Speeding up many-objective optimization by Monte Carlo approximations
Many state-of-the-art evolutionary vector optimization algorithms compute the contributing hypervolume for ranking candidate solutions. However, with an increasing number of objectives, calculating the volumes becomes intractable. Therefore, although hypervolume-based algorithms are often the method...
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| Vydáno v: | Artificial intelligence Ročník 204; s. 22 - 29 |
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| Hlavní autoři: | , , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
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Oxford
Elsevier B.V
01.11.2013
Elsevier |
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| ISSN: | 0004-3702, 1872-7921 |
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| Abstract | Many state-of-the-art evolutionary vector optimization algorithms compute the contributing hypervolume for ranking candidate solutions. However, with an increasing number of objectives, calculating the volumes becomes intractable. Therefore, although hypervolume-based algorithms are often the method of choice for bi-criteria optimization, they are regarded as not suitable for many-objective optimization. Recently, Monte Carlo methods have been derived and analyzed for approximating the contributing hypervolume. Turning theory into practice, we employ these results in the ranking procedure of the multi-objective covariance matrix adaptation evolution strategy (MO-CMA-ES) as an example of a state-of-the-art method for vector optimization. It is empirically shown that the approximation does not impair the quality of the obtained solutions given a budget of objective function evaluations, while considerably reducing the computation time in the case of multiple objectives. These results are obtained on common benchmark functions as well as on two design optimization tasks. Thus, employing Monte Carlo approximations makes hypervolume-based algorithms applicable to many-objective optimization. |
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| AbstractList | Many state-of-the-art evolutionary vector optimization algorithms compute the contributing hypervolume for ranking candidate solutions. However, with an increasing number of objectives, calculating the volumes becomes intractable. Therefore, although hypervolume-based algorithms are often the method of choice for bi-criteria optimization, they are regarded as not suitable for many-objective optimization. Recently, Monte Carlo methods have been derived and analyzed for approximating the contributing hypervolume. Turning theory into practice, we employ these results in the ranking procedure of the multi-objective covariance matrix adaptation evolution strategy (MO-CMA-ES) as an example of a state-of-the-art method for vector optimization. It is empirically shown that the approximation does not impair the quality of the obtained solutions given a budget of objective function evaluations, while considerably reducing the computation time in the case of multiple objectives. These results are obtained on common benchmark functions as well as on two design optimization tasks. Thus, employing Monte Carlo approximations makes hypervolume-based algorithms applicable to many-objective optimization. |
| Author | Bringmann, Karl Voß, Thomas Friedrich, Tobias Igel, Christian |
| Author_xml | – sequence: 1 givenname: Karl surname: Bringmann fullname: Bringmann, Karl organization: Max-Planck-Institut für Informatik, Saarbrücken, Germany – sequence: 2 givenname: Tobias surname: Friedrich fullname: Friedrich, Tobias email: friedrich@uni-jena.de organization: Friedrich-Schiller-Universität Jena, Germany – sequence: 3 givenname: Christian surname: Igel fullname: Igel, Christian organization: Department of Computer Science, University of Copenhagen, Denmark – sequence: 4 givenname: Thomas surname: Voß fullname: Voß, Thomas organization: Institut für Neuroinformatik, Ruhr-Universität, Bochum, Germany |
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| Cites_doi | 10.1016/j.ejor.2006.08.008 10.1109/4235.996017 10.1109/TEVC.2010.2077298 10.1162/EVCO_a_00012 10.1016/j.tcs.2010.09.026 10.1023/B:NACO.0000023416.59689.4e 10.1007/s10994-009-5102-1 10.1109/TEVC.2003.810758 10.1016/j.comgeo.2011.12.001 10.1162/evco.2007.15.1.1 10.1109/TEVC.2008.919001 10.4249/scholarpedia.1965 10.1109/4235.797969 10.1162/106365601750190398 10.1016/j.artint.2012.09.005 10.1162/EVCO_a_00009 10.1016/j.comgeo.2010.03.004 10.1162/evco.2009.17.4.17402 |
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| Keywords | Pareto-front approximation Multi-objective optimization Hypervolume indicator Evolutionary algorithm Monte Carlo method Dominating set Pareto optimum Hierarchical classification Objective analysis Multiobjective programming Covariance matrix Approximation algorithm Vector method Modeling Function evaluation Computation time Budget Objective function Vector optimization |
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| SubjectTerms | Algorithmics. Computability. Computer arithmetics Applied sciences Computer science; control theory; systems Decision theory. Utility theory Evolutionary algorithm Exact sciences and technology Hypervolume indicator Mathematical programming Multi-objective optimization Operational research and scientific management Operational research. Management science Pareto-front approximation Theoretical computing |
| Title | Speeding up many-objective optimization by Monte Carlo approximations |
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