Evolutionary Approach to Approximate Digital Circuits Design
In approximate computing, the requirement of perfect functional behavior can be relaxed because some applications are inherently error resilient. Approximate circuits, which fall into the approximate computing paradigm, are designed in such a way that they do not fully implement the logic behavior g...
Saved in:
| Published in: | IEEE transactions on evolutionary computation Vol. 19; no. 3; pp. 432 - 444 |
|---|---|
| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
New York
IEEE
01.06.2015
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Subjects: | |
| ISSN: | 1089-778X, 1941-0026 |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Abstract | In approximate computing, the requirement of perfect functional behavior can be relaxed because some applications are inherently error resilient. Approximate circuits, which fall into the approximate computing paradigm, are designed in such a way that they do not fully implement the logic behavior given by the specification and, hence, their accuracy can be exchanged for lower area, delay or power consumption. In order to automate the design process, we propose to evolve approximate digital circuits that show a minimal error for a supplied amount of resources. The design process, which is based on Cartesian genetic programming (CGP), can be repeated many times in order to obtain various tradeoffs between the accuracy and area. A heuristic seeding mechanism is introduced to CGP, which allows for improving not only the quality of evolved circuits, but also reducing the time of evolution. The efficiency of the proposed method is evaluated for the gate as well as the functional level evolution. In particular, approximate multipliers and median circuits that show very good parameters in comparison with other available implementations were constructed by means of the proposed method. |
|---|---|
| AbstractList | In approximate computing, the requirement of perfect functional behavior can be relaxed because some applications are inherently error resilient. Approximate circuits, which fall into the approximate computing paradigm, are designed in such a way that they do not fully implement the logic behavior given by the specification and, hence, their accuracy can be exchanged for lower area, delay or power consumption. In order to automate the design process, we propose to evolve approximate digital circuits that show a minimal error for a supplied amount of resources. The design process, which is based on Cartesian genetic programming (CGP), can be repeated many times in order to obtain various tradeoffs between the accuracy and area. A heuristic seeding mechanism is introduced to CGP, which allows for improving not only the quality of evolved circuits, but also reducing the time of evolution. The efficiency of the proposed method is evaluated for the gate as well as the functional level evolution. In particular, approximate multipliers and median circuits that show very good parameters in comparison with other available implementations were constructed by means of the proposed method. |
| Author | Vasicek, Zdenek Sekanina, Lukas |
