Metamodel-assisted optimization based on multiple kernel regression for mixed variables

Abstract While studies in metamodel-assisted optimization predominantly involve continuous variables, this paper explores the additional presence of categorical data, representing for instance the choice of a material or the type of connection. The common approach consisting in mapping them onto int...
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Autor*in:	Herrera, Manuel [verfasserIn] Guglielmetti, Aurore Xiao, Manyu Filomeno Coelho, Rajan

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2014

Schlagwörter:	Multiple kernel regression Mixed variables Metamodels Categorical variables Dummy coding

Anmerkung:	© Springer-Verlag Berlin Heidelberg 2014

Übergeordnetes Werk:	Enthalten in: Structural and multidisciplinary optimization - Berlin : Springer, 1989, 49(2014), 6 vom: 10. Jan., Seite 979-991
Übergeordnetes Werk:	volume:49 ; year:2014 ; number:6 ; day:10 ; month:01 ; pages:979-991

Links:	Volltext

DOI / URN:	10.1007/s00158-013-1029-z

Katalog-ID:	SPR001318640

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520			\|a Abstract While studies in metamodel-assisted optimization predominantly involve continuous variables, this paper explores the additional presence of categorical data, representing for instance the choice of a material or the type of connection. The common approach consisting in mapping them onto integers might lead to inconsistencies or poor approximation results. Therefore, an investigation of the best coding is necessary; however, to build accurate and flexible metamodels, a special attention should also be devoted to the treatment of the distinct nature of the variables involved. Consequently, a multiple kernel regression methodology is proposed, since it allows for selecting separate kernel functions with respect to the variable type. The validation of the advocated approach is carried out on six analytical benchmark test cases and on the structural responses of a rigid frame. In all cases, better performances are obtained by multiple kernel regression with respect to its single kernel counterpart, thereby demonstrating the potential offered by this approach, especially in combination with dummy coding. Finally, multi-objective surrogate-based optimization is performed on the rigid frame example, firstly to illustrate the benefit of dealing with mixed variables for structural design, then to show the reduction in terms of finite element simulations obtained thanks to the metamodels.
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700	1		\|a Filomeno Coelho, Rajan \|4 aut
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allfields	10.1007/s00158-013-1029-z doi (DE-627)SPR001318640 (SPR)s00158-013-1029-z-e DE-627 ger DE-627 rakwb eng Herrera, Manuel verfasserin aut Metamodel-assisted optimization based on multiple kernel regression for mixed variables 2014 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag Berlin Heidelberg 2014 Abstract While studies in metamodel-assisted optimization predominantly involve continuous variables, this paper explores the additional presence of categorical data, representing for instance the choice of a material or the type of connection. The common approach consisting in mapping them onto integers might lead to inconsistencies or poor approximation results. Therefore, an investigation of the best coding is necessary; however, to build accurate and flexible metamodels, a special attention should also be devoted to the treatment of the distinct nature of the variables involved. Consequently, a multiple kernel regression methodology is proposed, since it allows for selecting separate kernel functions with respect to the variable type. The validation of the advocated approach is carried out on six analytical benchmark test cases and on the structural responses of a rigid frame. In all cases, better performances are obtained by multiple kernel regression with respect to its single kernel counterpart, thereby demonstrating the potential offered by this approach, especially in combination with dummy coding. Finally, multi-objective surrogate-based optimization is performed on the rigid frame example, firstly to illustrate the benefit of dealing with mixed variables for structural design, then to show the reduction in terms of finite element simulations obtained thanks to the metamodels. Multiple kernel regression (dpeaa)DE-He213 Mixed variables (dpeaa)DE-He213 Metamodels (dpeaa)DE-He213 Categorical variables (dpeaa)DE-He213 Dummy coding (dpeaa)DE-He213 Guglielmetti, Aurore aut Xiao, Manyu aut Filomeno Coelho, Rajan aut Enthalten in Structural and multidisciplinary optimization Berlin : Springer, 1989 49(2014), 6 vom: 10. Jan., Seite 979-991 (DE-627)271602503 (DE-600)1481279-4 1615-1488 nnns volume:49 year:2014 number:6 day:10 month:01 pages:979-991 https://dx.doi.org/10.1007/s00158-013-1029-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 49 2014 6 10 01 979-991
