{"id":"https://openalex.org/W2091339908","doi":"https://doi.org/10.1007/s10589-007-9138-5","title":"Global optimization of truss topology with discrete bar areas\u2014Part\u00a0I: theory of relaxed problems","display_name":"Global optimization of truss topology with discrete bar areas\u2014Part\u00a0I: theory of relaxed problems","publication_year":2007,"publication_date":"2007-11-13","ids":{"openalex":"https://openalex.org/W2091339908","doi":"https://doi.org/10.1007/s10589-007-9138-5","mag":"2091339908"},"language":"en","primary_location":{"id":"doi:10.1007/s10589-007-9138-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10589-007-9138-5","pdf_url":null,"source":{"id":"https://openalex.org/S39243548","display_name":"Computational Optimization and Applications","issn_l":"0926-6003","issn":["0926-6003","1573-2894"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Optimization and Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5000532918","display_name":"Wolfgang Achtziger","orcid":null},"institutions":[{"id":"https://openalex.org/I200332995","display_name":"TU Dortmund University","ror":"https://ror.org/01k97gp34","country_code":"DE","type":"education","lineage":["https://openalex.org/I200332995"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Wolfgang Achtziger","raw_affiliation_strings":["Institute of Applied Mathematics, University of Dortmund, FB Mathematics, LS X, 44221, Dortmund, Germany","Institute of Applied Mathematics, University of Dortmund, Dortmund, Germany 44221#TAB#"],"affiliations":[{"raw_affiliation_string":"Institute of Applied Mathematics, University of Dortmund, FB Mathematics, LS X, 44221, Dortmund, Germany","institution_ids":["https://openalex.org/I200332995"]},{"raw_affiliation_string":"Institute of Applied Mathematics, University of Dortmund, Dortmund, Germany 44221#TAB#","institution_ids":["https://openalex.org/I200332995"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5035840714","display_name":"Mathias Stolpe","orcid":"https://orcid.org/0000-0002-5858-1595"},"institutions":[{"id":"https://openalex.org/I96673099","display_name":"Technical University of Denmark","ror":"https://ror.org/04qtj9h94","country_code":"DK","type":"education","lineage":["https://openalex.org/I96673099"]}],"countries":["DK"],"is_corresponding":false,"raw_author_name":"Mathias Stolpe","raw_affiliation_strings":["Department of Mathematics, Technical University of Denmark, Matematiktorvet Building 303 S, 2800, Kgs. Lyngby, Denmark","Department of Mathematics, Technical University of Denmark, Kgs. Lyngby, Denmark 2800#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Technical University of Denmark, Matematiktorvet Building 303 S, 2800, Kgs. Lyngby, Denmark","institution_ids":["https://openalex.org/I96673099"]},{"raw_affiliation_string":"Department of Mathematics, Technical University of Denmark, Kgs. Lyngby, Denmark 2800#TAB#","institution_ids":["https://openalex.org/I96673099"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5000532918"],"corresponding_institution_ids":["https://openalex.org/I200332995"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":11.0055,"has_fulltext":false,"cited_by_count":39,"citation_normalized_percentile":{"value":0.98093964,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"40","issue":"2","first_page":"247","last_page":"280"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11115","display_name":"Topology Optimization in Engineering","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11115","display_name":"Topology Optimization in Engineering","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11870","display_name":"Structural Analysis and Optimization","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10571","display_name":"Robotic Mechanisms and Dynamics","score":0.9975000023841858,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6656627655029297},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.6476826667785645},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6154698133468628},{"id":"https://openalex.org/keywords/hessian-matrix","display_name":"Hessian matrix","score":0.6088473200798035},{"id":"https://openalex.org/keywords/global-optimization","display_name":"Global optimization","score":0.5277312994003296},{"id":"https://openalex.org/keywords/truss","display_name":"Truss","score":0.503868043422699},{"id":"https://openalex.org/keywords/heuristic","display_name":"Heuristic","score":0.4995236396789551},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.4891253113746643},{"id":"https://openalex.org/keywords/branch-and-bound","display_name":"Branch and bound","score":0.4649558961391449},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.46271631121635437},{"id":"https://openalex.org/keywords/continuous-optimization","display_name":"Continuous optimization","score":0.45577266812324524},{"id":"https://openalex.org/keywords/discrete-optimization","display_name":"Discrete