the random number generator (OPTIONAL).	Integer	0
listOfBits	Number of bits for each design variable.	List of Integers	{8, 8}
listOfMinimumValues	Minimum values for each design variable.	List of Doubles	{-10.0, -5.0}
listOfMaximumValues	Maximum values for each design variable.	List of Doubles	{5.0, 2.0}
listOfNames	List with the design variable names (OPTIONAL).	List of Strings	{"Variable 1", "Variable 2"}

and objectiveFunctions must be a user-defined function that receives the design variables and computes the objective functions. It must be defined as follows:

bool objectiveFunctions(Scalar *vars, Scalar *f)
{
    1) Read the design variables vars[0], vars[1], vars[2], ..., vars[N]
    2) Compute the objective functions f[0], f[1], f[2], ..., f[nf]
    3) Return false if the objective function evaluation was not performed
       correctly or true otherwise.
}

For more information, see the example file mgeocpp_testcases.cpp.

Compilers

MGEOcpp must be compiled with a compile that supports:

C++11 standards (REQUIRED);
OpenMP (OPTIONAL, see ENABLE_OPENMP flag at CMakeLists.txt).

The supported compiler is g++ 4.8.1.

Please, let me know if you could successfully compile MGEOcpp with other compilers.

Dependencies

The following packages are necessary to compile MGEOcpp:

autoconf
automake
make
cmake
A C++ compiler that supports the C++11 standards

How to Compile

First, clone the source tree:

git clone https://github.com/ronisbr/mgeocpp.git
cd mgeocpp

Then, to compile the source code using the default example, execute:

cmake ./
make

Finally, the executable file mgeocpp_testcases should be created.

Note: if the C++ does not support OpenMP, then the option ENABLE_OPENMP in CMakeLists.txt file must be disabled.

Operational Systems

MGEOcpp should work on any operational system that has support for the required packages. However it has been only tested on openSUSE 13.1 Linux.

Please, let me know if you could successfully run MGEOcpp in other operational systems.

License

This project is released under the BSD 3-Clause License (see LICENSE file).

Authors

Ronan Arraes Jardim Chagas created MGEOcpp.

References

[1] F. L. de Sousa, F. M. Ramos, P. Paglione, and R. M. Girardi, "New stochastic algorithm for design optimization," AIAA Journal, vol. 41, no. 9, pp. 1808-1818, 2003.

[2] A. P. C. Cuco, F. L. de Sousa, V. V. Vlassov, and A. J. da Silva Neto, "Multi-objective design optimization of a new space radiator," Optimization and Engineering, vol. 12, no. 3, pp. 393-406, 2011.

[3] F. L. de Sousa and W. K. Takahashi, Generalized extremal optimization applied to three-dimensional truss design," in 18th Internation Congress of Mechanical Enginering. Ouro Preto, MG, Brazil: Associação Brasileira de Engenharia e Ciências Mecânicas, 2005.

[4] A. P. C. Cuco, F. L. de Sousa, and A. J. S. Neto, "A multi-objective methodology for spacecraft equipment layouts," Optimization and Engineering (Online), 2014.

[5] I. Mainenti-Lopes, L. C. G. Souza, and F. L. de Sousa, "Design of a nonlinear controller for a rigid-flexible satellite using multi-objective generalized extremal optimization with real codification," Shock and Vibration, vol. 19, pp. 947-956, 2012.

[6] R. L. Galski, F. L. de Sousa, and F. M. Ramos, "Application of a new multiobjective evolutionary algorithm to the optimum design of a remote sensing satellite constellation," in 5th International Conference of Inverse Problems in Engineering: Theory and Practice, Cambridge, UK, 2005.

[7] R. A. J. Chagas, R. L. Galski, F. L. de Sousa, "OrbGEO - An Orbit Selection Tool for Satellite Constellations Using the Multiobjective Generalized Extremal Optimization (MGEO) Algorithm", in 6th International Conference on Systems & Concurrent Engineering for Space Applications, Stuttgart, Germany, 2014 (in press).

ronisbr / mgeocpp