A faster algorithm for calculating hypervolume
We present an algorithm for calculating hypervolume exactly, the Hypervolume by Slicing Objectives (HSO) algorithm, that is faster than any that has previously been published. HSO processes objectives instead of points, an idea that has been considered before but that has never been properly evaluat...
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| Veröffentlicht in: | IEEE transactions on evolutionary computation 2006-02, Vol.10 (1), p.29-38 |
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| container_title | IEEE transactions on evolutionary computation |
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| creator | While, L. Hingston, P. Barone, L. Huband, S. |
| description | We present an algorithm for calculating hypervolume exactly, the Hypervolume by Slicing Objectives (HSO) algorithm, that is faster than any that has previously been published. HSO processes objectives instead of points, an idea that has been considered before but that has never been properly evaluated in the literature. We show that both previously studied exact hypervolume algorithms are exponential in at least the number of objectives and that although HSO is also exponential in the number of objectives in the worst case, it runs in significantly less time, i.e., two to three orders of magnitude less for randomly generated and benchmark data in three to eight objectives. Thus, HSO increases the utility of hypervolume, both as a metric for general optimization algorithms and as a diversity mechanism for evolutionary algorithms. |
| doi_str_mv | 10.1109/TEVC.2005.851275 |
| format | Article |
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HSO processes objectives instead of points, an idea that has been considered before but that has never been properly evaluated in the literature. We show that both previously studied exact hypervolume algorithms are exponential in at least the number of objectives and that although HSO is also exponential in the number of objectives in the worst case, it runs in significantly less time, i.e., two to three orders of magnitude less for randomly generated and benchmark data in three to eight objectives. Thus, HSO increases the utility of hypervolume, both as a metric for general optimization algorithms and as a diversity mechanism for evolutionary algorithms.</description><identifier>ISSN: 1089-778X</identifier><identifier>EISSN: 1941-0026</identifier><identifier>DOI: 10.1109/TEVC.2005.851275</identifier><identifier>CODEN: ITEVF5</identifier><language>eng</language><publisher>New York, NY: IEEE</publisher><subject>Algorithmics. Computability. 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HSO processes objectives instead of points, an idea that has been considered before but that has never been properly evaluated in the literature. We show that both previously studied exact hypervolume algorithms are exponential in at least the number of objectives and that although HSO is also exponential in the number of objectives in the worst case, it runs in significantly less time, i.e., two to three orders of magnitude less for randomly generated and benchmark data in three to eight objectives. Thus, HSO increases the utility of hypervolume, both as a metric for general optimization algorithms and as a diversity mechanism for evolutionary algorithms.</description><subject>Algorithmics. Computability. Computer arithmetics</subject><subject>Algorithms</subject><subject>Applied sciences</subject><subject>Australia Council</subject><subject>Benchmarking</subject><subject>Computer science</subject><subject>Computer science; control theory; systems</subject><subject>Evolutionary algorithms</subject><subject>Evolutionary computation</subject><subject>Exact sciences and technology</subject><subject>Extraterrestrial measurements</subject><subject>hypervolume</subject><subject>Mathematical analysis</subject><subject>multiobjective optimization</subject><subject>Optimization</subject><subject>performance metrics</subject><subject>Polynomials</subject><subject>Random number generation</subject><subject>Size measurement</subject><subject>Slicing</subject><subject>Software engineering</subject><subject>Theoretical computing</subject><subject>Utilities</subject><issn>1089-778X</issn><issn>1941-0026</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2006</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNp9kEtLw0AQgIMoWKt3wUsQ1FPi7Cb7OkqpDyh4qeJt2Wx325Q86m4i9N-7IYWCB08zzHwzzHxRdI0gRQjE43L-OUsxAEk5QZiRk2iCRI4SAExPQw5cJIzxr_PowvstAMoJEpMofYqt8p1xsarWrSu7TR3b1sVaVbqvVFc263iz3xn301Z9bS6jM6sqb64OcRp9PM-Xs9dk8f7yNntaJJpkvEuYAAwabK6xQcwSw8SqYIJybQrBVxZRGq7MkeXMFgKLkKoiK0yoipXNUDaNHsa9O9d-98Z3si69NlWlGtP2XnJBEadABvL-XxJzAJEJHsDbP-C27V0TvpCcEkozBCxAMELatd47Y-XOlbVye4lADp7l4FkOnuXoOYzcHfYqH6xZpxpd-uMcyzlGJA_czciVxphjm_CMYpL9AtlIhBg</recordid><startdate>20060201</startdate><enddate>20060201</enddate><creator>While, L.</creator><creator>Hingston, P.</creator><creator>Barone, L.</creator><creator>Huband, S.</creator><general>IEEE</general><general>Institute of Electrical and Electronics Engineers</general><general>The Institute of Electrical and Electronics Engineers, Inc. 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| identifier | ISSN: 1089-778X |
| ispartof | IEEE transactions on evolutionary computation, 2006-02, Vol.10 (1), p.29-38 |
| issn | 1089-778X 1941-0026 |
| language | eng |
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| source | IEEE Electronic Library (IEL) |
| subjects | Algorithmics. Computability. Computer arithmetics Algorithms Applied sciences Australia Council Benchmarking Computer science Computer science control theory systems Evolutionary algorithms Evolutionary computation Exact sciences and technology Extraterrestrial measurements hypervolume Mathematical analysis multiobjective optimization Optimization performance metrics Polynomials Random number generation Size measurement Slicing Software engineering Theoretical computing Utilities |
| title | A faster algorithm for calculating hypervolume |
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