| Author_xml | – sequence: 1 givenname: Zdenek surname: Vasicek fullname: Vasicek, Zdenek email: vasicek@fit.vutbr.cz organization: IT4Innovations Centre of Excellence, Brno Univ. of Technol., Brno, Czech Republic – sequence: 2 givenname: Lukas surname: Sekanina fullname: Sekanina, Lukas email: sekanina@fit.vutbr.cz organization: IT4Innovations Centre of Excellence, Brno Univ. of Technol., Brno, Czech Republic |
| BookMark | eNp9kD9PwzAQxS1UJNrCB0AskZhTfInj2BJLlZY_UiWWgtgsx3GLq5AU20Htt8dRKgYGpjvp3rt795ugUdM2GqFrwDMAzO_Wy7dilmAgsyRNKeTZGRoDJxBjnNBR6DHjcZ6z9ws0cW6HgzIDPkb3y--27rxpG2mP0Xy_t61UH5Fvh_5gPqXX0cJsjZd1VBirOuNdtNDObJtLdL6RtdNXpzpFrw_LdfEUr14en4v5KlYJT32cZXijKygZIzTXSpJEYc5JSbFOK8iYrsJYy7RiEirFS5KVnEqQUNKc4FynU3Q77A2JvjrtvNi1nW3CSQGUZZQHAiyoYFAp2zpn9UbsbYhvjwKw6CGJHpLoIYkTpODJ_3hUeLTH4a009b_Om8FptNa_lygj4UtIfwAZmnat |
| CODEN | ITEVF5 |
| CitedBy_id | crossref_primary_10_1109_TEVC_2022_3169641 crossref_primary_10_1007_s10710_017_9312_1 crossref_primary_10_1080_09747338_2023_2214514 crossref_primary_10_1088_1742_6596_2107_1_012065 crossref_primary_10_1109_TVLSI_2019_2940943 crossref_primary_10_1007_s10710_016_9275_7 crossref_primary_10_1016_j_swevo_2021_100986 crossref_primary_10_1109_TEVC_2016_2591064 crossref_primary_10_1109_TCAD_2019_2915328 crossref_primary_10_1145_3711683 crossref_primary_10_1145_3527156 crossref_primary_10_1016_j_asoc_2020_106246 crossref_primary_10_1007_s10710_019_09360_6 crossref_primary_10_1007_s00500_015_1791_5 crossref_primary_10_1109_MCI_2018_2807019 crossref_primary_10_1109_TR_2016_2604918 crossref_primary_10_1109_JPROC_2020_2999613 crossref_primary_10_1007_s42979_022_01045_9 crossref_primary_10_1109_TCAD_2022_3149717 crossref_primary_10_1016_j_eswa_2025_129083 crossref_primary_10_1109_JETCAS_2020_3032495 crossref_primary_10_1016_j_micpro_2018_01_002 crossref_primary_10_1049_iet_ipr_2019_0580 crossref_primary_10_1109_JPROC_2020_3006451 crossref_primary_10_1109_TEVC_2014_2367111 crossref_primary_10_1049_iet_cdt_2017_0188 crossref_primary_10_1145_3094124 crossref_primary_10_1016_j_compeleceng_2023_108921 crossref_primary_10_1049_2024_6623637 crossref_primary_10_1109_TC_2023_3345163 crossref_primary_10_1016_j_micpro_2019_102975 crossref_primary_10_1038_s41928_024_01157_5 crossref_primary_10_1109_TCAD_2022_3197509 crossref_primary_10_1109_JPROC_2020_3014430 crossref_primary_10_1145_3492733 crossref_primary_10_1080_21681724_2021_1914183 crossref_primary_10_1109_TVLSI_2020_2967149 crossref_primary_10_1016_j_asoc_2020_106466 crossref_primary_10_1109_ACCESS_2018_2889110 crossref_primary_10_1109_TC_2018_2859960 crossref_primary_10_1007_s40031_023_00918_8 crossref_primary_10_1109_TCAD_2024_3506860 crossref_primary_10_1007_s10710_015_9257_1 crossref_primary_10_1109_ACCESS_2024_3467375 crossref_primary_10_12677_OJCS_2021_103003 crossref_primary_10_1109_TC_2016_2632722 crossref_primary_10_1109_TEVC_2017_2672689 crossref_primary_10_1016_j_knosys_2016_03_009 crossref_primary_10_1145_3716845 crossref_primary_10_1016_j_cie_2022_108792 crossref_primary_10_1016_j_matpr_2022_06_386 |