spelling	10.1007/s00158-013-1029-z doi (DE-627)SPR001318640 (SPR)s00158-013-1029-z-e DE-627 ger DE-627 rakwb eng Herrera, Manuel verfasserin aut Metamodel-assisted optimization based on multiple kernel regression for mixed variables 2014 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag Berlin Heidelberg 2014 Abstract While studies in metamodel-assisted optimization predominantly involve continuous variables, this paper explores the additional presence of categorical data, representing for instance the choice of a material or the type of connection. The common approach consisting in mapping them onto integers might lead to inconsistencies or poor approximation results. Therefore, an investigation of the best coding is necessary; however, to build accurate and flexible metamodels, a special attention should also be devoted to the treatment of the distinct nature of the variables involved. Consequently, a multiple kernel regression methodology is proposed, since it allows for selecting separate kernel functions with respect to the variable type. The validation of the advocated approach is carried out on six analytical benchmark test cases and on the structural responses of a rigid frame. In all cases, better performances are obtained by multiple kernel regression with respect to its single kernel counterpart, thereby demonstrating the potential offered by this approach, especially in combination with dummy coding. Finally, multi-objective surrogate-based optimization is performed on the rigid frame example, firstly to illustrate the benefit of dealing with mixed variables for structural design, then to show the reduction in terms of finite element simulations obtained thanks to the metamodels. Multiple kernel regression (dpeaa)DE-He213 Mixed variables (dpeaa)DE-He213 Metamodels (dpeaa)DE-He213 Categorical variables (dpeaa)DE-He213 Dummy coding (dpeaa)DE-He213 Guglielmetti, Aurore aut Xiao, Manyu aut Filomeno Coelho, Rajan aut Enthalten in Structural and multidisciplinary optimization Berlin : Springer, 1989 49(2014), 6 vom: 10. Jan., Seite 979-991 (DE-627)271602503 (DE-600)1481279-4 1615-1488 nnns volume:49 year:2014 number:6 day:10 month:01 pages:979-991 https://dx.doi.org/10.1007/s00158-013-1029-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 49 2014 6 10 01 979-991
allfields_unstemmed	10.1007/s00158-013-1029-z doi (DE-627)SPR001318640 (SPR)s00158-013-1029-z-e DE-627 ger DE-627 rakwb eng Herrera, Manuel verfasserin aut Metamodel-assisted optimization based on multiple kernel regression for mixed variables 2014 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag Berlin Heidelberg 2014 Abstract While studies in metamodel-assisted optimization predominantly involve continuous variables, this paper explores the additional presence of categorical data, representing for instance the choice of a material or the type of connection. The common approach consisting in mapping them onto integers might lead to inconsistencies or poor approximation results. Therefore, an investigation of the best coding is necessary; however, to build accurate and flexible metamodels, a special attention should also be devoted to the treatment of the distinct nature of the variables involved. Consequently, a multiple kernel regression methodology is proposed, since it allows for selecting separate kernel functions with respect to the variable type. The validation of the advocated approach is carried out on six analytical benchmark test cases and on the structural responses of a rigid frame. In all cases, better performances are obtained by multiple kernel regression with respect to its single kernel counterpart, thereby demonstrating the potential offered by this approach, especially in combination with dummy coding. Finally, multi-objective surrogate-based optimization is performed on the rigid frame example, firstly to illustrate the benefit of dealing with mixed variables for structural design, then to show the reduction in terms of finite element simulations obtained thanks to the metamodels. Multiple kernel regression (dpeaa)DE-He213 Mixed variables (dpeaa)DE-He213 Metamodels (dpeaa)DE-He213 Categorical variables (dpeaa)DE-He213 Dummy coding (dpeaa)DE-He213 Guglielmetti, Aurore aut Xiao, Manyu aut Filomeno Coelho, Rajan aut Enthalten in Structural and multidisciplinary optimization Berlin : Springer, 1989 49(2014), 6 vom: 10. Jan., Seite 979-991 (DE-627)271602503 (DE-600)1481279-4 1615-1488 nnns volume:49 year:2014 number:6 day:10 month:01 pages:979-991 https://dx.doi.org/10.1007/s00158-013-1029-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 49 2014 6 10 01 979-991
allfieldsGer	10.1007/s00158-013-1029-z doi (DE-627)SPR001318640 (SPR)s00158-013-1029-z-e DE-627 ger DE-627 rakwb eng Herrera, Manuel verfasserin aut Metamodel-assisted optimization based on multiple kernel regression for mixed variables 2014 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag Berlin Heidelberg 2014 Abstract While studies in metamodel-assisted optimization predominantly involve continuous variables, this paper explores the additional presence of categorical data, representing for instance the choice of a material or the type of connection. The common approach consisting in mapping them onto integers might lead to inconsistencies or poor approximation results. Therefore, an investigation of the best coding is necessary; however, to build accurate and flexible metamodels, a special attention should also be devoted to the treatment of the distinct nature of the variables involved. Consequently, a multiple kernel regression methodology is proposed, since it allows for selecting separate kernel functions with respect to the variable type. The validation of the advocated approach is carried out on six analytical benchmark test cases and on the structural responses of a rigid frame. In all cases, better performances are obtained by multiple kernel regression with respect to its single kernel counterpart, thereby demonstrating