MGEOjulia is a Julia 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).
The code was based on MGEOCpp
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 MGEOjulia codes in Julia the algorithm presented in the MGEO flowchart.
The minimal working code for MGEOjulia is:
using MGEOjulia
designVars = confDesignVars(N, {listOfBits}, {listOfMinimumValues}, {listOfMaximumValues}, {listOfNames})
mgeoData = MGEOStructure(nf, tau, ngenMax, runMax, designVars)
paretoFrontier = MGEOrun(mgeoData, f_obj)
savePFtoCSV("output.csv", designVars, paretoFrontier)
where
| Parameter | Description | Type | Example |
|---|---|---|---|
| N | Number of design variables. | Int64 | 2 |
| nf | Number of objective functions. | Int64 | 2 |
| tau | Parameter to set the determinism of the search. | Float64 | 3.0 |
| ngenMax | Maximum number of generations that will be created. | Int64 | 30000 |
| runMax | Maximum number of independent runs. | Int64 | 50 |
| listOfBits | Number of bits for each design variable. | Array{Int64,1} | [8, 8] |
| listOfMinimumValues | Minimum values for each design variable. | Array{Float64,1} | [-10.0, -5.0] |
| listOfMaximumValues | Maximum values for each design variable. | Array{Float64,1} | [5.0, 2.0] |
| listOfNames | List with the design variable names (OPTIONAL). | Array{Strings,1} | ["Variable 1", "Variable 2"] |
and f_obj must be a user-defined function that receives the design variables and computes the objective functions. It must be defined as follows:
function f_obj(vars::Array{Float64,1})
1) Read the design variables vars[1], vars[2], vars[3], ..., vars[N]
2) Compute the objective functions f[1], f[2], f[3], ..., f[nf]
3) Return (valid, f), where variable valid is false if the objective
function evaluation was not performed correctly or true otherwise.
end
For more information, see the example file mgeojulia_testcases.cpp.
The package is tested against julia v0.5, but it should also work in julia v0.4.
This project is released under the BSD 3-Clause License (see LICENSE.md file).
Ronan Arraes Jardim Chagas created MGEOjulia.
[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.