| Cites_doi | 10.1109/TEVC.2006.871253 10.1109/AHS.2010.5546262 10.1109/MCI.2006.1597058 10.1109/TCAD.2012.2217962 10.1007/s10710-006-9005-7 10.1007/978-3-642-17310-3 10.1109/ICCAD.2011.6105401 10.1145/1837274.1837491 10.1007/3-540-61723-X_970 10.1109/EH.2000.869344 10.1007/s10710-011-9141-6 10.1109/ETS.2013.6569370 10.1145/2228360.2228504 10.1007/s10710-011-9132-7 10.1007/978-3-642-29139-5_23 10.1109/MICRO.2012.48 10.1023/A:1010066330916 10.1109/TSMCB.2006.872259 10.1166/jolpe.2011.1157 10.1109/4235.788489 10.1145/1108956.1108957 10.1016/j.asoc.2008.08.004 10.1145/1993498.1993518 10.1109/ICES.2013.6613278 10.1109/4235.996017 10.7873/DATE.2013.280 10.1109/EH.1999.785429 |
| ContentType | Journal Article |
| Copyright | Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) Jun 2015 |
| Copyright_xml | – notice: Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) Jun 2015 |
| DBID | 97E RIA RIE AAYXX CITATION 7SC 7SP 8FD JQ2 L7M L~C L~D |
| DOI | 10.1109/TEVC.2014.2336175 |
| DatabaseName | IEEE Xplore (IEEE) IEEE All-Society Periodicals Package (ASPP) 1998–Present IEEE Xplore Digital Library CrossRef Computer and Information Systems Abstracts Electronics & Communications Abstracts Technology Research Database ProQuest Computer Science Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional |
| DatabaseTitle | CrossRef Technology Research Database Computer and Information Systems Abstracts – Academic Electronics & Communications Abstracts ProQuest Computer Science Collection Computer and Information Systems Abstracts Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Professional |
| DatabaseTitleList | Technology Research Database |
| Database_xml | – sequence: 1 dbid: RIE name: IEEE Electronic Library (IEL) url: https://ieeexplore.ieee.org/ sourceTypes: Publisher |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering Statistics Computer Science |
| EISSN | 1941-0026 |
| EndPage | 444 |
| ExternalDocumentID | 3704210641 10_1109_TEVC_2014_2336175 6848841 |
| Genre | orig-research |
| GrantInformation_xml | – fundername: IT4Innovations Centre of Excellence grantid: CZ.1.05/1.1.00/02.0070 – fundername: Brno University of Technology grantid: FIT-S-14-2297 |
| GroupedDBID | -~X .DC 0R~ 29I 4.4 5GY 5VS 6IF 6IK 6IL 6IN 97E AAJGR AARMG AASAJ AAWTH ABAZT ABJNI ABQJQ ABVLG ACGFO ACGFS ACIWK ADZIZ AENEX AETIX AGQYO AGSQL AHBIQ AI. AIBXA AKJIK AKQYR ALLEH ALMA_UNASSIGNED_HOLDINGS ATWAV BEFXN BFFAM BGNUA BKEBE BPEOZ CHZPO CS3 EBS EJD HZ~ H~9 IEGSK IFIPE IFJZH IPLJI JAVBF LAI M43 O9- OCL P2P PQQKQ RIA RIE RIL RNS TN5 VH1 AAYXX CITATION 7SC 7SP 8FD JQ2 L7M L~C L~D |
| ID | FETCH-LOGICAL-c293t-550fed1b88467eca42c0994b60e3d158edfedea3d8a1dc9b45b96a1a1b67407e3 |
| IEDL.DBID | RIE |
| ISICitedReferencesCount | 91 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000356517700009&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 1089-778X |
| IngestDate | Sun Nov 30 04:47:14 EST 2025 Tue Nov 18 20:44:38 EST 2025 Sat Nov 29 03:13:47 EST 2025 Tue Aug 26 16:40:05 EDT 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 3 |
| Keywords | Cartesian genetic programming (CGP) population seeding digital circuits Approximate computing |
| Language | English |
| License | https://ieeexplore.ieee.org/Xplorehelp/downloads/license-information/IEEE.html |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c293t-550fed1b88467eca42c0994b60e3d158edfedea3d8a1dc9b45b96a1a1b67407e3 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| PQID | 1685691098 |
| PQPubID | 85418 |
