{"id":"https://openalex.org/W1536347593","doi":"https://doi.org/10.1007/978-3-642-01020-0_28","title":"Multiobjective Decomposition of Positive Integer Matrix: Application to Radiotherapy","display_name":"Multiobjective Decomposition of Positive Integer Matrix: Application to Radiotherapy","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W1536347593","doi":"https://doi.org/10.1007/978-3-642-01020-0_28","mag":"1536347593"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-642-01020-0_28","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-01020-0_28","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","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/A5054715902","display_name":"Thibaut Lust","orcid":"https://orcid.org/0000-0001-8433-518X"},"institutions":[{"id":"https://openalex.org/I130929987","display_name":"University of Mons","ror":"https://ror.org/02qnnz951","country_code":"BE","type":"education","lineage":["https://openalex.org/I130929987"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Thibaut Lust","raw_affiliation_strings":["Laboratory of Mathematics & Operational Research, Facult\u00e9 Polytechnique de Mons, 9, rue de Houdain, 7000, Mons, Belgium","Laboratory of Mathematics & Operational Research, Facult\u00e9\u00e9 Polytechnique de Mons, Mons, Belgium 7000#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratory of Mathematics & Operational Research, Facult\u00e9 Polytechnique de Mons, 9, rue de Houdain, 7000, Mons, Belgium","institution_ids":["https://openalex.org/I130929987"]},{"raw_affiliation_string":"Laboratory of Mathematics & Operational Research, Facult\u00e9\u00e9 Polytechnique de Mons, Mons, Belgium 7000#TAB#","institution_ids":["https://openalex.org/I130929987"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5082427090","display_name":"Jacques Teghem","orcid":null},"institutions":[{"id":"https://openalex.org/I130929987","display_name":"University of Mons","ror":"https://ror.org/02qnnz951","country_code":"BE","type":"education","lineage":["https://openalex.org/I130929987"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Jacques Teghem","raw_affiliation_strings":["Laboratory of Mathematics & Operational Research, Facult\u00e9 Polytechnique de Mons, 9, rue de Houdain, 7000, Mons, Belgium","Laboratory of Mathematics & Operational Research, Facult\u00e9\u00e9 Polytechnique de Mons, Mons, Belgium 7000#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratory of Mathematics & Operational Research, Facult\u00e9 Polytechnique de Mons, 9, rue de Houdain, 7000, Mons, Belgium","institution_ids":["https://openalex.org/I130929987"]},{"raw_affiliation_string":"Laboratory of Mathematics & Operational Research, Facult\u00e9\u00e9 Polytechnique de Mons, Mons, Belgium 7000#TAB#","institution_ids":["https://openalex.org/I130929987"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.15600624,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"335","last_page":"349"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.987500011920929,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.987500011920929,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10848","display_name":"Advanced Multi-Objective Optimization Algorithms","score":0.9847000241279602,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11798","display_name":"Optimal Experimental Design Methods","score":0.9801999926567078,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/collimator","display_name":"Collimator","score":0.7309325337409973},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.6908758878707886},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.6063390970230103},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.5968097448348999},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.5922590494155884},{"id":"https://openalex.org/keywords/integer-matrix","display_name":"Integer matrix","score":0.5145315527915955},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4722033441066742},{"id":"https://openalex.org/keywords/multileaf-collimator","display_name":"Multileaf collimator","score":0.45982861518859863},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.45648738741874695},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.45577386021614075},{"id":"https://openalex.org/keywords/heuristic","display_name":"Heuristic","score":0.4537329077720642},{"id":"https://openalex.org/keywords/pareto-principle","display_name":"Pareto principle","score":0.4429696798324585},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4382655620574951},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.4165690243244171},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3723893165588379},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.23828768730163574},{"id":"https://openalex.org/keywords/linear-particle-accelerator","display_name":"Linear particle accelerator","score":0.2055656611919403},{"id":"https://openalex.org/keywords/beam","display_name":"Beam (structure)","score":0.14980444312095642},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1472839117050171},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.13493189215660095},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.10676923394203186},{"id":"https://openalex.org/keywords/symmetric-matrix","display_name":"Symmetric matrix","score":0.09709551930427551},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.07433554530143738}],"concepts":[{"id":"https://openalex.org/C2779200277","wikidata":"https://www.wikidata.org/wiki/Q1164658","display_name":"Collimator","level":2,"score":0.7309325337409973},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.6908758878707886},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.6063390970230103},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.5968097448348999},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.5922590494155884},{"id":"https://openalex.org/C62555958","wikidata":"https://www.wikidata.org/wiki/Q6042601","display_name":"Integer matrix","level":5,"score":0.5145315527915955},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4722033441066742},{"id":"https://openalex.org/C161471255","wikidata":"https://www.wikidata.org/wiki/Q374703","display_name":"Multileaf collimator","level":4,"score":0.45982861518859863},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.45648738741874695},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.45577386021614075},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.4537329077720642},{"id":"https://openalex.org/C137635306","wikidata":"https://www.wikidata.org/wiki/Q182667","display_name":"Pareto principle","level":2,"score":0.4429696798324585},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4382655620574951},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.4165690243244171},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3723893165588379},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.23828768730163574},{"id":"https://openalex.org/C180048950","wikidata":"https://www.wikidata.org/wiki/Q836828","display_name":"Linear particle accelerator","level":3,"score":0.2055656611919403},{"id":"https://openalex.org/C168834538","wikidata":"https://www.wikidata.org/wiki/Q3705329","display_name":"Beam (structure)","level":2,"score":0.14980444312095642},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1472839117050171},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.13493189215660095},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.10676923394203186},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.09709551930427551},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.07433554530143738},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","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/C139018669","wikidata":"https://www.wikidata.org/wiki/Q6961560","display_name":"Nonnegative matrix","level":4,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/978-3-642-01020-0_28","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-01020-0_28","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},{"id":"pmh:oai:orbi.umons.ac.be:20.500.12907/25639","is_oa":false,"landing_page_url":"https://orbi.umons.ac.be/handle/20.500.12907/25639","pdf_url":null,"source":{"id":"https://openalex.org/S7407055454","display_name":"ORBi UMONS","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Conference EMO'2009, Nantes, France [FR], 2009","raw_type":"info:eu-repo/semantics/conferenceObject"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W119169328","https://openalex.org/W142294586","https://openalex.org/W173999961","https://openalex.org/W595181173","https://openalex.org/W1502046716","https://openalex.org/W1876311682","https://openalex.org/W1931244053","https://openalex.org/W1989099434","https://openalex.org/W1994444070","https://openalex.org/W2014158133","https://openalex.org/W2017708378","https://openalex.org/W2054509091","https://openalex.org/W2066746997","https://openalex.org/W2077234559","https://openalex.org/W2084991719","https://openalex.org/W2153654605","https://openalex.org/W2157771622","https://openalex.org/W2169315729"],"related_works":["https://openalex.org/W2166586408","https://openalex.org/W2048541553","https://openalex.org/W2366105249","https://openalex.org/W2744457076","https://openalex.org/W907318690","https://openalex.org/W2031044433","https://openalex.org/W2084991719","https://openalex.org/W1536347593","https://openalex.org/W2596394976","https://openalex.org/W2326743147"],"abstract_inverted_index":null,"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