the potential offered by this approach, especially in combination with dummy coding. Finally, multi-objective surrogate-based optimization is performed on the rigid frame example, firstly to illustrate the benefit of dealing with mixed variables for structural design, then to show the reduction in terms of finite element simulations obtained thanks to the metamodels. Multiple kernel regression (dpeaa)DE-He213 Mixed variables (dpeaa)DE-He213 Metamodels (dpeaa)DE-He213 Categorical variables (dpeaa)DE-He213 Dummy coding (dpeaa)DE-He213 Guglielmetti, Aurore aut Xiao, Manyu aut Filomeno Coelho, Rajan aut Enthalten in Structural and multidisciplinary optimization Berlin : Springer, 1989 49(2014), 6 vom: 10. Jan., Seite 979-991 (DE-627)271602503 (DE-600)1481279-4 1615-1488 nnns volume:49 year:2014 number:6 day:10 month:01 pages:979-991 https://dx.doi.org/10.1007/s00158-013-1029-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 49 2014 6 10 01 979-991
allfieldsSound	10.1007/s00158-013-1029-z doi (DE-627)SPR001318640 (SPR)s00158-013-1029-z-e DE-627 ger DE-627 rakwb eng Herrera, Manuel verfasserin aut Metamodel-assisted optimization based on multiple kernel regression for mixed variables 2014 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag Berlin Heidelberg 2014 Abstract While studies in metamodel-assisted optimization predominantly involve continuous variables, this paper explores the additional presence of categorical data, representing for instance the choice of a material or the type of connection. The common approach consisting in mapping them onto integers might lead to inconsistencies or poor approximation results. Therefore, an investigation of the best coding is necessary; however, to build accurate and flexible metamodels, a special attention should also be devoted to the treatment of the distinct nature of the variables involved. Consequently, a multiple kernel regression methodology is proposed, since it allows for selecting separate kernel functions with respect to the variable type. The validation of the advocated approach is carried out on six analytical benchmark test cases and on the structural responses of a rigid frame. In all cases, better performances are obtained by multiple kernel regression with respect to its single kernel counterpart, thereby demonstrating the potential offered by this approach, especially in combination with dummy coding. Finally, multi-objective surrogate-based optimization is performed on the rigid frame example, firstly to illustrate the benefit of dealing with mixed variables for structural design, then to show the reduction in terms of finite element simulations obtained thanks to the metamodels. Multiple kernel regression (dpeaa)DE-He213 Mixed variables (dpeaa)DE-He213 Metamodels (dpeaa)DE-He213 Categorical variables (dpeaa)DE-He213 Dummy coding (dpeaa)DE-He213 Guglielmetti, Aurore aut Xiao, Manyu aut Filomeno Coelho, Rajan aut Enthalten in Structural and multidisciplinary optimization Berlin : Springer, 1989 49(2014), 6 vom: 10. Jan., Seite 979-991 (DE-627)271602503 (DE-600)1481279-4 1615-1488 nnns volume:49 year:2014 number:6 day:10 month:01 pages:979-991 https://dx.doi.org/10.1007/s00158-013-1029-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 49 2014 6 10 01 979-991
language	English
source	Enthalten in Structural and multidisciplinary optimization 49(2014), 6 vom: 10. Jan., Seite 979-991 volume:49 year:2014 number:6 day:10 month:01 pages:979-991
sourceStr	Enthalten in Structural and multidisciplinary optimization 49(2014), 6 vom: 10. Jan., Seite 979-991 volume:49 year:2014 number:6 day:10 month:01 pages:979-991
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Multiple kernel regression Mixed variables Metamodels Categorical variables Dummy coding
isfreeaccess_bool	false
container_title	Structural and multidisciplinary optimization
authorswithroles_txt_mv	Herrera, Manuel @@aut@@ Guglielmetti, Aurore @@aut@@ Xiao, Manyu @@aut@@ Filomeno Coelho, Rajan @@aut@@
publishDateDaySort_date	2014-01-10T00:00:00Z
hierarchy_top_id	271602503
id	SPR001318640
language_de	englisch
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author	Herrera, Manuel
spellingShingle	Herrera, Manuel misc Multiple kernel regression misc Mixed variables misc Metamodels misc Categorical variables misc Dummy coding Metamodel-assisted optimization based on multiple kernel regression for mixed variables
authorStr	Herrera, Manuel
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topic_title	Metamodel-assisted optimization based on multiple kernel regression for mixed variables Multiple kernel regression (dpeaa)DE-He213 Mixed variables (dpeaa)DE-He213 Metamodels (dpeaa)DE-He213 Categorical variables (dpeaa)DE-He213 Dummy coding (dpeaa)DE-He213
topic	misc Multiple kernel regression misc Mixed variables misc Metamodels misc Categorical variables misc Dummy coding
topic_unstemmed	misc Multiple kernel regression misc Mixed variables misc Metamodels misc Categorical variables misc Dummy coding
topic_browse	misc Multiple kernel regression misc Mixed variables misc Metamodels misc Categorical variables misc Dummy coding
format_facet	Elektronische Aufsätze Aufsätze Elektronische Ressource
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title	Metamodel-assisted optimization based on multiple kernel regression for mixed variables
ctrlnum	(DE-627)SPR001318640 (SPR)s00158-013-1029-z-e
title_full	Metamodel-assisted optimization based on multiple kernel regression for mixed variables