| PageCount | 13 |
| ParticipantIDs | ieee_primary_6848841 crossref_primary_10_1109_TEVC_2014_2336175 crossref_citationtrail_10_1109_TEVC_2014_2336175 proquest_journals_1685691098 |
| PublicationCentury | 2000 |
| PublicationDate | 2015-June 2015-6-00 20150601 |
| PublicationDateYYYYMMDD | 2015-06-01 |
| PublicationDate_xml | – month: 06 year: 2015 text: 2015-June |
| PublicationDecade | 2010 |
| PublicationPlace | New York |
| PublicationPlace_xml | – name: New York |
| PublicationTitle | IEEE transactions on evolutionary computation |
| PublicationTitleAbbrev | TEVC |
| PublicationYear | 2015 |
| Publisher | IEEE The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Publisher_xml | – name: IEEE – name: The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| References | ref13 ref12 ref15 murakawa (ref14) 1996 gordon (ref17) 2005 ref33 ref11 ref32 ref10 ref2 ref1 ref16 ref19 ref18 greenwood (ref22) 2007 ref24 ref20 ref21 miller (ref31) 2011 miller (ref30) 2000; 1 ref28 ref27 ref29 ref8 ref7 ref9 knuth (ref34) 1998 ref4 ref3 ref6 ref5 sentovich (ref25) 1992 knieper (ref23) 2010 petrlik (ref26) 2013 |
| References_xml | – ident: ref32 doi: 10.1109/TEVC.2006.871253 – ident: ref27 doi: 10.1109/AHS.2010.5546262 – start-page: 116 year: 2013 ident: ref26 article-title: Multiobjective evolution of approximate multiple constant multipliers publication-title: IEEE Design Diagnost Electron Circuits Syst Symp – year: 2005 ident: ref17 article-title: Exploiting development to enhance the scalability of hardware evolution – ident: ref8 doi: 10.1109/MCI.2006.1597058 – ident: ref2 doi: 10.1109/TCAD.2012.2217962 – ident: ref33 doi: 10.1007/s10710-006-9005-7 – year: 2011 ident: ref31 publication-title: Cartesian Genetic Programming doi: 10.1007/978-3-642-17310-3 – ident: ref13 doi: 10.1109/ICCAD.2011.6105401 – start-page: 250 year: 2010 ident: ref23 article-title: Coping with resource fluctuations: The run-time reconfigurable functional unit row classifier architecture publication-title: Proc Int Conf Evolvable Syst – ident: ref12 doi: 10.1145/1837274.1837491 – start-page: 62 year: 1996 ident: ref14 article-title: Evolvable hardware at function level publication-title: Parallel Problem Solving from Nature - PPSN IV doi: 10.1007/3-540-61723-X_970 – ident: ref18 doi: 10.1109/EH.2000.869344 – ident: ref9 doi: 10.1007/s10710-011-9141-6 – ident: ref1 doi: 10.1109/ETS.2013.6569370 – ident: ref4 doi: 10.1145/2228360.2228504 – ident: ref19 doi: 10.1007/s10710-011-9132-7 – ident: ref20 doi: 10.1007/978-3-642-29139-5_23 – ident: ref5 doi: 10.1109/MICRO.2012.48 – year: 2007 ident: ref22 publication-title: Introduction to Evolvable Hardware – ident: ref29 doi: 10.1023/A:1010066330916 – year: 1992 ident: ref25 article-title: SIS: A system for sequential circuit synthesis – ident: ref16 doi: 10.1109/TSMCB.2006.872259 – ident: ref3 doi: 10.1166/jolpe.2011.1157 – ident: ref24 doi: 10.1109/4235.788489 – volume: 1 start-page: 8 year: 2000 ident: ref30 article-title: Principles in the evolutionary design of digital circuits-Part I publication-title: Genet Program Evolvable Mach – ident: ref11 doi: 10.1145/1108956.1108957 – ident: ref15 doi: 10.1016/j.asoc.2008.08.004 – ident: ref6 doi: 10.1145/1993498.1993518 – ident: ref10 doi: 10.1109/ICES.2013.6613278 – year: 1998 ident: ref34 publication-title: The Art of Computer Programming Sorting and Searching – ident: ref28 doi: 10.1109/4235.996017 – ident: ref7 doi: 10.7873/DATE.2013.280 – ident: ref21 doi: 10.1109/EH.1999.785429 |
