
Attainment Function Tools Library
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The empirical first-order attainment function (EAF) is used to assess the
performance of stochastic multiobjective optimisers such as multiobjective
evolutionary algorithms [3].  It is an estimator for the first-order
attainment function, which provides information about the location and, to
some extent, the variability of the random sets of non-dominated objective
vectors produced by such optimisers when applied to given problem instances.

This library computes the EAF from non-dominated sets of two objective
vectors and perform statistical hypothesis tests using the
empirical first or second-order attainment functions, as described in [4].
It is based on the original work of Andreia P. Guerreiro,
Carlos M. Fonseca, Manuel López-Ibáñez and Luís Paquete available
on http://eden.dei.uc.pt/~cmfonsec/software.html.

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License
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Copyright © 2013 Humberto Alves, 2011 Andreia P. Guerreiro, Carlos M. Fonseca,
Manuel López-Ibáñez and Luís Paquete

This program is free software. You can redistribute it and/or modify it
under the terms of the GNU General Public License as published by the Free
Software Foundation; either version 2 of the License, or (at your option)
any later version.

This program is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License for
more details.

Appropriate reference to this software should be made when describing
research in which it played a substantive role, so that it may be replicated
and verified by others.  The EAF computation problem and the algorithms
which this software implements are described in detail in [1].

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Download
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The latest version of this software may be downloaded from
https://bitbucket.org/hjalves/libaft/get/tip.tar.gz

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Building and Usage
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In GNU/Linux, the shared library can be compiled from source by running make.

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References and related literature
---------------------------------

[1] C. M. Fonseca, A. P. Guerreiro, M. López-Ibáñez, and L. Paquete, "On the
    computation of the empirical attainment function," in Evolutionary
    Multi-Criterion Optimization. Sixth International Conference, EMO 2011
    (R. H. C. Takahashi et al., eds.), vol. 6576 of Lecture Notes in Computer
    Science, pp. 106-120, Berlin: Springer, 2011. To appear.

[2] Manuel López-Ibáñez, Luís Paquete, and Thomas Stützle, "Exploratory
    analysis of stochastic local search algorithms in biobjective optimization,"
    in Experimental Methods for the Analysis of Optimization Algorithms
    (T. Bartz-Beielstein, M. Chiarandini, L. Paquete, and M. Preuss, eds.),
    ch. 9, pp. 209-222, Springer Berlin Heidelberg, 2010.

[3] V. Grunert da Fonseca and C. M. Fonseca, "The attainment-function approach
    to stochastic multiobjective optimizer assessment and comparison," in
    Experimental Methods for the Analysis of Optimization Algorithms
    (T. Bartz-Beielstein, M. Chiarandini, L. Paquete, and M. Preuss, eds.),
    ch. 5, pp. 103-130, Springer Berlin Heidelberg, 2010.

[4] C. M. Fonseca, V. Grunert da Fonseca, and L. Paquete, "Exploring the
    performance of stochastic multiobjective optimisers with the second-order
    attainment function," in Evolutionary Multi-Criterion Optimization. Third
    International Conference, EMO 2005 (C. A. Coello Coello, A. Hernández
    Aguirre, and E. Zitzler, eds.), vol. 3410 of Lecture Notes in Computer
    Science, pp. 250-264, Berlin: Springer, 2005.

[5] V. Grunert da Fonseca, C. M. Fonseca, and A. O. Hall, "Inferential
    performance assessment of stochastic optimisers and the attainment
    function," in  Evolutionary Multi-Criterion Optimization. First
    International Conference, EMO 2001 (E. Zitzler, K. Deb, L. Thiele,
    C. A. Coello Coello, and D. Corne, eds.), vol. 1993 of Lecture Notes in
    Computer Science, pp. 213-225, Berlin: Springer, 2001.

[6] C. M. Fonseca and P. J. Fleming, "On the performance assessment and
    comparison of stochastic multiobjective optimizers," in Parallel Problem
    Solving from Nature - PPSN IV (H.-M. Voigt, W. Ebeling, I. Rechenberg,
    and H.-P. Schwefel, eds.), vol. 1141 of Lecture Notes in Computer Science,
    pp. 584-593, Berlin: Springer, 1996.