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author_browse	Herrera, Manuel Guglielmetti, Aurore Xiao, Manyu Filomeno Coelho, Rajan
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doi_str_mv	10.1007/s00158-013-1029-z
title_sort	metamodel-assisted optimization based on multiple kernel regression for mixed variables
title_auth	Metamodel-assisted optimization based on multiple kernel regression for mixed variables
abstract	Abstract While studies in metamodel-assisted optimization predominantly involve continuous variables, this paper explores the additional presence of categorical data, representing for instance the choice of a material or the type of connection. The common approach consisting in mapping them onto integers might lead to inconsistencies or poor approximation results. Therefore, an investigation of the best coding is necessary; however, to build accurate and flexible metamodels, a special attention should also be devoted to the treatment of the distinct nature of the variables involved. Consequently, a multiple kernel regression methodology is proposed, since it allows for selecting separate kernel functions with respect to the variable type. The validation of the advocated approach is carried out on six analytical benchmark test cases and on the structural responses of a rigid frame. In all cases, better performances are obtained by multiple kernel regression with respect to its single kernel counterpart, thereby demonstrating the potential offered by this approach, especially in combination with dummy coding. Finally, multi-objective surrogate-based optimization is performed on the rigid frame example, firstly to illustrate the benefit of dealing with mixed variables for structural design, then to show the reduction in terms of finite element simulations obtained thanks to the metamodels. © Springer-Verlag Berlin Heidelberg 2014
abstractGer	Abstract While studies in metamodel-assisted optimization predominantly involve continuous variables, this paper explores the additional presence of categorical data, representing for instance the choice of a material or the type of connection. The common approach consisting in mapping them onto integers might lead to inconsistencies or poor approximation results. Therefore, an investigation of the best coding is necessary; however, to build accurate and flexible metamodels, a special attention should also be devoted to the treatment of the distinct nature of the variables involved. Consequently, a multiple kernel regression methodology is proposed, since it allows for selecting separate kernel functions with respect to the variable type. The validation of the advocated approach is carried out on six analytical benchmark test cases and on the structural responses of a rigid frame. In all cases, better performances are obtained by multiple kernel regression with respect to its single kernel counterpart, thereby demonstrating the potential offered by this approach, especially in combination with dummy coding. Finally, multi-objective surrogate-based optimization is performed on the rigid frame example, firstly to illustrate the benefit of dealing with mixed variables for structural design, then to show the reduction in terms of finite element simulations obtained thanks to the metamodels. © Springer-Verlag Berlin Heidelberg 2014
abstract_unstemmed	Abstract While studies in metamodel-assisted optimization predominantly involve continuous variables, this paper explores the additional presence of categorical data, representing for instance the choice of a material or the type of connection. The common approach consisting in mapping them onto integers might lead to inconsistencies or poor approximation results. Therefore, an investigation of the best coding is necessary; however, to build accurate and flexible metamodels, a special attention should also be devoted to the treatment of the distinct nature of the variables involved. Consequently, a multiple kernel regression methodology is proposed, since it allows for selecting separate kernel functions with respect to the variable type. The validation of the advocated approach is carried out on six analytical benchmark test cases and on the structural responses of a rigid frame. In all cases, better performances are obtained by multiple kernel regression with respect to its single kernel counterpart, thereby demonstrating the potential offered by this approach, especially in combination with dummy coding. Finally, multi-objective surrogate-based optimization is performed on the rigid frame example, firstly to illustrate the benefit of dealing with mixed variables for structural design, then to show the reduction in terms of finite element simulations obtained thanks to the metamodels. © Springer-Verlag Berlin Heidelberg 2014
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container_issue	6
title_short	Metamodel-assisted optimization based on multiple kernel regression for mixed variables
url	https://dx.doi.org/10.1007/s00158-013-1029-z
remote_bool	true
author2	Guglielmetti, Aurore Xiao, Manyu Filomeno Coelho, Rajan
author2Str	Guglielmetti, Aurore Xiao, Manyu Filomeno Coelho, Rajan
ppnlink	271602503
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doi_str	10.1007/s00158-013-1029-z
up_date	2024-07-03T21:45:24.897Z
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Metamodel-assisted optimization based on multiple kernel regression for mixed variables

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