| SSID | ssj0014519 |
| Score | 2.4550335 |
| Snippet | In approximate computing, the requirement of perfect functional behavior can be relaxed because some applications are inherently error resilient. Approximate... |
| SourceID | proquest crossref ieee |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 432 |
| SubjectTerms | Approximation methods Circuit synthesis Delays Logic gates Power demand Sociology Statistics |
| Title | Evolutionary Approach to Approximate Digital Circuits Design |
| URI | https://ieeexplore.ieee.org/document/6848841 https://www.proquest.com/docview/1685691098 |
| Volume | 19 |
| WOSCitedRecordID | wos000356517700009&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVIEE databaseName: IEEE Electronic Library (IEL) customDbUrl: eissn: 1941-0026 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0014519 issn: 1089-778X databaseCode: RIE dateStart: 19970101 isFulltext: true titleUrlDefault: https://ieeexplore.ieee.org/ providerName: IEEE |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV3PS8MwFH7M4WEenG6K0yk9eBK7NWvTJuBl7AceZHiYsltJ01cpyCZdN_S_N2mzoiiCt0CTUPIleV-S974HcO1SHyVLIjuhRNgejYjNYyFs6iKTgjMv4UWg8EMwm7HFgj_W4LaKhUHEwvkMe7pYvOXHK7nRV2V9n6nppqPU94LAL2O1qhcDLZNSOtNzxRjZwrxgEof355PnkXbi8noD11UWm36zQUVSlR87cWFeps3__dgRHBoaaQ1L3I-hhssWNHcpGiyzYltw8EVvsAUNTS1LZeY23E22ZtqJ7MMaGm1xK1-V5fdUcVm0xumLTitijdJMbtJ8bY0Ll48TeJpO5qN72-RSsKUy6LmtDiIJxiRimm-gFN5AKm7oRb6Dbkwow1h9RuHGTJBY8kihxn1BBIn8QJ350D2F-nK1xDOwlFl1tAg94zopuL4SoQpQlI4M1P4RsQ44u9ENpREa1_kuXsPiwOHwUAMSakBCA0gHbqomb6XKxl-V2xqBqqIZ_A50dxCGZh2uQ-Iz6itGxNn5760uoKH6pqXzVxfqebbBS9iXW4VGdlVMsU9Wo85L |
| linkProvider | IEEE |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV3PS8MwFH6MKagHp5vidGoPnsRuzdp0CXgZ-8HEOTxM2a2k6asMZJOuG_rfm7TZUBTBW6AJKfmSvC_Je98DuHKpj5LFoR1TImyPhsTmkRA2dZFJwZkX8yxQeNgajdhkwh8LcLOJhUHEzPkM67qYveVHc7nUV2UNn6nppqPUt6jnNZ08WmvzZqCFUnJ3eq44I5uYN0zi8Ma499zRblxevem6ymbTb1YoS6vyYy_ODEy_9L9fO4B9QyStdo78IRRwVobSOkmDZdZsGfa-KA6WYVeTy1ybuQK3vZWZeCL5sNpGXdxK53n5farYLFrd6YtOLGJ1polcTtOF1c2cPo7gqd8bdwa2yaZgS2XSU1sdRWKMSMg040ApvKZU7NALfQfdiFCGkfqMwo2YIJHkocKN-4IIEvotdepD9xiKs_kMT8BShtXRMvSM67Tg-lKEKkhROrKldpCQVcFZj24gjdS4znjxGmRHDocHGpBAAxIYQKpwvWnyluts_FW5ohHYVDSDX4XaGsLArMRFQHxGfcWJODv9vdUl7AzGD8NgeDe6P4Nd1Q_NXcFqUEyTJZ7DtlwpZJKLbLp9Ajw30ZI |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Evolutionary+Approach+to+Approximate+Digital+Circuits+Design&rft.jtitle=IEEE+transactions+on+evolutionary+computation&rft.au=Vasicek%2C+Zdenek&rft.au=Sekanina%2C+Lukas&rft.date=2015-06-01&rft.pub=The+Institute+of+Electrical+and+Electronics+Engineers%2C+Inc.+%28IEEE%29&rft.issn=1089-778X&rft.eissn=1941-0026&rft.volume=19&rft.issue=3&rft.spage=432&rft_id=info:doi/10.1109%2FTEVC.2014.2336175&rft.externalDBID=NO_FULL_TEXT&rft.externalDocID=3704210641 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1089-778X&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1089-778X&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1089-778X&client=summon |