optimization","score":0.4487692713737488},{"id":"https://openalex.org/keywords/nonlinear-programming","display_name":"Nonlinear programming","score":0.42473304271698},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4122937321662903},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.29911941289901733},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.23848730325698853}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6656627655029297},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.6476826667785645},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6154698133468628},{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.6088473200798035},{"id":"https://openalex.org/C164752517","wikidata":"https://www.wikidata.org/wiki/Q5570875","display_name":"Global optimization","level":2,"score":0.5277312994003296},{"id":"https://openalex.org/C173534245","wikidata":"https://www.wikidata.org/wiki/Q1328068","display_name":"Truss","level":2,"score":0.503868043422699},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.4995236396789551},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.4891253113746643},{"id":"https://openalex.org/C93693863","wikidata":"https://www.wikidata.org/wiki/Q897659","display_name":"Branch and bound","level":2,"score":0.4649558961391449},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.46271631121635437},{"id":"https://openalex.org/C92995354","wikidata":"https://www.wikidata.org/wiki/Q5165499","display_name":"Continuous optimization","level":4,"score":0.45577266812324524},{"id":"https://openalex.org/C145671259","wikidata":"https://www.wikidata.org/wiki/Q1493786","display_name":"Discrete optimization","level":3,"score":0.4487692713737488},{"id":"https://openalex.org/C115527620","wikidata":"https://www.wikidata.org/wiki/Q769909","display_name":"Nonlinear programming","level":3,"score":0.42473304271698},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4122937321662903},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.29911941289901733},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.23848730325698853},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C122357587","wikidata":"https://www.wikidata.org/wiki/Q6934508","display_name":"Multi-swarm optimization","level":3,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10589-007-9138-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10589-007-9138-5","pdf_url":null,"source":{"id":"https://openalex.org/S39243548","display_name":"Computational Optimization and Applications","issn_l":"0926-6003","issn":["0926-6003","1573-2894"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Optimization and Applications","raw_type":"journal-article"},{"id":"pmh:oai:pure.atira.dk:publications/e428514e-e8ed-4f96-a7bc-c31d4555103b","is_oa":false,"landing_page_url":"https://orbit.dtu.dk/en/publications/e428514e-e8ed-4f96-a7bc-c31d4555103b","pdf_url":null,"source":{"id":"https://openalex.org/S4306400705","display_name":"Technical University of Denmark, DTU Orbit (Technical University of Denmark, DTU)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I96673099","host_organization_name":"Technical University of Denmark","host_organization_lineage":["https://openalex.org/I96673099"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Achtziger , W & Stolpe , M 2008 , ' Global optimization of truss topology with discrete bar areas\u2014Part I: Theory of relaxed problems ' , Computational Optimization and Applications , vol. 40 , no. 2 , pp. 247-280 . https://doi.org/10.1007/s10589-007-9138-5","raw_type":"article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W100573512","https://openalex.org/W203192772","https://openalex.org/W1568307856","https://openalex.org/W1575923498","https://openalex.org/W1812813109","https://openalex.org/W1970321781","https://openalex.org/W1977244564","https://openalex.org/W1979682513","https://openalex.org/W1988183637","https://openalex.org/W2006917077","https://openalex.org/W2018476085","https://openalex.org/W2035238076","https://openalex.org/W2037909160","https://openalex.org/W2038873290","https://openalex.org/W2040794831","https://openalex.org/W2065323347","https://openalex.org/W2070543752","https://openalex.org/W2071910487","https://openalex.org/W2081636333","https://openalex.org/W2081730441","https://openalex.org/W2089986028","https://openalex.org/W2131687653","https://openalex.org/W2136885855","https://openalex.org/W2180914311","https://openalex.org/W2484584864","https://openalex.org/W2495457432","https://openalex.org/W2995530868","https://openalex.org/W4237218133","https://openalex.org/W4249667877"],"related_works":["https://openalex.org/W2353523849","https://openalex.org/W2366218906","https://openalex.org/W2359046253","https://openalex.org/W4375949242","https://openalex.org/W1527736507","https://openalex.org/W4378977544","https://openalex.org/W4309490307","https://openalex.org/W2373554757","https://openalex.org/W2065543187","https://openalex.org/W2037420682"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}